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If the ratio of specific heat of a gas at constant pressure to that at constant volume is γ, the change in internal energy of a mass of gas, when the volume changes from V to 2V at constant pressure P, is:

1. R / (γ − 1)
2. PV
3. PV / (γ − 1)
4. γ PV / (γ − 1)

Correct answer: PV / (γ − 1)

Solution

The change in internal energy of an ideal gas is given by ΔU = nCvΔT. Using the relation Cp - Cv = R and γ = Cp/Cv, we find Cv = R / (γ - 1). At constant pressure, the work done is PΔV = PV, and the heat added is Q = nCpΔT. The change in internal energy is then ΔU = Q - PΔV = PV / (γ - 1).

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