The ratio of the specific heats $$\frac{{{C_p}}}{{{C_V}}} = \gamma $$   in terms of degrees of freedom $$\left( n \right)$$ is given by

Solution :
The specific heat of gas at constant volume in terms of degree of freedom $$n$$ is $${C_V} = \frac{n}{2}R$$
Also $${C_p} - {C_V} = R$$
So $${C_p} = \frac{n}{2}R + R = R\left( {1 + \frac{n}{2}} \right)$$
Now, $$\gamma = \frac{{{C_p}}}{{{C_V}}} = \frac{{R\left( {1 + \frac{n}{2}} \right)}}{{\frac{n}{2}R}} = \frac{2}{n} + 1$$