Physics Book - User contributions [en]

Faraday's Law

2018-11-25T20:08:42Z

Brian1277:

Faraday's Law (claimed by Daliya Francis Spring 2018)
focuses on how a time-varying magnetic field produces a "curly" non-Coulomb electric field, thereby inducing an emf.

==Faraday's Law==

Faraday's Law summarizes the ways voltage can be generated as a result of a time-varying magnetic flux. It helps connect magnetic field and electric field in a quantifiable way. Faraday's law is one of four laws in Maxwell's equations. It tells us that in the presence of a time-varying magnetic field or current (which induces a time-varying magnetic field), there is an emf with a magnitude equal to the change in magnetic flux. It serves as a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

==Curly Electric Field==

[[File:curly.jpg]]

===Mathematical Model===

'''Faraday's Law'''

emf = <math>{\frac{-d{{Φ}}_{mag}}{dt}}</math>

where emf = <math>\oint\vec{E}_{NC}\bullet d\vec{l}</math> and <math>{{Φ}}_{mag}\equiv\int\vec{B}\bullet\hat{n}dA</math>

In other words: The emf along a round-trip is equal to the rate of change of the magnetic flux on the area encircled by the path.

Direction: With the thumb of your right hand pointing in the direction of the ''-dB/dt'', your fingers curl around in the direction of Enc.

The meaning of the minus sign: If the thumb of your right hand points in the direction of ''-dB/dt'' (that is, the opposite of the direction in which the magnetic field is increasing), your fingers curl around in the direction along which the path integral of electric field is positive. Similarly, the direction of the induced current can be explained using Lenz's Law. Lenz's law states that the induced current from the non-Coulombic electric field is induced in such a way that it produces a magnetic field that opposes the first magnetic field to keep the magnetic flux constant.

'''Formal Version of Faraday's Law'''

<math>\oint\vec{E}_{NC}\bullet d\vec{l} = {\frac{-d}{dt}}\int\vec{B}\bullet\hat{n}dA</math> (sign given by right-hand rule)

====Problem Solving Tips====
To find the direction of the curly electric field, one must find the direction of <math> \frac{-dB}{dt} </math>. Do this using the change in magnetic field as the basis of finding the <math> \frac{-dB}{dt} </math>.

The easiest way to do this is to imagine the a vector for the initial magnetic field, and a vector for the final magnetic field. Then, draw the change in magnetic field vector, <math> \Delta \mathbf{B} </math>, and then the negative vector of that change in magnetic field gives <math> \frac{-dB}{dt} </math>:

[[File:neg_change_B_dt.jpg]]

Pointing the thumb of your right hand in the direction of <math> \frac{-dB}{dt} </math> allows you to curl your fingers in the direction of <math> \mathbf{E_{NC}} </math>.

In this chapter we have seen that a changing magnetic flux induces an emf:

[[File:tips5.png]]

according to Faraday’s law of induction. For a conductor which forms a closed loop, the
emf sets up an induced current ''I =|ε|/R'' , where ''R'' is the resistance of the loop. To
compute the induced current and its direction, we follow the procedure below:

1. For the closed loop of area on a plane, define an area vector A and let it point in
the direction of your thumb, for the convenience of applying the right-hand rule later.
Compute the magnetic flux through the loop using

[[File:tips4.png]]

Determine the sign of the magnetic flux [[File:tips3.png]]

2. Evaluate the rate of change of magnetic flux [[File:tips2.png]] . Keep in mind that the change
could be caused by

[[File:tips.png]]

Determine the sign of [[File:tips2.png]]

3. The sign of the induced emf is the opposite of that of [[File:tips2.png]]. The direction of the
induced current can be found by using Lenz’s law or right hand rule (discussed previously).

===Computational Model===

==More on Faraday's Law==

Moving a magnet near a coil is not the only way to induce an emf in the coil. Another way to induce emf in a coil is to bring another coil with a steady current near the first coil, thereby changing the magnetic field (and flux) surrounding the first coil, inducing an emf and a current. Also, rotating a bar magnet (or coil) near a coil produces a time-varying magnetic field in the coil since rotating the magnet changes the magnetic field in the coil. The key to inducing the emf in the second coil is to change the magnetic field around it somehow, either by bringing an object that has its own magnetic field around that coil, or changing the current in that object, changing its magnetic field.

Faraday's law can be used to calculate motional emf as well. A bar on two current-carrying rails connected by a resistor moves along the rails, using magnetic force to induce a current in the wire. There is a magnetic field going into the page. One way to calculate the motional emf is to use the [http://www.physicsbook.gatech.edu/Motional_Emf magnetic force], but an easier way is to use Faraday's law.

