# Thermodynamic Potentials in Proper Variables

1. Nov 19, 2015

### coca-cola

1. The problem statement, all variables and given/known data
A solid has energy (for one mole):

$U_1 =\frac{S^2}{a_1}+b_1V(V-2V_0)$

Write H, F, and G in terms of their proper variables.

2. Relevant equations

Maxwell's relations and
H=U+PV
F=U-TS
G=U-TS+PV

3. The attempt at a solution

H, for example:

I have tried writing dV as a sum of partial derivatives times total differentials:

$dV=\frac{\partial V}{\partial S}dS+\frac{\partial V}{\partial P}dP$

I have no idea how to get V in terms of S and P.

I have similar problems for the other cases.

Thanks for any help!

2. Nov 19, 2015

### DrDu

Under relevant equations you mentioned Maxwells equations.

3. Nov 19, 2015

### coca-cola

Maxwell's relations. I still don't know how that gives anything concrete.

4. Nov 19, 2015

### DrDu

Well, probably the first step is to find pressure as $p=-\frac{\partial U}{\partial V}|_S$ and an analogous relation for temperature. For the rest, you don't even need differentials.

Last edited: Nov 19, 2015
5. Nov 19, 2015

### coca-cola

How did you find that?

6. Nov 19, 2015

### DrDu

Sorry, I was already thinking in temperature when writing down this. I corrected the expression in #4.

7. Nov 19, 2015

### coca-cola

Thanks sir! Your response helped me solve the problem.