The ratio of the specific heats C _ P C _ v = γ in terms of degrees...

Mayer's formula is derived by using the difference between the specific heat of a gas at the constant pressure $( {C}_{p} )$ and its specific heat at constant volume $( {C}_{v} )$ which is equal to the universal gas constant $( R )$ divided with the molecular weight (M) of the gas expressed in $“ J ”$

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

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

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

$\gamma = 1 + \dfrac{2}{n}$