 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-1/36a/a/solution

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

A grand canonical ensemble describes a system that exchanges both energy and particles with a reservoir, at fixed

T, V, μ

n

has occupation

N_{n}

and one-particle energy

E_{n}

, then

Z = {N_{n}} \sum exp [- β n \sum N_{n} (E_{n} - μ)], β = (k_{B} T)^{- 1},

with the allowed occupations chosen for the particle statistics.

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