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.
- At very low temperatures, the heat capacities of solids approach zero because no more energy levels are accessible to the system.
- Chemical reactions near absolute zero will have entropies approaching fixed, predictable values, helping chemists calculate equilibrium conditions.
- 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
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Examples
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Connectedness
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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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- (directly relates to how entropy behaves)
- (if you're wondering about the other laws of thermodynamics)
- (for understanding absolute zero)
- (for understanding energy behavior near absolute zero)
- (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
Atkins, Peter, and Julio de Paula. Physical Chemistry. 10th Edition. 2014.
Callen, Herbert. Thermodynamics and an Introduction to Thermostatistics. 2nd Edition. 1985.
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