Chemistry Q53 – JEE-MAIN 2025

Home Chemistry Chemical ThermodynamicsQuestion #306

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

| w_{r e v e r s i b l e} |

for expansion in infinite stages. (b)

| w_{i r r e v e r s i b l e} |

for expansion in single stage. (c)

| w_{r e v e r s i b l e} |

for compression in infinite stages. (d)

| w_{i r r e v e r s i b l e} |

for compression in single stage. Choose the correct answer from the options given below :

Clue 1 of 3: Work and Reversibility

Understand that reversible processes represent the theoretical maximum work output (for expansion) or minimum work input (for compression) for a given change.

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Ninja Strategy•Extreme Cases and Reversibility

Recognize that irreversible compression yields the largest magnitude of work, and reversible expansion/compression have equal magnitudes, which are greater than irreversible expansion.

🧠 Full Solution Path

Step 1: Compare Work Magnitudes for Expansion and Compression✦ Active

For isothermal expansion, work is done by the system ( $W < 0$ ). Reversible expansion (infinite stages) yields the maximum work output, so $| w_{r e v e r s i b l e, e x p a n s i o n} | > | w_{i r r e v e r s i b l e, e x p a n s i o n} |$ . This means $| a | > | b |$ . For isothermal compression, work is done on the system ( $W > 0$ ). Irreversible compression (single stage) requires the maximum work input, so $| w_{i r r e v e r s i b l e, c o m p r e s s i o n} | > | w_{r e v e r s i b l e, c o m p r e s s i o n} |$ . This means $| d | > | c |$ .

Step 2: Compare Reversible Expansion and Compression○ Expand

The magnitude of work done in a reversible isothermal expansion is equal to the magnitude of work done in a reversible isothermal compression between the same initial and final states (just reversed). Therefore, $| w_{r e v e r s i b l e, e x p a n s i o n} | = | w_{r e v e r s i b l e, c o m p r e s s i o n} |$ . This means $| a | = | c |$ .

Step 3: Combine Relationships to Determine Order○ Expand

Combining the relationships from Step 1 and Step 2: We have $| a | = | c |$ , $| a | > | b |$ , and $| d | > | c |$ . Arranging these in decreasing order of magnitude gives $d > c = a > b$ .

💡 Teacher's Secret Hint

Remember that 'work done by the system' is negative, and 'work done on the system' is positive. The question asks for the magnitude, so we consider the absolute values.

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Chemistry Question 53 – JEE-MAIN 2025

Clue 1 of 3: Work and Reversibility

🧠 Full Solution Path