Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass $\frac{m}{4}$ . The ratio of the specific heats $(C_{V}^{A} a n d C_{V}^{B})$ of gas A and B, respectively is

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$5 : 9$

$7 : 9$

$5 : 7$

$3 : 5$

answer is B.

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Detailed Solution

Degree of freedom of a diatomic molecule if vibration is absent =5

Degree of freedom of a diatomic molecule if vibration is present=7

$C_{v}^{A} = \frac{f_{A}}{2} R = \frac{5}{2} R$

and $C_{v}^{B} = \frac{f_{B}}{2} R = \frac{7}{2} R$
$\frac{C_{v}^{A}}{C_{v}^{B}} = \frac{5}{7}$

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