Statistical pressure for a canonical ensemble

  • #1
Eulersheep
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So the pressure for a canonical ensemble is:

P = kbT dZ/dV

P = pressure

P = -∑pi dEi/dV
Z = ∑e-βEi

pi is the probability of being in microstate i
Ei is the energy of state i
β = 1/kbT

<E> = U = average energy

U = -1/Z dZ/dβ = -d(Ln(Z))/dβ

How can the pressure (given above) be derived in terms of the partition function?
 

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