Extremum of thermodynamic potentials: confusion

In summary, there are two formulations of the second law of thermodynamics that involve minimizing the energy of a system while keeping temperature and entropy constant. One version, as shown in Steven Blundell's book, also includes keeping volume constant. However, another version does not mention keeping volume constant but still results in the minimization of energy.
  • #1
Dazed&Confused
191
3
An alternative formulation of the second law is that the energy of the system [itex]U[/itex] is minimised if the temperature and entropy of the system are held constant.
However, [tex] dU= TdS -pdV[/tex]
which means that [itex]U[/itex] is presumably constant if the volume [itex]V[/itex] and the entropy [itex] S[/itex] are kept constant. How then can [itex]U[/itex] change so that it is minimised?
 
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  • #2
The formulation doesn't say anything about keeping volume constant.
 
  • #3
Thanks for replying. I have seen two versions. One is in Steven Blundell's book where he derives the availability which satisfies
[itex] dA= dU + p_0dV -T_0dS \leq 0 [/itex] where the subscripted variables are the reservoir ones. He then states that if [itex]V, S[/itex] are constant then [itex] dA = dU \leq 0[/itex] so that [itex] U[/itex] is minimised.

The other version uses a completely different approach but crucially no mention is made of [itex] V[/itex] being constant as you say.
 

FAQ: Extremum of thermodynamic potentials: confusion

1. What is an extremum of a thermodynamic potential?

An extremum of a thermodynamic potential is a point where the potential reaches either a maximum or minimum value. It represents a state of equilibrium in a thermodynamic system, where there is no net flow of energy or matter.

2. How is an extremum of a thermodynamic potential related to confusion?

The concept of an extremum of a thermodynamic potential can be confusing because it is often used in different ways and can have different meanings depending on the context. It is important to clearly define and understand the specific thermodynamic potential being referred to in order to avoid confusion.

3. Can an extremum of a thermodynamic potential change over time?

Yes, an extremum of a thermodynamic potential can change over time if the system is not in a state of equilibrium. As the system evolves and reaches a new equilibrium state, the extremum of the potential may shift to a different point.

4. How are the different thermodynamic potentials related to each other?

The various thermodynamic potentials, such as internal energy, enthalpy, and Gibbs free energy, are related to each other through mathematical transformations. Each potential represents different aspects of a thermodynamic system and can be used to describe and analyze different types of processes.

5. Why are extremums of thermodynamic potentials important in thermodynamics?

Extremums of thermodynamic potentials are important because they represent states of equilibrium in a thermodynamic system. They can be used to determine the conditions at which a system is at equilibrium, and they also provide valuable information about the stability and behavior of the system.

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