The C_p/ C_v ratio for a gas mixture consisting of 4g of helium and 32g of oxygen is

$\begin{array}{l}{\mathrm{C}}_{{\mathrm{P}}_{\mathrm{mix}}}=\frac{{\mathrm{n}}_1{\mathrm{c}}_{\mathrm{P}1}+{\mathrm{n}}_2{\mathrm{c}}_{\mathrm{P}2}}{{\mathrm{n}}_1+{\mathrm{n}}_2}\\ {\mathrm{n}}_1=\frac{4}{4}=1,{\mathrm{n}}_2=\frac{32}{32}=1\\ {\mathrm{c}}_{{\mathrm{P}}_{\mathrm{mix}}}=\frac{1\times \frac{5}{2}\mathrm{R}+1\times \frac{7}{2}\mathrm{R}}{1+1}\\ \Rightarrow {\mathrm{c}}_{{\mathrm{P}}_{\mathrm{mix}}}=3\mathrm{R}\\ {\mathrm{c}}_{{\mathrm{V}}_{\mathrm{mix}}}=\frac{1\times \frac{3}{2}\mathrm{R}+1\times \frac{5}{2}\mathrm{R}}{1+1}\\ \Rightarrow {\mathrm{c}}_{{\mathrm{V}}_{\mathrm{mix}}}=2\mathrm{R}\\ \Rightarrow {\mathrm{\chi }}_{\text{mix }}=\frac{{\mathrm{c}}_{{\mathrm{P}}_{\mathrm{mix}}}}{{\mathrm{c}}_{\mathrm{Vmix}}}=\frac{3\mathrm{R}}{2\mathrm{R}}=1.5\end{array}$