Extremum of thermodynamic potentials: confusion

  • #1
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
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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.

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