List - I (Ideal gas and process, K = constant) List - II (Molar heat capacity at moderate temperature) (P) NH 3 gas and PV 2 = K (1) 6 13 R (Q) CO 2 gas and TV 3 = K (2) 2 7 R (R) Ar gas and P

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List - I (Ideal gas and process, K = constant) List - II (Molar heat capacity at moderate temperature) (P) NH 3 ​ gas and PV 2 = K (1) 6 13 ​ R (Q) CO 2 ​ gas and TV 3 = K (2) 2 7 ​ R (R) Ar gas and PT = K (3) 2R (S) SO 2 ​ gas V = KT 2 (4) 4R (5) 5R

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The polytropic molar heat capacity formula $C = C_{v} + \frac{R}{1 - x}$ (for $P V^{x} = co n s t an t$ ):

* For (P): For non-linear NH₃, $C_{v} = 3 R$ . Given $P V^{2} = K ⟹ x = 2$ , so $C = 3 R + \frac{R}{1 - 2} = 2R$ (3).

* For (R): For monatomic Ar, $C_{v} = \frac{3}{2} R$ . Since $PT = K ⟹ P (P V) \propto K ⟹ P V^{1/2} = co n s t an t ⟹ x = \frac{1}{2}$ , so $C = \frac{3}{2} R + \frac{R}{1 - 1/2} = \frac{7}{2} R$ (2).

* For (S): For non-linear SO₂, $C_{v} = 3 R$ . Since $V = K T^{2} ⟹ T \propto V^{1/2} ⟹ P V^{1/2} = co n s t an t ⟹ x = \frac{1}{2}$ , so $C = 3 R + 2 R = 5R$ (5).

* Matching these gives P $\to$ 3, Q $\to$ 1, R $\to$ 2, S $\to$ 5, which uniquely corresponds to option (B).

List - I (Ideal gas and process, K = constant)	List - II (Molar heat capacity at moderate temperature)
(P) $NH_{3}$ gas and $PV^{2} = K$	(1) $\frac{13}{6} R$
(Q) $CO_{2}$ gas and $TV^{3} = K$	(2) $\frac{7}{2} R$
(R) Ar gas and $PT = K$	(3) 2R
(S) $SO_{2}$ gas $V = KT^{2}$	(4) 4R
	(5) 5R

Chemistry - Thermodynamics - I Question with Solution | TestHub

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