Faraday's law, using the change in magnetic flux, can be used to find the motional emf, where the changing factor in the magnetic flux is the area of the circuit as the bar moves, while magnetic field is kept constant.

[[File:motionalemf.jpg]]

==Examples==

===Simple===

[[File:solenoid.ring.jpg|center|alt=Diagram for simple example]]

''Adapted from the'' Matter & Interactions ''textbook, variation of P12 (4th ed)''.

The solenoid radius is 4 cm and the ring radius is 20 cm. B = 0.8 T inside the solenoid and approximately 0 outside the solenoid. What is the magnetic flux through the outer ring?

''Solution:''

Because the magnetic field outside the solenoid is 0, there is no flux between the ring and solenoid. So the flux in the ring is due to the area of the solenoid, so we use the area of the solenoid to find the flux through the outer ring rather than the area of the ring itself:

<math> \phi = BAcos(\theta)</math>

<math>= (0.8 T)(\pi)(0.04 m)^2cos(0) </math>

<math>= 4.02 x 10^{-3} T*m^2 </math>

===Middle===

[[File:rectanglecoilsolenoid.jpg|center|alt=Diagram for simple example]]

''Adapted from the'' Matter & Interactions ''textbook, variation of P27 (4th ed)''.

A very long, tightly wound solenoid has a circular cross section of radius 2 cm (only a portion of the very long solenoid is shown). The magnetic field outside the solenoid is negligible. Throughout the inside of the solenoid the magnetic field ''B'' is uniform, to the left as shown, but varying with time ''t: B'' = (.06+.02<math>t^2</math>)T. Surrounding the circular solenoid is a loop of 7 turns of wire in the shape of a rectangle 6 cm by 12 cm. The total resistance of the 7-turn loop is 0.2 ohms.

(a) At ''t'' = 2 s, what is the direction of the current in the 7-turn loop? Explain briefly.

(b) At ''t'' = 2 s, what is the magnitude of the current in the 7-turn loop? Explain briefly.

''Solution''

'''(a)''' The direction of the current in the loop is clockwise.

'''(b)'''

B(t) = (.06+.02<math>t^2</math>)

A = (π)(0.02 m)^2 = .00126 <math>m^2</math>

<math>|{ε}| = AN\frac{dB(t)}{dt}</math>

<math>|{ε}|</math> = (.00126 <math>m^2</math>)(7)<math>\frac{d(.06+.02t^2)}{dt}</math> = (.00882)(.02)(2t) = .0003528t

'''At ''t'' = 2 s:'''

<math>|{ε}|</math> = .0003528(2) = .0007056 V

<math>i = \frac{{ε}}{R}</math>

<math>i = \frac{{.0007056 V}}{0.2 ohms}</math> = '''.00353 A'''

===Difficult===

[[File:difficultfaraday.png]]

A square loop (dimensions L⇥L, total resistance R) is located halfway inside a region with uniform magnetic field B0. The magnitude of the magnetic field suddenly begins to increase linearly in time, eventually quadrupling in a time T.

'''(a) What current (magnitude and direction), if any, is induced in the loop at time T?
'''

<math> |emf| = \frac{-{Φ}_{B}}{Δt} = \frac{A(B_f - B_i)}{T} = \frac{L^2(4B_o - B_o)}{T} = \frac{3B_oL^2}{T}</math>

emf = IR = <math>\frac{3B_oL^2}{TR}</math>

'''(b) What net force (magnitude and direction), if any, is induced on the loop at time T?
'''

<math> F_{top} </math> and <math> F_{bottom} </math> cancel out.
<math> F_{left} </math> = 0 because the left side is out of <math> \vec{B} </math> region.

<math> \vec{F}</math> = <math> \vec{F}_{right} </math> = I <math> \vec{L} \times \vec{B} = (ILB)[(\hat{y} \times - \hat{z} )] = \frac{3B_oL^2}{TR}(4B_o L)(- \hat{x}) = \frac{3{B_o}^2 L^3}{TR}(- \hat{x})</math>

'''(c) What net torque (magnitude and direction), if any, is induced on the loop at time T?
'''

<math> \vec{τ} = \vec{μ} \times \vec{B} = 0 </math> because <math>\vec{μ}</math> and <math>\vec{B}</math> are anti-parallel.

==Connectedness==

Faraday's Law is one of Maxwell's equations which describe the essence of electric and magnetic fields. Maxwell's equations effectively summarize and connect all that we have learned throughout the course of Physics 2.

As an electrical engineer, Faraday's Law is relevant to my major.

== Faraday’s Law Applications ==

Physics 2 content has a lot of important concepts that we as engineers can use to make our jobs easier. Whether it be a direct application of a rule or some derivation of a rule. I know I personally struggle with a concept until I get a concrete real life application that I can see the material applied in. This section of the page will discuss how Faraday’s law is applied to concepts that you as students maybe more familiar with in your day to day life.

