# Maxwell's relations (thermodynamics): validity

1. Dec 11, 2007

### plmokn2

1. The problem statement, all variables and given/known data
I came across a slightly unusual question today. It started out fine, just asking me to derive a maxwell relation but then asked under what conditions is this relationship valid.

2. Relevant equations

3. The attempt at a solution
In deriving the relation I need to assume U, V and p are functions of state, but I can't think of any system where this wouldn't be the case. Also the first law must take the form TdS-pdV which only applies for simple gas systems without any extra freedom. But is that is?

If someone could let me know if I'm missing something obvious here (or just confirm I'm right) I'd appreciate it.
Thanks

2. Dec 12, 2007

### Shooting Star

Probably, it's the mathematical fact that the order of partial differentiation of an analytic function of two variables does not matter.

del/del x(del f/del y) = del/del y(del f/del x).

3. Dec 12, 2007

Thanks