A mixture contains n₁ moles of monoatomic gas and n₂ moles of diatomic gas. If $\mathrm{\gamma }$ = 1.50, the ratio ${\mathrm{n}}_1:{\mathrm{n}}_2$:

$$\begin{gathered} {\mathrm{\gamma }}_{\mathrm{mixture}}=\frac{{\mathrm{n}}_1{\mathrm{C}}_{{\mathrm{P}}_1}+{\mathrm{n}}_2{\mathrm{C}}_{{\mathrm{P}}_2}}{{\mathrm{n}}_1{\mathrm{C}}_{{\mathrm{V}}_1}+{\mathrm{n}}_2{\mathrm{C}}_{{\mathrm{V}}_2}} \\ \Rightarrow 1.5=\frac{{\mathrm{n}}_2\left({\displaystyle \frac{5}{2}}\mathrm{R}\right)+{\mathrm{n}}_2\left({\displaystyle \frac{7}{2}}\mathrm{R}\right)}{{\mathrm{n}}_1\left({\displaystyle \frac{3}{2}}\mathrm{R}\right)+{\mathrm{n}}_2\left({\displaystyle \frac{5}{2}}\mathrm{R}\right)} \\ \Rightarrow 1.5=\frac{5{\mathrm{n}}_1+7{\mathrm{n}}_2}{3{\mathrm{n}}_1+5{\mathrm{n}}_2} \\ \Rightarrow {\mathrm{n}}_2={\mathrm{n}}_1 \end{gathered}$$