 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/35b/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

With

v_{g} ≫ v_{l}

and

v_{g} = k_{B} T / p

, the coexistence equation becomes

\frac{1}{p} \frac{d p}{d T} = \frac{L}{k _{B} T ^{2}} .

For constant

L

this integrates to

p (T) = p_{0} exp (- \frac{L}{k _{B} T}),

where

p_{0}

is constant. For

N

gas particles,

V_{g} = N k_{B} T / p (T)

, and therefore

\frac{d V _{g}}{d T} = V_{g} (\frac{1}{T} - \frac{L}{k _{B} T ^{2}}) .

 New to topics? Read the docs here!