List - I List - II (P) Isothermal reversible expansion of an ideal gas (1) Δ S system 0 (Q) Isothermal free expansion of an ideal gas (2) Δ S system

Question

List - I List - II (P) Isothermal reversible expansion of an ideal gas (1) Δ S system ​ > 0 (Q) Isothermal free expansion of an ideal gas (2) Δ S system ​ < 0 (R) Adiabatic reversible expansion of an ideal gas (3) Δ S surrounding ​ = 0 (S) Adiabatic irreversible compression of an ideal gas (4) Δ S universe ​ > 0 (5) Δ S universe ​ = 0

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P: Isothermal reversible expansion of an ideal gas.

For a reversible process, $Δ S_{u ni v erse} = 0$ . For expansion, $Δ S_{sys t e m} > 0$ . Since it's isothermal, $Δ S_{s u rro u n d in g} = - Δ S_{sys t e m} < 0$ .

So, P $\to$ (1) $Δ S_{sys t e m} > 0$ , (5) $Δ S_{u ni v erse} = 0$ .

Q: Isothermal free expansion of an ideal gas.

Free expansion is irreversible. For an ideal gas, $Δ U = 0$ and $w = 0$ , so $q = 0$ .

$Δ S_{sys t e m} = n R ln (V_{2} / V_{1}) > 0$ . Since $q = 0$ , $Δ S_{s u rro u n d in g} = 0$ .

For an irreversible process, $Δ S_{u ni v erse} > 0$ .

So, Q $\to$ (1) $Δ S_{sys t e m} > 0$ , (3) $Δ S_{s u rro u n d in g} = 0$ , (4) $Δ S_{u ni v erse} > 0$ .

R: Adiabatic reversible expansion of an ideal gas.

For an adiabatic process, $q = 0$ , so $Δ S_{s u rro u n d in g} = 0$ .

For a reversible process, $Δ S_{u ni v erse} = 0$ .

Since it's an expansion, $Δ S_{sys t e m} > 0$ .

So, R $\to$ (3) $Δ S_{s u rro u n d in g} = 0$ , (5) $Δ S_{u ni v erse} = 0$ .

S: Adiabatic irreversible compression of an ideal gas.

For an adiabatic process, $q = 0$ , so $Δ S_{s u rro u n d in g} = 0$ .

For an irreversible process, $Δ S_{u ni v erse} > 0$ .

For compression, $Δ S_{sys t e m}$ can be positive or negative depending on the exact path, but for an irreversible compression, the overall entropy of the system often increases due to internal friction or non-equilibrium states.

So, S $\to$ (1) $Δ S_{sys t e m} > 0$ , (3) $Δ S_{s u rro u n d in g} = 0$ , (4) $Δ S_{u ni v erse} > 0$ .

Matching:

P $\to$ 1, 5

Q $\to$ 1, 3, 4

R $\to$ 3, 5

S $\to$ 1, 3, 4

This matches option A.

List - I	List - II
(P) Isothermal reversible expansion of an ideal gas	(1) $Δ S_{system} > 0$
(Q) Isothermal free expansion of an ideal gas	(2) $Δ S_{system} < 0$
(R) Adiabatic reversible expansion of an ideal gas	(3) $Δ S_{surrounding} = 0$
(S) Adiabatic irreversible compression of an ideal gas	(4) $Δ S_{universe} > 0$
	(5) $Δ S_{universe} = 0$

Chemistry - Thermodynamics - II Question with Solution | TestHub

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JEE Main 2027 (Class 12)