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## Homework Statement

Define the Helmholtz free energy as F=E-TS.

Show that the internal energy E=-T

^{2}[itex]\frac{∂}{∂T}[/itex]([itex]\frac{F}{T}[/itex])

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## Homework Equations

S=([itex]\frac{∂F}{∂T}[/itex])

_{V}

Perhaps [itex]\beta[/itex]=[itex]\frac{1}{\tau}[/itex]

and [itex]\tau[/itex]=k

_{B}T

## The Attempt at a Solution

E = F+TS

E = F+T([itex]\frac{∂F}{∂T}[/itex])

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.

.

. (some steps to final equation)

.

.

E=-T

^{2}[itex]\frac{∂}{∂T}[/itex]([itex]\frac{F}{T}[/itex])

_{V}

Any help/hints would be greatly appreciated. My partial derivatives are a bit rusty. Thanks