A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio of C_p and C_v is

For ${\mathrm{m}}_1=16\mathrm{gm}{;}_2{\mathrm{He}}^4{\mathrm{M}}_1=4$
$\begin{array}{l}{\mathrm{n}}_1=\frac{{\mathrm{m}}_1}{{\mathrm{M}}_1}=\frac{16}{4}=4\mathrm{moles};{\mathrm{C}}_{{\mathrm{V}}_1}=\frac{3}{2}\mathrm{R};{\mathrm{C}}_{{\mathrm{P}}_1}=\frac{5}{2}\mathrm{R}\\ {\text{ For }}_8{\mathrm{O}}^{16},{\mathrm{m}}_2=16\mathrm{gm};{\mathrm{M}}_2=32\mathrm{gm},\\ {\mathrm{C}}_{{\mathrm{V}}_2}=\frac{5}{2}\mathrm{R};{\mathrm{C}}_{{\mathrm{P}}_2}=\frac{7}{2}\mathrm{R};{\mathrm{n}}_2=\frac{{\mathrm{m}}_2}{{\mathrm{M}}_2}=\frac{16}{32}=0.5\mathrm{mole}\\ {\mathrm{C}}_{{\mathrm{V}}_{\text{mix }}}=\frac{{\mathrm{n}}_1{\mathrm{C}}_{{\mathrm{V}}_1}+{\mathrm{n}}_2{\mathrm{C}}_{{\mathrm{V}}_2}}{{\mathrm{n}}_1+{\mathrm{n}}_2}=\frac{4\times \frac{3}{2}\mathrm{R}+\frac{0.5\times 5}{2}\mathrm{R}}{4+0.5}\\ {\mathrm{C}}_{{\mathrm{V}}_{\text{mix }}}=\frac{14.5}{4.5\times 2}\end{array}$
$\begin{array}{l}{\mathrm{C}}_{\text{pmix }}=\frac{{\mathrm{n}}_1{\mathrm{C}}_{{\mathrm{p}}_1}+{\mathrm{n}}_2{\mathrm{C}}_{{\mathrm{p}}_2}}{{\mathrm{n}}_1+{\mathrm{n}}_2}=\frac{23.5}{9}\mathrm{R}\\ \mathrm{\gamma }=\frac{{\mathrm{C}}_{\text{pmix }}}{{\mathrm{C}}_{\mathrm{V}\text{ mix }}}=\frac{\frac{23.5}{4}\mathrm{R}}{\frac{14.5}{9}\mathrm{R}}=1.62\end{array}$