An ideal gas exists in a state with pressure P₀, volume V₀. It is… | JEE Main 2025 (3 Apr, Shift 2)

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Thermodynamic Processes

An ideal gas exists in a state with pressure $P_0$ , volume $V_0$ . It is isothermally expanded to 4 times of its initial volume $(V_0)$ , then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

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Answer: (b)

Cyclic process: $\Delta U = 0$ , so net heat $=$ net work.
Isothermal $V_0 \to 4V_0$ : $W_1 = P_0V_0\ln 4 = 2P_0V_0\ln 2$ .
Pressure after expansion is $P_0/4$ ; isobaric $4V_0 \to V_0$ : $W_2 = \dfrac{P_0}{4}(V_0 - 4V_0) = -0.75\,P_0V_0$ .
Isochoric: $W_3 = 0$ .
$Q = P_0V_0(2\ln 2 - 0.75)$ , so the answer is (b).

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