# A query on the equation $TdS = dU + PdV$ (relating to phase changes)

$$TdS=dU+PdV$$

is one of my favourite equations in all of physics. I have used it many times, in particular to obtain the Helmholtz free energy; my favourite state function. One thing I am not 100% sure of though is whether this equation is still valid during phase changes. I believe it is, as I believe you should be able to take a revisable path, whence I think this equation should hold, but I thought I would ask.

Is this equation valid through phase changes? Or have I got it wrong?

• You have it right. – Chet Miller Jul 12 '19 at 23:34

$$dU = TdS - pdV$$ The first term is associated with energy change during phase changes (entropy in a volume changes),
while the second term is about volume changes in the gas and the energy associated (constant $$N$$ and $$T$$). When a phase change occurs the entropy of that substance changes even as its temperature stays the same. A substance in solid phase has low entropy; in liquid phase, it has medium entropy; in gas phase, it has high entropy. So changes into different phases change entropy (heat increase/decrease)