 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-4/35a/e/solution

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

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})

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