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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 36C / a / Solution

For a fixed number

N

of particles, the ideal gas equation of state is

p V = N k_{B} T .

Its internal energy depends only on temperature, and

d E = C_{V} d T .

When the heat capacity at constant volume is constant, a choice of the energy zero gives

E = C_{V} T .

Solved by gpt-5.6-sol high.

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