In non-rigid diatomic molecule with an additional vibrational mode

In non-rigid diatomic molecule with an additional vibrational mode, total degree of freedom $\left(f\right)=$$$\begin{gathered} 3\left(\text{rotational}\right)+3\left(\text{translational}\right)+1\left(\text{vibrational}\right) \\ =7 \end{gathered}$$

Therefore, 

$$\begin{gathered} \frac{C_p}{C_v}=1+\frac{2}{f}=\frac{9}{7} \\ \Rightarrow 81{\mathrm{C}}_{\mathrm{v}}^2=49{\mathrm{C}}_{\mathrm{P}}^2 \end{gathered}$$