Deriving Maxwell's Relation with Thermodynamic Variables

[mdwerner]

Homework Statement

Derive the following general relation : $$\left(\frac{\partial T}{\partial V}\right)_{S} = - \frac{1}{C_{V}} T \left(\frac{\partial p}{\partial T}\right)_{V}$$

Homework Equations

Maxwell's Relation : $$\left(\frac{\partial T}{\partial V}\right)_{S} = - \left(\frac{\partial p}{\partial S}\right)_{V}$$

The Attempt at a Solution

The similarity of the question to the maxwell's relation is the only thing I could recognize - but I don't see what to do? Any suggestions will be appreciated.

 

[Mindscrape]

First try writing out the differentials for T and 1/Cv to see if that gives you any inspiration.

 

[mdwerner]

I don't understand, what do you mean by the differentials of T and 1 / C_V ? A derivative? if so, with respect to what?
One thing I had considered would be to multiply this function by $$\frac{\partial S}{\partial T}$$ but that seems to jumble the left side of the equation...

 

[Mindscrape]

T is $$\frac{\partial U}{\partial S}$$

and

1/Cv is $$\frac{\partial T}{\partial U}$$