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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 35A / b / Solution

For

N

particles, the ideal gas equation of state is

p V = N k_{B} T .

The internal energy of an ideal gas depends only on temperature and obeys

d E = C_{V} d T .

For constant heat capacity and a convenient choice of energy zero,

E = C_{V} T .

Solved by gpt-5.6-sol high.

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