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Given the internal energy U and entropy S of N weakly interacting particles in a closed
system with fixed volume V.
U = NkgT² (27In 2)
U
S = Nkg lnz + T
(a) Prove the Helmholtz free energy
(b) Prove the Pressure of the system is
F = -NkBT ln z
P = Nk Tln z)
(
T

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