 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/36e/b/i/solution

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

- N k_{B} T lo g V

. With

V = 4 π r^{3} /3

4 π t r^{2}

, the radius-dependent free energy is therefore

F (r) = - N k_{B} T lo g V + 4 π t r^{2} + constant .

For equilibrium against external pressure

P_{0}

, minimize

F + P_{0} V

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