If one mole of a monatomic gas ($\mathrm{\gamma }$ = 5/3) is mixed with one mole of a diatomic gas ($\mathrm{\gamma }$ = 7/5), the value of $\gamma$ for the mixture is

$\frac{n_1+n_2}{\gamma -1}=\frac{n_1}{{\gamma }_1-1}+\frac{n_2}{{\gamma }_2-1}$
where ${\mathrm{\gamma }}_1 \mathrm{and} {\mathrm{\gamma }}_2$denote the ratio of two specific heats of Bas 1 and gas 2 when they are mixed in the ratio of n₁ and n₂ moles.
The resultant value of the mixture is represented by $\mathrm{\gamma }$.
$\frac{2}{\gamma -1}=\frac{1}{{\displaystyle \frac{5}{3}}-1}+\frac{1}{{\displaystyle \frac{7}{5}}-1} \Rightarrow \gamma = 1.5$