According to law of equipartition of energy the molar specific heat...

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

${C}_{v} = \dfrac{f}{2}R = \dfrac{7}{2}R$