The change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure P is ( γ is the ratio of specific heat at constant pressure to that of volume) ( γ = (Cp)/(Cv)) (a) (PV)/(γ - 1) (b) (PV)/(γ + 1) (c) ((γ - 1))/(PV) (d) ((γ + 1))/(PV)

Answer: (a). Δ U = nCvΔ T with Cv = (R)/(γ - 1), so Δ U = (nRΔ T)/(γ - 1). At constant pressure nRΔ T = PΔ V = P(2V - V) = PV. Δ U = (PV)/(γ - 1), so the answer is (a).

The change in internal energy of the mass of gas, when the volume… | MHT CET 2026 (13 Apr, Shift 1)

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Thermodynamic Processes

The change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure P is ( $\gamma$ is the ratio of specific heat at constant pressure to that of volume) ( $\gamma = \frac{C_p}{C_v}$ )

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Answer: (a)

$\Delta U = nC_v\Delta T$ with $C_v = \dfrac{R}{\gamma - 1}$ , so $\Delta U = \dfrac{nR\Delta T}{\gamma - 1}$ .
At constant pressure $nR\Delta T = P\Delta V = P(2V - V) = PV$ .
$\Delta U = \dfrac{PV}{\gamma - 1}$ , so the answer is (a).

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