- #1
SalfordPhysics
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Homework Statement
For a single molecule, derive the internal energy U = 3/2kBT
In terms of the partition function Z, F = -kBTlnZ
Where Z = V(aT)3/2
Homework Equations
Thermodynamic identity: δF = -SδT - pδV
p = kBT/V
S = kB[ln(Z) + 3/2]
The Attempt at a Solution
U = F + TS
δU = δF + δT.S + δS.T
= -SδT - pδV + δT.S + δS.T
δU = -pδV + TδS
(δS/δU)V = 1/T
However, don't have a variable U in S to differentiate with respect to.