Consider two ideal diatomic gases $A$ and $B$ at some temperature T. Molecules of the gas A are rigid, and have a mass $\mathrm{m}$. Molecules of the gas B have an additional
vibrational mode, and have a mass $\frac{m}{4}$. The ratio of the
specific heats $\left(C_{V}^{A}\right.$ and $\left.C_{V}^{B}\right)$ of gas $A$ and $B$, respectively is:
Correct Option: , 4
(4) Specific heat of gas at constant volume
$C_{v}=\frac{1}{2} f R ; f=$ degree of freedom
For gas A (diatomic)
$\mathrm{f}=5(3$ translational $+2$ rotational $)$
$\therefore C_{v}^{A}=\frac{5}{2} R$
For gas B (diatomic) in addition to ( 3 translational + 2 rotational) 2 vibrational degree of freedom.
$\therefore \quad C_{v}^{B}=\frac{7}{2} R$ Hence $\frac{C_{v}^{A}}{C_{v}^{B}}=\frac{\frac{5}{2} R}{\frac{7}{2} R}=\frac{5}{7}$