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Homework Statement
prove that for a free expansion the following equality holds:
[tex]\left( \frac{\partial T}{\partial V} \right) _{U} = - \frac{1}{C_{V}} \left[ T \left(\frac{\partial P}{\partial T} \right)_{V} - P \right][/tex]
Homework Equations
thermodynamic potentials, maxwell equations etc.
The Attempt at a Solution
I've tried playing around with the equations a little, but didn't get anywhere. I thought that [itex] \left( \frac{\partial T}{\partial V} \right)_{U} [/itex] should be zero, because if the energy remains constant, so should the temperature.