JEE Main 2025 Apr 2 Shift 2, Chemistry Q13: Basic Concepts of Thermodynamic

JEE Main2025Apr 2, Shift 2Chemistry

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.

(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
C
c = a $>$ d $>$ b
D
a $>$ c $>$ b $>$ d

Solution

For an isothermal process the reversible work magnitude is the same for expansion and compression:

$∣ w_{rev,exp} ∣ = ∣ w_{rev,comp} ∣ = n R T ln \frac{V _{f}}{V _{i}}$ , so $a = c$ .

For single-step (irreversible) expansion against the lower final pressure, the work done by the gas is smaller in magnitude than the reversible expansion: $∣ w_{irr,exp} ∣ < ∣ w_{rev,exp} ∣$ , i.e. $b < a$ .

For single-step (irreversible) compression at the higher external pressure, the work done on the gas is larger than the reversible compression: $∣ w_{irr,comp} ∣ > ∣ w_{rev,comp} ∣$ , i.e. $d > c$ .

Combining: $d > c = a > b$ .

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JEE Main 2025 Apr 2 Shift 2, Chemistry Q13: Basic Concepts of Thermodynamic

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