Match the List-I with List-II List-I (Isothermal process for ideal gas system) List-II Work done ( V f boldsymbol V i ) --- --- A. Reversible expansion I. w =0 B. Free expansion II. w =- nRT ln frac V f V i C. Irreversible expansion III. w =- p ex ( V f - V i ) D. Irreversible compression IV. w =- p ex ( V i - V f ) Choose the correct answer from the options given below :

Chemistry · Thermodynamics & Thermochemistry

JEE Main 2026 — 24 January, Morning Shift — Question 57

Match the List-I with List-II

List-I (Isothermal process for ideal gas system)	List-II Work done $\left(\mathbf{V}_{\mathbf{f}} \boldsymbol{>} \mathbf{V}_{\mathbf{i}}\right)$
A. Reversible expansion	I. $\mathrm{w}=0$
B. Free expansion	II. $\mathrm{w}=-\mathrm{nRT} \ln \frac{\mathrm{V}_{\mathrm{f}}}{\mathrm{V}_{\mathrm{i}}}$
C. Irreversible expansion	III. $\mathrm{w}=-\mathrm{p}_{\mathrm{ex}}\left(\mathrm{V}_{\mathrm{f}}-\mathrm{V}_{\mathrm{i}}\right)$
D. Irreversible compression	IV. $\mathrm{w}=-\mathrm{p}_{\mathrm{ex}}\left(\mathrm{V}_{\mathrm{i}}-\mathrm{V}_{\mathrm{f}}\right)$

Choose the correct answer from the options given below :

Option A:
A-IV, B-I, C-III, D-II
Option B:
A-IV, B-II, C-III, D-I
Option C:
A-I, B-III, C-II, D-IV
Option D:
A-II, B-I, C-III, D-IV
Correct

Answer: D

Step-by-step solution

(A) $\mathrm{W}_{\text {Rev. }}=-\int \mathrm{P}_{\text {gas }} \mathrm{dV}$ $\mathrm{W}_{\text {Rev. Isot. Exp. }}=-\mathrm{nRT} \ln \left[\frac{\mathrm{V}_{\mathrm{f}}}{\mathrm{V}_{\mathrm{i}}}\right]$ (A) → (II) (B) Free expansion $\mathrm{W}_{\text {irrev. }}=-\mathrm{P}_{\text {ext }} \Delta \mathrm{V}$ $\mathrm{P}_{\text {ext }}=0$ $\mathrm{W}=0$ (B) $\rightarrow$ (I) (C) Irreversible expansion $\mathrm{W}_{\text {irrev. }}=-\mathrm{P}_{\text {ext }} \Delta \mathrm{V}$ $\mathrm{W}_{\text {irrev. }}=-\mathrm{P}_{\text {ext }}\left(\mathrm{V}_{\mathrm{f}}-\mathrm{V}_{\mathrm{i}}\right)$ (C) → (III) (D) Irreversible compression $\mathrm{W}_{\text {irrev. }}=-\mathrm{P}_{\text {ext }} \Delta \mathrm{V}$ $\mathrm{W}_{\text {irrev. }}=-\mathrm{P}_{\text {ext }}\left(\mathrm{V}_{\mathrm{i}}-\mathrm{V}_{\mathrm{f}}\right)$

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Exam: JEE Main 2026
Paper: 24 January, Morning Shift
Subject: Chemistry
Chapter: Thermodynamics & Thermochemistry
Topic: Work Done in Different Cases