- #1

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## Homework Statement

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

E

_{r}= h

^{2}/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(E

_{r}) e

^{-BEr}

= ∑ (2r+1) e

^{-Bh2/2I * r(r+1)}

= (2r+1) / (1 - e

^{-B}) right? since i am summing over energies E

_{r}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!