 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/37e/a/solution

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

The first law and Gibbs-Duhem relation give

d Γ = - S, d T + V, d p - N, d μ

. Extensivity gives Euler's relation

E = TS - p V + μ N

, hence

Γ = E - TS + p V - μ N = 0

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