Lecture 10: Third Law of Thermodynamics

Note

The history of thermodynamics is a story of people and concepts. The cast of characters is large. At least ten scientists played major roles in creating thermodynamics, and their work spanned more than a century. The list of concepts, on the other hand, is surprisingly small; there are just three leading concepts in thermodynamics: energy, entropy, and absolute temperature. – W.H. Cropper

Warning

This lecture corresponds to Chapter 18 of the textbook.

Summary

Attention

So far, we have focused on the first and second laws of thermodynamics. We made important progress: we realized that the qualitative formulation of the second law of thermodynamics can be formalized with the discovery of a new function of state: the entropy. What the first and second laws of thermodynamics did not tell us is what the absolute value of the entropy is. This is where the third law provides crucial insight. There are three different formulations of the third law of thermodynamics:

Nernst:: Near absolute zero, all processes in a system at internal equilibrium occur without a change in entropy.
Planck:: The entropy of all systems in internal equilibrium is the same at absolute zero, and can be assigned a value of zero.
Simon:: The contribution to the entropy of a system by each aspect of the system in internal thermodynamic equilibrium tends to zero as $T \to 0$ .

Consequences of the third law

All heat capacities all tend to zero as $T \to 0$ .
Thermal expansion coefficients tend to zero as $T \to 0$ .
The ideal gas approximation fails as $T \to 0$ .
Curie’s law ceases to hold.
The absolute zero of temperature cannot be attained.

In general, the third law points to the fact that many of our “simple” thermodynamic models, such as the ideal gas equation and Curie’s law of paramagnets, need substantial modification if they are to give correct predictions as $T \to 0$ .

Comparison of the Three Laws of Thermodynamics

Law	Statement	Consequences / Interpretation
First Law	The total energy of an isolated system is conserved. Energy can be transformed from one form to another, but cannot be created or destroyed.	Defines internal energy as a state function. Introduces the concepts of work and heat. Basis for energy conservation.
Second Law	The entropy of an isolated system tends to increase. No process is possible where the only result is heat transfer from a colder to a hotter body.	Establishes directionality of processes. Introduces irreversibility. Provides the thermodynamic definition of entropy.
Third Law	As the temperature approaches absolute zero, the entropy of a perfect crystal approaches zero.	Heat capacity vanishes as temperature approaches zero. Absolute zero cannot be attained.

Key Definitions

Note

Aspects:: Aspects are subsystems that are only weakly coupled to each other. For example, the thermal properties of a material and the forces between quarks in a nucleus.

A full list of terms, including the ones provided here, can be found in the Index.

Learning Material

Copy of Slides

The slides for Lecture 10 are available in pdf format here: pdf

Screencast

Test your knowledge

The second law of thermodynamics is concerned with changes in entropy, it does not provide information about the absolute value for entropy.
1. True.
2. False.
3. The answer depends on the conditions of reversibility.
The third law of thermodynamics provides information on the feasibility or spontaneity of a reaction.
1. True
2. False
3. It depends if the temperature is zero or not.
Take any system, not necessarily in internal equilibrium, we can say that
1. The entropy is zero at $T=0$ .
2. The entropy is low at $T=0$ but not necessarily zero.
Imagine you study a system of weakly interacting particles. This interaction $V$ is so small that no experiment performed at room temperature can detect its effect. What can you say about its calculated entropy at $T=0$ if you neglect that extremely weak interaction?
1. This description will unavoidably fail at low temperature as there is always a temperature low enough for which $k_BT$ is of the same magnitude as $V$ .
2. This description will be correct, even at low temperature since experiment indicates the effect of $V$ is negligible.
One important consequence of the third law of thermodynamics is that heat capacity tends to zero as $T\to0$ . What can you conclude from this?
1. As $T\to 0$ , it becomes increasingly harder to heat up the system.
2. As $T\to 0$ , it becomes increasingly easier to cool down the system.
3. As $T\to 0$ , it becomes increasingly harder to cool down the system.
Imagine a gas that can be accurately described using the ideal gas law. Do you expect this description to break down at low or high $T$ ?
1. At high $T$ since the molecules are more likely to interact as they bounce against each other more often.
2. At low $T$ since the weak interactions, neglected by the model, start to be comparable in magnitude with $k_BT$ .
3. It depends on the type of materials. After all, the third law of thermodynamics has no experimental validity.
Mathematically, the efficiency of a Carnot engine could in principle be as high as 100% if the cold reservoir were maintained at $T=0$ . This would violate the second law of thermodynamics.
1. False. The second law of thermodynamics says nothing about the efficiency of a Carnot engine.
2. True. However, this is not an issue since the third law of thermodynamics prevents the temperature of the cold reservoir to attain $T=0$ .
3. False. This has nothing to do with the second or third laws of thermodynamics. It has to do with RPI weather machine that does not have to obey common sense or even less so the laws of physics
4. True. The importance of the second law of thermodynamics is largely exaggerated.

Hint

Find the answer keys on this page: Answers to selected test your knowledge questions. Don’t cheat! Try solving the problems on your own first!

Homework Assignment

Solve the following problems from the textbook: