Deriving an Thermodynamic Equation of State

[Duy028]

Homework Statement

Derive the following:

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

Homework Equations

Use the partner equation:

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

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!

 

[gabbagabbahey]

Hi Duy028, welcome to PF!

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!

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?

 

[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.