The ratio of the specific heats $\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{v}}}=\mathrm{ }\mathrm{\gamma }$ in terms of degrees of freedom (n) is given by:

Mayer's formula is derived by using the difference between the specific heat of a gas at the constant pressure $\left(C_p\right)$ and its specific heat at constant volume $\left(C_v\right)$ which is equal to the universal gas constant $\left(R\right)$ divided with the molecular weight (M) of the gas expressed in $“J”$

${\mathrm{C}}_{\mathrm{V}}=\frac{\mathrm{n}}{2}\mathrm{R}$
${\mathrm{C}}_{\mathrm{P}}={\mathrm{C}}_{\mathrm{V}}+\mathrm{R}=\frac{\mathrm{n}}{2}\mathrm{R}+\mathrm{R}=\left(\frac{\mathrm{n}}{2}+1\right)\mathrm{R}\mathrm{ }$

$\gamma =\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{V}}}=\frac{\left(\frac{\mathrm{n}}{2}+1\right)\mathrm{R}}{\frac{\mathrm{n}}{2}\mathrm{R}}$

$=\left(\frac{\mathrm{n}}{2}+1\right)\frac{2}{\mathrm{n}}\mathrm{ }$

$\gamma =1+\frac{2}{\mathrm{n}}$