According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume…

A diatomic gas has 5 degrees of freedom apart from vibrational degree of freedom. For each additional vibrational mode, degree of freedom is increased by $2$. So new degree of freedom,

$f=5+2=7$

Therefore, we require molar specific heat capacity at constant volume, which is given by

$C_v=\frac{f}{2}R=\frac{7}{2}R$