== Hydroelectric Generators ==
Generators create energy by transforming mechanical motion into electrical energy, but hydroelectric generators use the power of falling water to turn a large turbine which is connected to a large magnet. Around this magnet is a large coil of tightly wound wire. The conceptual creation of electricity is the same as Faraday’s Law except alternating current is being produced, but the idea that a changing magnetic field in a coil of wire induces an electromotive force is still the same. The difference is the magnetic field changes sign and flips resulting in the same thing to occur in the induced EMF. Although the calculations here are slightly more difficult the concepts are the same.

== Transformers ==

Transformers use a similar concept for Faraday’s Law but it’s slightly different. The job of a transformer is to either step up or step down the voltage on the power line. Transformers have a constant magnetic field associated with it due to an iron core. The power supply voltage is adjusted by altering the number of turns of wire around the iron core which in turn alters the EMF of the electricity.

Cartoon of Hydroelectric Plant
https://etrical.files.wordpress.com/2009/12/hydrohow.jpg
Turbine Picture
http://theprepperpodcast.com/wp-content/uploads/2016/02/108-All-About-Hydro-Power-Generators-1054x500.jpg
Transformer Diagram https://en.wikipedia.org/wiki/Transformer#/media/File:Transformer3d_col3.svg

==History==

In 1831, eletromagnetic induction was discovered by Michael Faraday.

===Faraday's Law Experiment ===

[[File:experiment.png]]

Faraday showed that no current is registered in the galvanometer when bar magnet is
stationary with respect to the loop. However, a current is induced in the loop when a
relative motion exists between the bar magnet and the loop. In particular, the
galvanometer deflects in one direction as the magnet approaches the loop, and the
opposite direction as it moves away.

Faraday’s experiment demonstrates that an electric current is induced in the loop by
changing the magnetic field. The coil behaves as if it were connected to an emf source.
Experimentally it is found that the induced emf depends on the rate of change of
magnetic flux through the coil.

Test it out yourself [https://phet.colorado.edu/en/simulation/faradays-law here]

==See also==
===Further Readings===

''Matter and Interactions, Volume II: Electric and Magnetic Interactions, 4th Edition''

''The Electric Life of Michael Faraday'' (2009) by Alan Hirshfield

''Electromagnetic Induction Phenomena'' (2012) by D. Schieber

===External Links===

https://www.youtube.com/watch?v=KGTZPTnZBFE

https://www.nde-ed.org/EducationResources/HighSchool/Electricity/electroinduction.htm

http://www.famousscientists.org/michael-faraday/

http://www.bbc.co.uk/history/historic_figures/faraday_michael.shtml

==References==

''Matter and Interactions, 4th Edition''

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

https://files.t-square.gatech.edu/access/content/group/gtc-970b-7c13-52a7-9627-cdc3154438c6/Test%20Preparation/Old%20Test/2212_Test4_Key-1.pdf

https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction

Faraday's Law

2018-11-25T19:42:05Z

Brian1277:

Faraday's Law (claimed by Daliya Francis Spring 2018); claimed by Kwangjun Jung Fall 2018

focuses on how a time-varying magnetic field produces a "curly" non-Coulomb electric field, thereby inducing an emf.

==Faraday's Law==

Faraday's Law summarizes the ways voltage can be generated as a result of a time-varying magnetic flux. It helps connect magnetic field and electric field in a quantifiable way. Faraday's law is one of four laws in Maxwell's equations. It tells us that in the presence of a time-varying magnetic field or current (which induces a time-varying magnetic field), there is an emf with a magnitude equal to the change in magnetic flux. It serves as a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

==Curly Electric Field==

[[File:curly.jpg]]

===Mathematical Model===

'''Faraday's Law'''

emf = <math>{\frac{-d{{Φ}}_{mag}}{dt}}</math>

where emf = <math>\oint\vec{E}_{NC}\bullet d\vec{l}</math> and <math>{{Φ}}_{mag}\equiv\int\vec{B}\bullet\hat{n}dA</math>

In other words: The emf along a round-trip is equal to the rate of change of the magnetic flux on the area encircled by the path.

Direction: With the thumb of your right hand pointing in the direction of the ''-dB/dt'', your fingers curl around in the direction of Enc.

The meaning of the minus sign: If the thumb of your right hand points in the direction of ''-dB/dt'' (that is, the opposite of the direction in which the magnetic field is increasing), your fingers curl around in the direction along which the path integral of electric field is positive. Similarly, the direction of the induced current can be explained using Lenz's Law. Lenz's law states that the induced current from the non-Coulombic electric field is induced in such a way that it produces a magnetic field that opposes the first magnetic field to keep the magnetic flux constant.

