If one mole of a monoatomic gas $(\gamma =\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.)$ is mixed with one mole of a diatomic gas $(\gamma =\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$5$}\right.)$,the value of $\gamma$  for the mixture is

$\begin{array}{l}{\gamma }_1=\frac{5}{3}meansgasismonoatomicorC{v}_1=\frac{3}{2}R\\ {\gamma }_2=\frac{7}{5}meansgasisdiatomicorC{v}_2=\frac{5}{2}R\\ Cv\left(ofthemixture\right)\\ =\frac{n_{1}C{v}_1+n_{2}C{v}_2}{n_1+n_2}=\frac{\left(1\right)\left(\frac{3}{2}R\right)+\left(1\right)\left(\frac{5}{2}R\right)}{1+1}=2R\\ C_p\left(ofthemixture\right)=Cv+R=3R\\ \therefore \gamma mixture=\frac{C_p}{C_v}=\frac{3R}{2R}=1.5\\ \end{array}$