The Third Law of Thermodynamics

Claimed by Emma Gele, Fall 2025

This page describes the Third Law of Thermodynamics, which relates the absolute entropy of a system to its temperature. This principle helps us to understand the behavior of materials at very low temperatures.

The Main Idea

The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero temperature is exactly zero.

Entropy ([math]\displaystyle{ S }[/math]) is a measure of the disorder or randomness in a system.

Temperature ([math]\displaystyle{ T }[/math]) is measured in Kelvin.

The principle can be expressed as:

[math]\displaystyle{ S \rightarrow 0 \quad \text{as} \quad T \rightarrow 0 , \text{K} }[/math]

where:

[math]\displaystyle{ S }[/math] is the entropy of the system

[math]\displaystyle{ T }[/math] is the absolute temperature

This implies that as a system approaches absolute zero, its thermal motion ceases, and it reaches a unique ground state with minimal disorder.

1. At very low temperatures, the heat capacities of solids approach zero because no more energy levels are accessible to the system.
2. Chemical reactions near absolute zero will have entropies approaching fixed, predictable values, helping chemists calculate equilibrium conditions.
3. Absolute zero cannot be reached in practice because extracting all thermal energy from a system would require infinite steps, consistent with the Third Law.

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Connectedness

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2. How is it connected to your major?
3. Is there an interesting industrial application?

History

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The Third Law was independently formulated by Walther Nernst in the early 20th century. He observed that chemical reactions slow and effectively stop as temperature approaches absolute zero, leading to the Nernst Heat Theorem, which states that the entropy change of a chemical reaction approaches zero as temperature approaches absolute zero.

See also

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• Second Law of Thermodynamics and Entropy

(directly relates to how entropy behaves)

• First Law of Thermodynamics

(if you're wondering about the other laws of thermodynamics)

• Temperature

(for understanding absolute zero)

• Thermal Energy

(for understanding energy behavior near absolute zero)

• Specific Heat

(a consequence of the Third Law, specific heats drops as T → 0)

• Thermal Energy, Dissipation, and Transfer of Energy
• The Maxwell-Boltzmann Distribution
• Transformation of Energy

Further reading

Books, Articles or other print media on this topic

External links

Internet resources on this topic

References

Khan Academy – “The Laws of Thermodynamics” https://www.khanacademy.org/science/physics/thermodynamics

HyperPhysics – “Third Law of Thermodynamics” http://hyperphysics.phy-astr.gsu.edu/hbase/Thermo/therthird.html

ChemLibreTexts – “Third Law of Thermodynamics” https://chem.libretexts.org

OpenStax University Physics – Thermodynamics Chapter https://openstax.org/details/books/university-physics-volume-2

Crash Course Chemistry #18 – “Thermodynamics” https://youtu.be/4Mc7FfyPzX0

MITK12 – “What Is Absolute Zero?” https://youtu.be/5l5kpZJ1KnE

Tyler DeWitt – “Entropy and the Laws of Thermodynamics” https://youtu.be/2Fv3H-iinl0