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?