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 stages. (b) |w_ irreversible | for expansion in single stage. (c) |w_ reversible | for compression in infinite stages. (d) |w_ irreversible | for compression in single stage. Choose the correct answer from the options given below :

Thermodynamics PYQ — JEE Main 2025 · 2 Apr · Shift 2 · Q9 with Solution

View written solutionFree

Correct answer: A

Key idea: work at constant temperature depends on path

For an ideal gas undergoing isothermal change:

Reversible process gives the maximum magnitude of work in expansion.
Reversible process gives the minimum magnitude of work required in compression.
Irreversible single-stage process gives less work in expansion and more work required in compression.

So we compare the four cases carefully.

Expansion

(a) Reversible expansion in infinite stages

For reversible isothermal expansion,

|w_{\text{rev, exp}}| = nRT \ln \frac{V_2}{V_1}

This is the maximum work obtainable during expansion.

(b) Irreversible expansion in single stage

For single-stage irreversible expansion against constant external pressure,

|w_{\text{irr, exp}}| = P_{\text{ext}}(V_2 - V_1)

For the same initial and final states,

|w_{\text{rev, exp}}| > |w_{\text{irr, exp}}|

Hence,

a>b

Compression

(c) Reversible compression in infinite stages

For reversible isothermal compression,

|w_{\text{rev, comp}}| = nRT \ln \frac{V_1}{V_2}

Its magnitude is the same as reversible expansion between the same two states:

c=a

(d) Irreversible compression in single stage

For single-stage compression, the external pressure is kept constant and greater than the gas pressure. The work magnitude is

|w_{\text{irr, comp}}| = P_{\text{ext}}(V_1 - V_2)

For compression, irreversible path requires more work than reversible compression, so

d>c

Therefore,

d>c=a

Overall order

Combining both results:

d>c=a>b

This matches Option A.

Check options

A: $d>c=a>b$ ✅ correct
B: $c=a>d>b$ ❌ since for compression, irreversible requires more work than reversible, so $d>c$
C: $a>c>b>d$ ❌ because $a=c$ and also $d$ should be largest
D: $a>b>c>d$ ❌ incorrect ordering

Final answer

\boxed{d>c=a>b}

So the correct option is A.

More from Thermodynamics

View written solutionFree

Correct answer: A

Key idea: work at constant temperature depends on path

For an ideal gas undergoing isothermal change:

Reversible process gives the maximum magnitude of work in expansion.
Reversible process gives the minimum magnitude of work required in compression.
Irreversible single-stage process gives less work in expansion and more work required in compression.

So we compare the four cases carefully.

Expansion

(a) Reversible expansion in infinite stages

For reversible isothermal expansion,

|w_{\text{rev, exp}}| = nRT \ln \frac{V_2}{V_1}

This is the maximum work obtainable during expansion.

(b) Irreversible expansion in single stage

For single-stage irreversible expansion against constant external pressure,

|w_{\text{irr, exp}}| = P_{\text{ext}}(V_2 - V_1)

For the same initial and final states,

|w_{\text{rev, exp}}| > |w_{\text{irr, exp}}|

Hence,

a>b

Compression

(c) Reversible compression in infinite stages

For reversible isothermal compression,

|w_{\text{rev, comp}}| = nRT \ln \frac{V_1}{V_2}

Its magnitude is the same as reversible expansion between the same two states:

c=a

(d) Irreversible compression in single stage

For single-stage compression, the external pressure is kept constant and greater than the gas pressure. The work magnitude is

|w_{\text{irr, comp}}| = P_{\text{ext}}(V_1 - V_2)

For compression, irreversible path requires more work than reversible compression, so

d>c

Therefore,

d>c=a

Overall order

Combining both results:

d>c=a>b

This matches Option A.

Check options

A: $d>c=a>b$ ✅ correct
B: $c=a>d>b$ ❌ since for compression, irreversible requires more work than reversible, so $d>c$
C: $a>c>b>d$ ❌ because $a=c$ and also $d$ should be largest
D: $a>b>c>d$ ❌ incorrect ordering

Final answer

\boxed{d>c=a>b}

So the correct option is A.

Thermodynamics question

Thermodynamics question

(a) Reversible expansion in infinite stages

(b) Irreversible expansion in single stage

(c) Reversible compression in infinite stages

(d) Irreversible compression in single stage

More from Thermodynamics

Thermodynamics question

Thermodynamics question

(a) Reversible expansion in infinite stages

(b) Irreversible expansion in single stage

(c) Reversible compression in infinite stages

(d) Irreversible compression in single stage

More from Thermodynamics