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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 35B / b / Solution

Equality of chemical potentials gives

d μ_{l} = d μ_{g}

along coexistence. Since

d μ = - s d T + v d p,

one obtains

(v_{g} - v_{l}) \frac{d p}{d T} = s_{g} - s_{l} .

Using

L = T (s_{g} - s_{l})

gives the Clausius-Clapeyron relation

\frac{d p}{d T} = \frac{L}{T ( v _{g} - v _{l} )} .

Solved by gpt-5.6-sol high.

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