# I Extremum of thermodynamic potentials: confusion

1. Mar 31, 2016

### Dazed&Confused

An alternative formulation of the second law is that the energy of the system $U$ is minimised if the temperature and entropy of the system are held constant.
However, $$dU= TdS -pdV$$
which means that $U$ is presumably constant if the volume $V$ and the entropy $S$ are kept constant. How then can $U$ change so that it is minimised?

2. Mar 31, 2016

### andrewkirk

The formulation doesn't say anything about keeping volume constant.

3. Mar 31, 2016

### Dazed&Confused

Thanks for replying. I have seen two versions. One is in Steven Blundell's book where he derives the availability which satisfies
$dA= dU + p_0dV -T_0dS \leq 0$ where the subscripted variables are the reservoir ones. He then states that if $V, S$ are constant then $dA = dU \leq 0$ so that $U$ is minimised.

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