'''Formal Version of Faraday's Law'''

<math>\oint\vec{E}_{NC}\bullet d\vec{l} = {\frac{-d}{dt}}\int\vec{B}\bullet\hat{n}dA</math> (sign given by right-hand rule)

====Problem Solving Tips====
To find the direction of the curly electric field, one must find the direction of <math> \frac{-dB}{dt} </math>. Do this using the change in magnetic field as the basis of finding the <math> \frac{-dB}{dt} </math>.

The easiest way to do this is to imagine the a vector for the initial magnetic field, and a vector for the final magnetic field. Then, draw the change in magnetic field vector, <math> \Delta \mathbf{B} </math>, and then the negative vector of that change in magnetic field gives <math> \frac{-dB}{dt} </math>:

[[File:neg_change_B_dt.jpg]]

Pointing the thumb of your right hand in the direction of <math> \frac{-dB}{dt} </math> allows you to curl your fingers in the direction of <math> \mathbf{E_{NC}} </math>.

In this chapter we have seen that a changing magnetic flux induces an emf:

[[File:tips5.png]]

according to Faraday’s law of induction. For a conductor which forms a closed loop, the
emf sets up an induced current ''I =|ε|/R'' , where ''R'' is the resistance of the loop. To
compute the induced current and its direction, we follow the procedure below:

1. For the closed loop of area on a plane, define an area vector A and let it point in
the direction of your thumb, for the convenience of applying the right-hand rule later.
Compute the magnetic flux through the loop using

[[File:tips4.png]]

Determine the sign of the magnetic flux [[File:tips3.png]]

2. Evaluate the rate of change of magnetic flux [[File:tips2.png]] . Keep in mind that the change
could be caused by

[[File:tips.png]]

Determine the sign of [[File:tips2.png]]

3. The sign of the induced emf is the opposite of that of [[File:tips2.png]]. The direction of the
induced current can be found by using Lenz’s law or right hand rule (discussed previously).

===Computational Model===

==More on Faraday's Law==

Moving a magnet near a coil is not the only way to induce an emf in the coil. Another way to induce emf in a coil is to bring another coil with a steady current near the first coil, thereby changing the magnetic field (and flux) surrounding the first coil, inducing an emf and a current. Also, rotating a bar magnet (or coil) near a coil produces a time-varying magnetic field in the coil since rotating the magnet changes the magnetic field in the coil. The key to inducing the emf in the second coil is to change the magnetic field around it somehow, either by bringing an object that has its own magnetic field around that coil, or changing the current in that object, changing its magnetic field.

Faraday's law can be used to calculate motional emf as well. A bar on two current-carrying rails connected by a resistor moves along the rails, using magnetic force to induce a current in the wire. There is a magnetic field going into the page. One way to calculate the motional emf is to use the [http://www.physicsbook.gatech.edu/Motional_Emf magnetic force], but an easier way is to use Faraday's law.

Faraday's law, using the change in magnetic flux, can be used to find the motional emf, where the changing factor in the magnetic flux is the area of the circuit as the bar moves, while magnetic field is kept constant.

[[File:motionalemf.jpg]]

==Examples==

===Simple===

[[File:solenoid.ring.jpg|center|alt=Diagram for simple example]]

''Adapted from the'' Matter & Interactions ''textbook, variation of P12 (4th ed)''.

The solenoid radius is 4 cm and the ring radius is 20 cm. B = 0.8 T inside the solenoid and approximately 0 outside the solenoid. What is the magnetic flux through the outer ring?

''Solution:''

Because the magnetic field outside the solenoid is 0, there is no flux between the ring and solenoid. So the flux in the ring is due to the area of the solenoid, so we use the area of the solenoid to find the flux through the outer ring rather than the area of the ring itself:

<math> \phi = BAcos(\theta)</math>

<math>= (0.8 T)(\pi)(0.04 m)^2cos(0) </math>

<math>= 4.02 x 10^{-3} T*m^2 </math>

===Middle===

[[File:rectanglecoilsolenoid.jpg|center|alt=Diagram for simple example]]

''Adapted from the'' Matter & Interactions ''textbook, variation of P27 (4th ed)''.

A very long, tightly wound solenoid has a circular cross section of radius 2 cm (only a portion of the very long solenoid is shown). The magnetic field outside the solenoid is negligible. Throughout the inside of the solenoid the magnetic field ''B'' is uniform, to the left as shown, but varying with time ''t: B'' = (.06+.02<math>t^2</math>)T. Surrounding the circular solenoid is a loop of 7 turns of wire in the shape of a rectangle 6 cm by 12 cm. The total resistance of the 7-turn loop is 0.2 ohms.

