JEE Main 2025 Apr 3 Shift 2, Physics Q5: Thermodynamic Processes

JEE Main2025Apr 3, Shift 2Physics

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 :

A
$P_{0} V_{0} (2 ln 2 - 0.75)$
B
$P_{0} V_{0} (ln 2 - 0.75)$
C
$P_{0} V_{0} (ln 2 - 0.25)$
D
$P_{0} V_{0} (2 ln 2 - 0.25)$

Solution

Track the three legs of the cycle. After isothermal expansion to $4 V_{0}$ , pressure drops to $P_{0} /4$ .

Leg 1 (isothermal, $V_{0} \to 4 V_{0}$ ): $W_{1} = P_{0} V_{0} ln 4 = 2 P_{0} V_{0} ln 2$ .

Leg 2 (isobaric at $P_{0} /4$ , $4 V_{0} \to V_{0}$ ): $W_{2} = \frac{P _{0}}{4} (V_{0} - 4 V_{0}) = - \frac{3 P _{0} V _{0}}{4}$ .

Leg 3 (isochoric): $W_{3} = 0$ .

For the full cycle, $Δ U = 0$ , so $Q_{cycle} = W_{cycle} = W_{1} + W_{2} + W_{3}$ :

$Q = 2 P_{0} V_{0} ln 2 - \frac{3 P _{0} V _{0}}{4} = P_{0} V_{0} (2 ln 2 - 0.75)$ .

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JEE Main 2025 Apr 3 Shift 2, Physics Q5: Thermodynamic Processes

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