 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/ii/paper-3/33c/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

For a fixed amount of gas, the first law of thermodynamics gives

d U = T d S - p d V

G = U + p V - TS

, so

d G = - S d T + V d p

. Equality of its mixed partial derivatives gives the Maxwell relation

(\frac{\partial S}{\partial p})_{T} = - (\frac{\partial V}{\partial T})_{p} .

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