# Deriving an Thermodynamic Equation of State

1. Oct 12, 2009

### Duy028

1. The problem statement, all variables and given/known data

Derive the following:

$$\left(\frac{\partial U}{\partial V}\right)_{T}=T\left(\frac{\partial p}{\partial T}\right)_{V}-p$$

2. Relevant equations

Use the partner equation:

$$\left(\frac{\partial H}{\partial p}\right)_{T}=-T\left(\frac{\partial V}{\partial T}\right)_{p}+V$$

3. The attempt at a solution

I just need help finding the derivation. All the links I've searched for so far lead me to other derivations that use these equations to derive other ones. Obviously, it's hard to google things with partial derivatives in it. Any help would be useful. Thanks!

2. Oct 12, 2009

### gabbagabbahey

Hi Duy028, welcome to PF!

We don't do your homework for you here, and we don't post links to solutions for your homework either.

Try the derivation yourself, and we'll help you through it where you get stuck. As a starting point, how is $U$ defined (1st Law)? How is $H$ defined?

3. Oct 12, 2009

### Duy028

Thanks anyways, but I slept on it and woke up having a clearer mind and found the solution. I'll be sure to be back if I have other problems and will remember to post my attempts.