For a gas of molecular weight $M$ specific heat capacity at constant pressure is  $\left(\gamma =\frac{C_P}{C_V}\right)$

According to Meyer's relation

        $C_P-C_V = R$ or $1-\frac{C_V}{C_P} = \frac{R}{C_P} = \frac{R}{C_P}$

or    $1-\frac{1}{\gamma } = \frac{R}{C_P}$                     $\left(\Rightarrow \gamma =\frac{C_P}{C_V}\right)$

or   $\frac{\gamma -1}{\gamma } = \frac{R}{C_P}$  or $C_P = \frac{\gamma R}{\left(\gamma -1\right)}$

$Specific heat capacity = \frac{molar heat caPacity }{molecular weight}\Rightarrow c=\frac{C}{M}$

Specific heat capacity at constant pressure  $=\frac{\gamma R}{M\left(\gamma -1\right)}$