(a) At ''t'' = 2 s, what is the direction of the current in the 7-turn loop? Explain briefly.

(b) At ''t'' = 2 s, what is the magnitude of the current in the 7-turn loop? Explain briefly.

''Solution''

'''(a)''' The direction of the current in the loop is clockwise.

'''(b)'''

B(t) = (.06+.02<math>t^2</math>)

A = (π)(0.02 m)^2 = .00126 <math>m^2</math>

<math>|{ε}| = AN\frac{dB(t)}{dt}</math>

<math>|{ε}|</math> = (.00126 <math>m^2</math>)(7)<math>\frac{d(.06+.02t^2)}{dt}</math> = (.00882)(.02)(2t) = .0003528t

'''At ''t'' = 2 s:'''

<math>|{ε}|</math> = .0003528(2) = .0007056 V

<math>i = \frac{{ε}}{R}</math>

<math>i = \frac{{.0007056 V}}{0.2 ohms}</math> = '''.00353 A'''

===Difficult===

[[File:difficultfaraday.png]]

A square loop (dimensions L⇥L, total resistance R) is located halfway inside a region with uniform magnetic field B0. The magnitude of the magnetic field suddenly begins to increase linearly in time, eventually quadrupling in a time T.

'''(a) What current (magnitude and direction), if any, is induced in the loop at time T?
'''

<math> |emf| = \frac{-{Φ}_{B}}{Δt} = \frac{A(B_f - B_i)}{T} = \frac{L^2(4B_o - B_o)}{T} = \frac{3B_oL^2}{T}</math>

emf = IR = <math>\frac{3B_oL^2}{TR}</math>

'''(b) What net force (magnitude and direction), if any, is induced on the loop at time T?
'''

<math> F_{top} </math> and <math> F_{bottom} </math> cancel out.
<math> F_{left} </math> = 0 because the left side is out of <math> \vec{B} </math> region.

<math> \vec{F}</math> = <math> \vec{F}_{right} </math> = I <math> \vec{L} \times \vec{B} = (ILB)[(\hat{y} \times - \hat{z} )] = \frac{3B_oL^2}{TR}(4B_o L)(- \hat{x}) = \frac{3{B_o}^2 L^3}{TR}(- \hat{x})</math>

'''(c) What net torque (magnitude and direction), if any, is induced on the loop at time T?
'''

<math> \vec{τ} = \vec{μ} \times \vec{B} = 0 </math> because <math>\vec{μ}</math> and <math>\vec{B}</math> are anti-parallel.

==Connectedness==

Faraday's Law is one of Maxwell's equations which describe the essence of electric and magnetic fields. Maxwell's equations effectively summarize and connect all that we have learned throughout the course of Physics 2.

As an electrical engineer, Faraday's Law is relevant to my major.

== Faraday’s Law Applications ==

Physics 2 content has a lot of important concepts that we as engineers can use to make our jobs easier. Whether it be a direct application of a rule or some derivation of a rule. I know I personally struggle with a concept until I get a concrete real life application that I can see the material applied in. This section of the page will discuss how Faraday’s law is applied to concepts that you as students maybe more familiar with in your day to day life.

== Hydroelectric Generators ==
Generators create energy by transforming mechanical motion into electrical energy, but hydroelectric generators use the power of falling water to turn a large turbine which is connected to a large magnet. Around this magnet is a large coil of tightly wound wire. The conceptual creation of electricity is the same as Faraday’s Law except alternating current is being produced, but the idea that a changing magnetic field in a coil of wire induces an electromotive force is still the same. The difference is the magnetic field changes sign and flips resulting in the same thing to occur in the induced EMF. Although the calculations here are slightly more difficult the concepts are the same.

== Transformers ==

Transformers use a similar concept for Faraday’s Law but it’s slightly different. The job of a transformer is to either step up or step down the voltage on the power line. Transformers have a constant magnetic field associated with it due to an iron core. The power supply voltage is adjusted by altering the number of turns of wire around the iron core which in turn alters the EMF of the electricity.

Cartoon of Hydroelectric Plant
https://etrical.files.wordpress.com/2009/12/hydrohow.jpg
Turbine Picture
http://theprepperpodcast.com/wp-content/uploads/2016/02/108-All-About-Hydro-Power-Generators-1054x500.jpg
Transformer Diagram https://en.wikipedia.org/wiki/Transformer#/media/File:Transformer3d_col3.svg

==History==

In 1831, eletromagnetic induction was discovered by Michael Faraday.

===Faraday's Law Experiment ===

[[File:experiment.png]]

Faraday showed that no current is registered in the galvanometer when bar magnet is
stationary with respect to the loop. However, a current is induced in the loop when a
relative motion exists between the bar magnet and the loop. In particular, the
galvanometer deflects in one direction as the magnet approaches the loop, and the
opposite direction as it moves away.

