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

For Gas A (diatomic),  degree of freedom (f) = 3+2 = 5  

For Gas B (diatomic + vibration),  degree of freedom (f) = 3+2 +2= 7

$\mathrm{In} \mathrm{general}, \mathrm{for} \mathrm{any} \mathrm{gas} \mathrm{Specific} \mathrm{heat} \mathrm{at} \mathrm{constant} \mathrm{volume} {\mathrm{C}}_{\mathrm{V}}=\frac{\mathrm{fR}}{2}$

Specific heat at constant volume of   $A=\frac{5}{2}RT$
Specific heat at constant volume of    $B=\frac{7}{2}RT$          

   $\therefore Ratio=\frac{5}{7}$