 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-1/36a/b/iv/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For

N

identical, noninteracting classical particles, the one-particle phase-space integrals factorize and indistinguishability supplies the Gibbs factor. Thus the classical ideal-gas partition function rule gives

Z_{N} = \frac{Z _{1}^{N}}{N !} = \frac{1}{N !} [\frac{4 π ^{2} m}{h ^{2} β ^{2} κ} (1 - e^{- β κ R^{2} /2})]^{N} .

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