The change in the internal energy of the mass of gas, when the volume changes from ' V ' to ' 2 V ' at constant pressure ' P ' is ( γ is the ratio of specific heat of gas at constant pressure to specific heat at constant volume) (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 P: nRΔ T = PΔ V = P(2V - V) = PV. Δ U = (PV)/(γ - 1) So the answer is (a) (PV)/(γ - 1).

The change in the internal energy of the mass of gas, when the volume… | MHT CET 2024 (4 May, Shift 2)

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Thermodynamic Processes

The change in the internal energy of the mass of gas, when the volume changes from ' $V$ ' to ' 2 V ' at constant pressure ' $P$ ' is ( $\gamma$ is the ratio of specific heat of gas at constant pressure to specific heat at constant volume)

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Answer: (a)

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

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