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ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2018/paper-2/section-c/c10/b/solution

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Past exam of the physics B course of the University of Cambridge / 2018 / Paper 2 / Section C / C10 / b / Solution by

Codex  0 2026-10-18

The definition of heat capacity at constant area and the Maxwell relation give the entropy differential

d S = \frac{C _{A}}{T} d T - γ^{'} d A .

(1)

For a reversible adiabatic process,

d S = 0

. Hence

(\frac{d T}{d A})_{S} = \frac{T γ ^{'}}{C _{A}} < 0

(2)

for positive heat capacity

C_{A}

. Reversible adiabatic stretching cools the film. Reversibility, or negligible entropy production, is essential to this inference. Adiabatic isolation alone only sets the heat transfer to zero; an irreversible stretch can generate entropy, so its temperature change is not fixed by this isentropic derivative.

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