According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

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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

$C_{v} = \frac{f}{2} R = \frac{7}{2} R$

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