Physics · Thermodynamics

JEE Main 2025 — 3 April, Evening Shift — Question 48

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 $\left(V_{0}\right)$ , 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

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

Answer: B

Step-by-step solution

$\Delta Q=\Delta v+\Delta \mathrm{W}$

For cyclic process

$\Delta Q=\Delta \mathrm{W}$

\begin{aligned} \mathrm{W} & =\mathrm{W}_{A B}+\mathrm{W}_{B C}+\mathrm{W}_{C A} \\ & =P_{0} V_{0} \ln \frac{4 V_{0}}{V_{0}}+\frac{P_{0}}{4}\left(V_{0}-4 V_{0}\right)+0 \\ & =P_{0} V_{0} \ln 4-\frac{3}{4} P_{0} V_{0} \\ & =P_{0} V_{0}(2 \ln 2-0.75) \end{aligned}

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 3 April, Evening Shift
Subject: Physics
Chapter: Thermodynamics
Topic: Different Thermodynamic Processes