# Thermodynamics Relations

1. Mar 6, 2017

### B30W01F

1. The problem statement, all variables and given/known data
I need to prove the following equation:

2. Relevant equations
The 4 maxwell relations and their derivations:
https://en.wikipedia.org/wiki/Maxwell_relations
3. The attempt at a solution
I started out with the fundamental equations of
dU=TdS - PdV
and as dS=0, and Cv=(dU/dT)v;
I simplified this to:
dT= -P(dV/Cv)

I did a similar procedure, only this time using the definition of enthalpy to get to
dT = V(dP/Cp)

But I don't know how to proceed from here. I've tried looking at the relations but i dont know what Im missing or if I'm going about this totally wrong...

Cheers

2. Mar 7, 2017

### Staff: Mentor

The Maxwell relations are not needed to solve this problem.

You can solve this problem by working with the following equations:
$$dS=\left(\frac{\partial S}{\partial P}\right)_VdP+\left(\frac{\partial S}{\partial V}\right)_PdV\tag{1}$$
$$dS=\left(\frac{\partial S}{\partial T}\right)_PdT+\left(\frac{\partial S}{\partial P}\right)_TdP\tag{2}$$
$$dS=\left(\frac{\partial S}{\partial T}\right)_VdT+\left(\frac{\partial S}{\partial V}\right)_TdV\tag{3}$$
$$dT=\left(\frac{\partial T}{\partial V}\right)_PdV+\left(\frac{\partial T}{\partial P}\right)_VdP\tag{4}$$

Chet

Last edited: Mar 8, 2017