Proving (∂T/∂V)s = -(∂P/∂S)v from the first law

[bon]

Homework Statement

First law can be written dU = TdS - PdV where the internal energy U may be written in terms of any two of T,P,V,S.

I have to show that (DT/DV)s = -(DP/DS)v

where D is partial d, and the subscripts s and v mean hold those constant..

Homework Equations

The Attempt at a Solution

Not really sure how to proceed at all?

 

[physicsworks]

This is one of the Maxwell relations.
If you have a function
$$f(x,y)=\left( \frac{\partial f}{\partial x} \right)_y dx + \left( \frac{\partial f}{\partial y} \right)_x dy = A dx + B dy$$
then, according to
$$\frac{\partial}{y} \left( \frac{\partial f}{\partial x} \right) = \frac{\partial}{\partial x} \left( \frac{\partial f}{\partial y} \right)$$
you have
$$\left( \frac{\partial A}{\partial y} \right)_x = \left( \frac{\partial B}{\partial x} \right)_y$$