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Match the $C_{P} / C_{V}$ ratio for ideal gases with different type of molecules :
Molecule Type $C_{P} / C_{V}$
(A) Monatomic (I) 7/5
(B) Diatomic rigid molecules (II) 9/7
(C) Diatomic non-rigid molecules (III) 4/3
(D) Triatomic rigid molecules (IV) 5/3

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$(A) - (I I), (B) - (I I I), (C) - (I), (D) - (I V)$

$(A) - (I V), (B) - (I I), (C) - (I), (D) - (I I I)$

$(A) - (I I I), (B) - (I V), (C) - (I I), (D) - (I)$

$(A) - (I V), (B) - (I), (C) - (I I), (D) - (I I I)$

answer is D.

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Detailed Solution

$C_{V} = \frac{f R}{2}, C_{P} = \frac{f R}{2} + R \Rightarrow \frac{C_{P}}{C_{V}} = \frac{f + 2}{f}, f i s d e g r e e s o f f r e e d o m .$

Gas	Translation	Rotation	Vibration	$\frac{C_{P}}{C_{V}}$
Monatomic	3	0	0	5/3
Diatomic Rigid	3	2	0	7/5
Diatomic non-Rigid	3	2	2	9/7
Triatomic rigid	3	3	0	4/3

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