What is the significance of the heat capacity ratio $\gamma = \frac{C_{P}}{C_{V}}$ for a gas?

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma$,the change in internal energy of a mass of gas,when the volume changes from $V$ to $2V$ at constant pressure $p$,is

The ratio of specific heats $\left(\frac{C_{P}}{C_{V}}\right)$ in terms of degree of freedom $(f)$ is given by

Find the ratio of specific heat at constant pressure $(C_p)$ to the specific heat at constant volume $(C_v)$ for $NH_3$.

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

An ideal gas has molar heat capacity $C_V$ at constant volume. The gas undergoes a process where the temperature changes as $T=T_0(1+\alpha V^2)$,where $T$ and $V$ are temperature and volume respectively,and $T_0$ and $\alpha$ are positive constants. The molar heat capacity $C$ of the gas is given as $C=C_V+R f(V)$,where $f(V)$ is a function of volume. The expression for $f(V)$ is