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swmmr1928

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## Homework Statement

Prove for the canonical ensemble

##\overline{(E-U)(p-\overline{p})}=kT[(\frac{\partial U} {\partial V})_{N,T} + p]##

Left hand side is covariance

E is energy

U is internal energy, average of E

p is microstate pressure

$$\overline{p}$$ is average pressure

V is volume

N is number of particles

T is temperature

## Homework Equations

##P=-\frac{\partial{U}} {\partial{V}}##

##P=kT(\frac{\partial{ln Q}}{\partial V})##

##U=kT^2(\frac{\partial{ln Q}}{\partial V})##

## The Attempt at a Solution

##\overline{(E-U)(p-\overline{p})}=Cov(E,p)=\overline{E*p}-\overline{E}*\overline{p}=\overline{E*p}-U*\overline{p}##

##\overline{E*p}=?##

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