[itex](\frac{\partial U}{\partial P})_T[/itex] derivation

[wololo]

Homework Statement

Homework Equations

Maxwell relations

The Attempt at a Solution

Here is how I proceeded. Am I allowed to go from line 1 to 2? It almost seems too simple.
[tex]
dU=TdS-PdV \\
(\frac{\partial U}{\partial P})_T=T(\frac{\partial S}{\partial P})_T-P(\frac{\partial V}{\partial P})_T \\
\text{We know that}-(\frac{\partial S}{\partial P})_T=(\frac{\partial V}{\partial T})_P \\
(\frac{\partial U}{\partial P})_T=-T(\frac{\partial V}{\partial T})_P-P(\frac{\partial V}{\partial P})_T \\
(\frac{\partial U}{\partial P})_T=-[T(\frac{\partial V}{\partial T})_P+P(\frac{\partial V}{\partial P})_T]
[/tex]

 

[Chestermiller]

This seems fine, as long as you are allowed to use the "we know that" equation, which comes from the Maxwell relations.