In a non-rigid diatomic molecule with an additional vibrational mode,what is the relationship between $C_v$ and $C_p$?

For hydrogen gas $C_p - C_v = a$ and for oxygen gas $C_p - C_v = b$. The relation between $a$ and $b$ is given by:

The molar specific heat of a gas as given from the kinetic theory is $\frac{5}{2} R$. If it is not specified whether it is $C_P$ or $C_V$,one could conclude that the molecules of the gas

Obtain the relation between specific heat capacity at constant pressure $(C_P)$ and specific heat capacity at constant volume $(C_V)$ for an ideal gas.

The specific heat of helium at constant volume is $12.6 \,J \,mol^{-1} \,K^{-1}$. The specific heat of helium at constant pressure in $J \,mol^{-1} \,K^{-1}$ is approximately (assume, the universal gas constant, $R=8.314 \,J \,mol^{-1} \,K^{-1}$)

Specific heats of an ideal gas at constant pressure and volume are denoted by $C_p$ and $C_v$ respectively. If $\gamma = \frac{C_p}{C_v}$ and $R$ is the universal gas constant,then $C_v$ is equal to: