Arrange the following in order of magnitude of work done by the system / on the system at constant temperature : (a) $\left|\mathrm{W}_{\text {reversible }}\right|$ for expansion in infinite stage. (b) $\left|\mathrm{w}_{\text {irreversible }}\right|$ for expansion in single stage. (c) $\left|\mathrm{w}_{\text {reversible }}\right|$ for compression in infinite stage. (d) $\left|\mathrm{w}_{\text {irreversible }}\right|$ for compression in single stage. Choose the correct answer from the options given below :

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Chemical Thermodynamics

Arrange the following in order of magnitude of work done by the system / on the system at constant temperature :
(a)

∣ W_{reversible} ∣

for expansion in infinite stage.
(b)

∣ w_{irreversible} ∣

for expansion in single stage.
(c)

∣ w_{reversible} ∣

for compression in infinite stage.
(d)

∣ w_{irreversible} ∣

for compression in single stage.

Choose the correct answer from the options given below :

(A) $a > b > c > d$
(B) $d > c = a > b$ ✓ Correct
(C) $c = a > d > b$
(D) $a > c > b > d$

Answer: (B)

Solution

Work is the area under the

P

–

V

curve. At constant temperature the reversible path, carried out in an infinite number of stages, gives the same magnitude of work for expansion and for compression, so

∣ w ∣_{rev,exp} = ∣ w ∣_{rev,comp}

, that is (a)

=

(c). In a single-stage irreversible expansion the gas works against the low final pressure, so this work is the smallest, making (b) the least. In a single-stage irreversible compression the surroundings press at the high final pressure, so this work is the largest, making (d) the greatest. The order of magnitudes is

d > c = a > b

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Single correct option

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JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Chemical Thermodynamics

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