Arrange the following isothermal processes in order of the magnitude of the work ( $p-V$ ) involved between states 1 and 2 . A. Expansion in single stage $\mathrm{w}_{\mathrm{A}}$ B. Expansion in multi stages $\mathrm{w}_{\mathrm{B}}$ C. Compression in single stage $\mathrm{w}_{\mathrm{C}}$ D. Compression in multi stages $\mathrm{w}_{\mathrm{D}}$

(C) $|\mathrm{w}_{\mathrm{C}}|>|\mathrm{w}_{\mathrm{D}}|>|\mathrm{w}_{\mathrm{B}}|>|\mathrm{w}_{\mathrm{A}}|$

(A) $|\mathrm{W}_{\mathrm{B}}|>|\mathrm{W}_{\mathrm{A}}|>|\mathrm{W}_{\mathrm{C}}|>|\mathrm{W}_{\mathrm{D}}|$

(B) $|\mathrm{w}_{\mathrm{C}}|>|\mathrm{w}_{\mathrm{D}}|>|\mathrm{w}_{\mathrm{A}}|>|\mathrm{w}_{\mathrm{B}}|$

(D) $|\mathrm{w}_{\mathrm{B}}|>|\mathrm{w}_{\mathrm{A}}|>|\mathrm{w}_{\mathrm{D}}|>|\mathrm{w}_{\mathrm{C}}|$

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Chemical Thermodynamics

Arrange the following isothermal processes in order of the magnitude of the work (

p - V

) involved between states 1 and 2 .
A. Expansion in single stage

w_{A}

B. Expansion in multi stages

w_{B}

C. Compression in single stage

w_{C}

D. Compression in multi stages

w_{D}

(A) $∣ W_{B} ∣ > ∣ W_{A} ∣ > ∣ W_{C} ∣ > ∣ W_{D} ∣$
(B) $∣ w_{C} ∣ > ∣ w_{D} ∣ > ∣ w_{A} ∣ > ∣ w_{B} ∣$
(C) $∣ w_{C} ∣ > ∣ w_{D} ∣ > ∣ w_{B} ∣ > ∣ w_{A} ∣$ ✓ Correct
(D) $∣ w_{B} ∣ > ∣ w_{A} ∣ > ∣ w_{D} ∣ > ∣ w_{C} ∣$

Answer: (C)

Solution

For an isothermal change between the same two states the work is

w = - \int p_{ext} d V

, and its magnitude depends on the opposing pressure at each step. In expansion the gas does most work when it pushes against the largest possible pressure throughout, i.e. in many small stages, so

∣ w_{B} ∣ > ∣ w_{A} ∣

. In compression the surroundings do most work when the largest constant pressure is applied in a single step, so

∣ w_{C} ∣ > ∣ w_{D} ∣

. Since compression is carried out against the higher pressures of the path, both compressions exceed both expansions in magnitude.

The order of magnitudes is

∣ w_{C} ∣ > ∣ w_{D} ∣ > ∣ w_{B} ∣ > ∣ w_{A} ∣

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Single correct option

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JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Chemical Thermodynamics

Solution

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