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

For a non-rigid diatomic gas, the degrees of freedom are distributed as follows:

Translational degrees of freedom = $3$
Rotational degrees of freedom = $2$
Vibrational degrees of freedom = $2$ (since each vibrational mode contributes to both kinetic and potential energy)

Total degrees of freedom $f = 3 + 2 + 2 = 7$

According to the law of equipartition of energy, the internal energy per mole of the gas is given by:

$U = \dfrac{f}{2}RT = \dfrac{7}{2}RT$

The molar specific heat at constant volume is:

$C_v = \dfrac{dU}{dT} = \dfrac{7}{2}R$

Answer: $(7/2) R$