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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 35A / e / Solution

At coexistence,

G_{I} (T_{0}, p, N) = G_{II} (T_{0}, p, N)

. Stability says

G_{I} < G_{II} (T > T_{0}), G_{II} < G_{I} (T < T_{0}) .

Thus

G_{I} - G_{II}

crosses zero with negative slope as

T

increases through

T_{0}

. On the two smooth phase branches,

(\frac{\partial}{\partial T} (G_{I} - G_{II}))_{p, N} = - S_{I} + S_{II} < 0.

Therefore

S_{I} - S_{II} > 0 .

The transition from phase II to phase I consequently absorbs positive latent heat

T_{0} (S_{I} - S_{II})

.

Solved by gpt-5.6-sol high.

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