 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/36b/a/solution

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

A canonical ensemble describes a system with fixed particle number and external parameters that exchanges energy with a heat bath at fixed temperature

T

. With

β = (k_{B} T)^{- 1}

Z (β) = i = 0 \sum \infty e^{- β E_{i}}, p_{i} = \frac{e ^{- β E_{i}}}{Z} .

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