During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. What is the ratio Cp/Cv for this gas?

Correct answer: 3/2

Solution

For an adiabatic process: P * V^gamma = constant and PV = nRT. Eliminating V: P^(1-gamma) * T^gamma = constant, so P proportional to T^(gamma/(gamma-1)). Given P proportional to T³: gamma/(gamma-1) = 3 => gamma = 3*(gamma-1) = 3*gamma - 3 => -2*gamma = -3 => gamma = 3/2.

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