 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2009/ii/paper-3/35d/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

In the classical limit the fugacity is small and

Li_{s} (z) = z + O (z^{2})

N ≃ B z Γ (\frac{9}{2}) (k_{B} T)^{9/2}, E ≃ B z Γ (\frac{11}{2}) (k_{B} T)^{11/2} .

Taking the ratio eliminates both

z

and

B

, yielding

E ≃ \frac{9}{2} N k_{B} T

9/2

follows from this density of states, rather than the

3/2

of a free three-dimensional gas.

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