 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/ii/paper-3/34d/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-05

For

N

particles of a classical monatomic ideal gas, the equation of state and internal energy are

p V = N k_{B} T, U = \frac{3}{2} N k_{B} T = \frac{3}{2} p V .

Only translational degrees of freedom contribute; the particle number is fixed throughout the thermodynamic cycle.

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