Faraday’s experiment demonstrates that an electric current is induced in the loop by
changing the magnetic field. The coil behaves as if it were connected to an emf source.
Experimentally it is found that the induced emf depends on the rate of change of
magnetic flux through the coil.

Test it out yourself [https://phet.colorado.edu/en/simulation/faradays-law here]

==See also==
===Further Readings===

''Matter and Interactions, Volume II: Electric and Magnetic Interactions, 4th Edition''

''The Electric Life of Michael Faraday'' (2009) by Alan Hirshfield

''Electromagnetic Induction Phenomena'' (2012) by D. Schieber

===External Links===

https://www.youtube.com/watch?v=KGTZPTnZBFE

https://www.nde-ed.org/EducationResources/HighSchool/Electricity/electroinduction.htm

http://www.famousscientists.org/michael-faraday/

http://www.bbc.co.uk/history/historic_figures/faraday_michael.shtml

==References==

''Matter and Interactions, 4th Edition''

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

https://files.t-square.gatech.edu/access/content/group/gtc-970b-7c13-52a7-9627-cdc3154438c6/Test%20Preparation/Old%20Test/2212_Test4_Key-1.pdf

https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction

Thermal Energy

2015-12-05T21:59:49Z

Brian1277: /* History */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. When we say change of "thermal" energy, we mean that it is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Thermal energy was discovered by a man named James Joule in the 1840s. Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. Joule carried one of the most famous experience demonstrating this fact. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

http://physics.weber.edu/schroeder/eee/chapter3.pdf

===External links===

http://www.eschooltoday.com/energy/kinds-of-energy/what-is-thermal-energy.html

http://study.com/academy/lesson/what-is-thermal-energy-definition-examples.html

==References==

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

http://physics.weber.edu/schroeder/eee/chapter3.pdf

[[Category:Energy]]

Thermal Energy

2015-12-05T21:44:16Z

Brian1277: /* The Main Idea */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. When we say change of "thermal" energy, we mean that it is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

http://physics.weber.edu/schroeder/eee/chapter3.pdf

===External links===

http://www.eschooltoday.com/energy/kinds-of-energy/what-is-thermal-energy.html

http://study.com/academy/lesson/what-is-thermal-energy-definition-examples.html

==References==

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

http://physics.weber.edu/schroeder/eee/chapter3.pdf

[[Category:Energy]]

Thermal Energy

2015-12-05T20:21:42Z

Brian1277: /* Further reading */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

http://physics.weber.edu/schroeder/eee/chapter3.pdf

===External links===

http://www.eschooltoday.com/energy/kinds-of-energy/what-is-thermal-energy.html

http://study.com/academy/lesson/what-is-thermal-energy-definition-examples.html

==References==

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

http://physics.weber.edu/schroeder/eee/chapter3.pdf

[[Category:Energy]]

Thermal Energy

2015-12-05T08:03:49Z

Brian1277: /* References */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 

http://physics.weber.edu/schroeder/eee/chapter3.pdf

===External links===

http://www.eschooltoday.com/energy/kinds-of-energy/what-is-thermal-energy.html

http://study.com/academy/lesson/what-is-thermal-energy-definition-examples.html

==References==

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

http://physics.weber.edu/schroeder/eee/chapter3.pdf

[[Category:Energy]]

Thermal Energy

2015-12-05T08:03:36Z

Brian1277: /* Further reading */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 

http://physics.weber.edu/schroeder/eee/chapter3.pdf

===External links===

http://www.eschooltoday.com/energy/kinds-of-energy/what-is-thermal-energy.html

http://study.com/academy/lesson/what-is-thermal-energy-definition-examples.html

==References==

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

[[Category:Energy]]

Thermal Energy

2015-12-05T08:02:20Z

Brian1277: /* References */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://www.eschooltoday.com/energy/kinds-of-energy/what-is-thermal-energy.html

http://study.com/academy/lesson/what-is-thermal-energy-definition-examples.html

==References==

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

[[Category:Energy]]

Thermal Energy

2015-12-05T08:02:03Z

Brian1277: /* References */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://www.eschooltoday.com/energy/kinds-of-energy/what-is-thermal-energy.html

http://study.com/academy/lesson/what-is-thermal-energy-definition-examples.html

==References==

Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 7 

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T08:01:20Z

Brian1277: /* External links */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://www.eschooltoday.com/energy/kinds-of-energy/what-is-thermal-energy.html

http://study.com/academy/lesson/what-is-thermal-energy-definition-examples.html

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T08:00:41Z

Brian1277: /* External links */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

