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## Homework Statement

[itex] -\left ( \frac{\partial U}{\partial V} \right )_{S, N} [/itex] is a definition of an imporant thermodynamic property,where S denote the entropy and the subscript 0 denotes reference state, so they must be constant. show what is this property. In your analysis, use the equation below.

[tex] \frac{U}{U_{0}} = (\frac{V}{V_{0}})^{-2/3}exp\left \{ \frac{2(S-S_0)}{3k_BN} \right \} [/tex]

## Homework Equations

As I thought this was done by first-order ordinary derivative equation, I tried to differentiate it, but I was unable to do so. As this is about entrophy, I think U means current energy and V means volume.

## The Attempt at a Solution

I think this is done by first-order ordinary derivative, but I can't specify.