Quantum Thermo statistical physics

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Homework Statement


rotational energy of diatomic gas (note : h = hbar)

Er = h2/2I * r(r+1) , r = 0,1,2 ...

it is (2r+1) fold degenerate

find the partition function and hence the heat capacity at low temperatures.

The Attempt at a Solution



Z = ∑ g(Er) e-BEr
= ∑ (2r+1) e-Bh2/2I * r(r+1)
= (2r+1) / (1 - e-B) right? since i am summing over energies Er and not over r? so the geometric series give me ∑ e-BEr = 1/ (1 - e-B) ??

so mean energy E = -dlnZ/dB = -e-B / (1-e-B)

so Cv = dE/dT = use product rule? then thats the answer?

thanks!
 

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