[http://www.eschooltoday.com/energy/kinds-of-energy/what-is-thermal-energy.html]

[http://study.com/academy/lesson/what-is-thermal-energy-definition-examples.html]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:58:51Z

Brian1277: /* See also */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]

[[Kinetic Energy]]

[[Work]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:58:41Z

Brian1277: /* See also */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==
[[The Energy Principle]]
[[Kinetic Energy]]
[[Work]]
===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:57:54Z

Brian1277: /* See also */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

[[Kinetic Energy]]
===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:56:59Z

Brian1277: /* See also */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

[[http:/http://www.physicsbook.gatech.edu/Kinetic_Energy Kinetic Energy]]
===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:56:39Z

Brian1277: /* See also */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

[http:/http://www.physicsbook.gatech.edu/Kinetic_Energy Kinetic Energy]
===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:54:54Z

Brian1277: /* Connectedness */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

One of the interesting industrial application of thermal energy is industrial thermal energy storage. Thermal energy storage is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation.

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:51:28Z

Brian1277: /* Connectedness */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I find thermal energy interesting because it relates into thermal dynamics which describes how thermal energy is converted to and from other forms of energy and how it affects matter. I just find it really interesting how simply differentiating a temperature of a system can bring various changes to that system.

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

e

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:46:48Z

Brian1277: /* Connectedness */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

e

'''How is it connected to your major?'''

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

'''Is there an interesting industrial application?'''

e

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:46:18Z

Brian1277: /* Connectedness */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?

I am a 1st year student in Mechanical Engineering. Under mechanical engineering there is a branch o physics called Thermodynamics which deals with heat and temperature and their relation to energy and work. Thermal Energy is one of the topic under Thermodynamics dealing with macroscopic variables especially internal energy.

#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:43:59Z

Brian1277: /* Difficult */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

6. Solve for Q and find its value

<math>Q = 8110J</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:42:33Z

Brian1277: /* Difficult */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{1water}=87°C, {T}_{1pan}=22°C, {T}_{2}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{2}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{2}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

4. Write the equation and list the knowns, repeating the steps above (final temperature above now becomes initial temperature)

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=26000J, Q=?, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C,{T}_{2}=70.404°C, {T}_{3}=82.5°C </math>

5. Plug the numbers into the equation

<math> 500*4.2*(82.5-70.404)+800*0.9*(82.5-70.404) = 26000 + Q</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:31:12Z

Brian1277: /* Difficult */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C, {T}_{f}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{f}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{f}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

3. Solve for <math>{T}_{f}</math> and find its value

<math>{T}_{f} = 70.404</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:29:46Z

Brian1277: /* Middling */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C, {T}_{f}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{f}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{f}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:29:36Z

Brian1277: /* Middling */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value
<math>{T}_{f}=69°C</math>

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C, {T}_{f}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{f}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{f}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:25:44Z

Brian1277: /* Difficult */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C, {T}_{f}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{f}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{f}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:25:37Z

Brian1277: /* Middling */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C, {T}_{f}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{f}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{f}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:25:29Z

Brian1277: /* Simple */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C, {T}_{f}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{f}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{f}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:25:20Z

Brian1277: /* Simple */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C, {T}_{f}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{f}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{f}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:25:03Z

Brian1277: /* Difficult */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C, {T}_{f}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{f}-87)</math>

<math>{dE}_{pan}=800*0.9*({T}_{f}-22)</math>

<math>{dE}_{water}+{dE}_{pan}=0 </math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:24:37Z

Brian1277: /* Difficult */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C, {T}_{f}=?</math>

2. Plug the numbers into the equation and find the final temperature

<math> {dE}_{water}= 500*4.2*({T}_{f}-87)

{dE}_{pan}=800*0.9*({T}_{f}-22)

{dE}_{water}+{dE}_{pan}=0 </math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:22:02Z

Brian1277: /* Difficult */

Work in progress by KwangJun Jung

Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system.

==The Main Idea==

All objects are made up of numerous particles or molecules. Within these objects, those particles or molecules are constantly moving or vibrating, generating heat. Thermal energy refers to the internal energy that comes from these moving particles or molecules within the objects. What we mean by a change of "thermal" energy is that part of the internal energy that is associated with a temperature change. In many situations it isn't possible to say how much of the internal energy is thermal, but if the heat capacity is known, we can use a thermometer to measure a change in the thermal energy.

[[File:thermal.jpg]]

===A Mathematical Model===

Change in thermal energy can be calculated by using the following mathematical equation. <math>{Q = m*C*dT}</math> where <math>{Q}</math> is the thermal energy in Joules, <math>{m}</math> is the mass of an object in grams, <math>{C}</math> is the object's specific heat capacity, and <math>{dT}</math> is the change in object's temperature in Celsius.

