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

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

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G1 Physics · Accepted Answer

Step 1: For an ideal gas, U = nCᵥT and Cₚ − Cᵥ = R. Step 2: γ = Cₚ/Cᵥ implies Cᵥ = R/(γ − 1). Step 3: Thus ΔU = nRΔT/(γ − 1) = Δ(PV)/(γ − 1). Step 4: At constant P, initial PV = PV and final PV = P(2V) = 2PV. Step 5: ΔU = (2PV − PV)/(γ − 1) = PV/(γ − 1). Final answer: (C) PV/(γ − 1).