 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/9d/a/solution

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

Since

p \propto L^{- 1} = V^{- 1/3}

d p / d V = - p / (3 V)

. At fixed occupations,

d E = \int E^{'} (p) (d p / d V) \overset{n}{ˉ} (p), d p, d V

. Equating this to

- P, d V

yields

P = (3 V)^{- 1} \int p E^{'} (p) \overset{n}{ˉ} (p), d p

 New to topics? Read the docs here!