[[File:equation.jpg]]

==Examples==

===Simple===

500g of water was heated from the initial temperature of 20°C to 50 °C. What is the change in thermal energy of water? (Heat capacity of water is 4.2J/g*°C)

1. List given things and equation

<math>Q = m*C*dT</math>

<math>Q=?, m=500g, C=4.2J/g*°C, dT={T}_{f}-{T}_{i}, {T}_{f}=50°C, {T}_{i}=20°C</math>

2. Plug the numbers into the equation and find the answer

<math>Q = 500g*4.2J/g*°C*(50°C-20°C)</math>

<math>Q = 63000J</math>

===Middling===

400g of water with initial temperature of 90°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 20°C (specific heat of 0.9 J/g*°C). After a short time, what is the temperature of the water?

1. Write the equation and list the knowns and unknowns

<math> {{dE}_{water}+{dE}_{pan} = 0}, dE = m*C*dT </math>

<math> {m}_{water} = 400g,{m}_{pan} = 800g, {C}_{water} = 4.2J/g*°C {C}_{Aluminum} = 0.9J/g*°C, {T}_{i water} = 90°C, {T}_{i pan} = 20°C, {T}_{f} = ?</math>

2. Plug the numbers into the equation

<math> 0 = 400g*4.2J/g*°C*({T}_{f}-90°C) + 800g*0.9J/g*°C*({T}_{f}-20°C)</math>

3. Solve for <math> {T}_{f}</math> and find its value

===Difficult===

500g of water with initial temperature of 87°C (specific heat of 4.2 J/g*°C) are poured into an aluminum pan whose mass is 800g with initial temperature of 22°C (specific heat of 0.9 J/g*°C). Then you place the pan on a hot electric stove. While the stove is heating the pan, you stir the water doing 26000J of work, rising temperature of a system to 82.5 °C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?

1. Write the equation and find the final temperature when water and pan first reached thermal equilibrium.

<math> {{dE}_{water}+{dE}_{pan} = W + Q}, dE = m*C*dT </math>

<math>W=0, Q=0, {m}_{water}=500g, {m}_{pan}=800g, {C}_{water}=4.2 J/g*°C, {C}_{aluminum}=0.9 J/g*°C, {T}_{iwater}=87°C, {T}_{ipan}=22°C</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==
Careful experiments show that the temperature increase of an object and its surroundings due to friction is directly related to the amount of mechanical energy lost. The most famous experimental demonstration of this fact was carried out by James Joule in the 1840’s. Joule hung some weights from pulleys so that as they fell, they turned a paddle-wheel apparatus immersed in a bucket of water. The friction between the paddles and the water raised the water’s temperature by an amount that was directly proportional to the distance that the weights fell. In our modern system of units, Joule found that raising the temperature of a kilogram of water by one degree Celsius required a loss in mechanical (gravitational) energy of approximately 4200 joules. Joule therefore proposed that this mechanical energy is not actually lost, but converted into a new type of energy: thermal energy, which manifests itself as an increase in temperature.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Thermal Energy

2015-12-05T07:18:18Z

Brian1277: /* Examples */

Thermal Energy

2015-12-04T08:25:17Z

Brian1277: /* Middling */

Thermal Energy

2015-12-04T08:24:31Z

Brian1277: /* Middling */

Thermal Energy

2015-12-04T08:23:43Z

Brian1277: /* Middling */

Thermal Energy

2015-12-04T08:21:21Z

Brian1277: /* Middling */

Thermal Energy

2015-12-04T08:20:48Z

Brian1277: /* Middling */

Thermal Energy

2015-12-04T08:20:00Z

Brian1277: /* Middling */

Thermal Energy

2015-12-04T08:19:06Z

Brian1277: /* Examples */

Thermal Energy

2015-12-04T07:27:21Z

Brian1277: /* Examples */

Thermal Energy

2015-12-04T07:26:57Z

Brian1277: /* Simple */

Thermal Energy

2015-12-04T07:26:11Z

Brian1277: /* Simple */

Thermal Energy

2015-12-03T21:59:32Z

Brian1277: /* Middling */

Thermal Energy

2015-12-03T21:58:44Z

Brian1277: /* Middling */

Thermal Energy

2015-12-03T21:58:20Z

Brian1277: /* Middling */

Thermal Energy

2015-12-03T21:56:46Z

Brian1277: /* Middling */

Thermal Energy

2015-12-03T21:56:33Z

Brian1277: /* Middling */

Thermal Energy

2015-12-03T21:55:53Z

Brian1277: /* Middling */

Thermal Energy

2015-12-03T21:42:15Z

Brian1277: /* Simple */