A cylinder consists of a gas mixture of helium and oxygen. If the...

Mass of helium, $m_{\mathrm{He}}=4 \mathrm{~g}$ Mass of oxygen, $m_{\mathrm{O}}=32 \mathrm{~g}$ Helium is a monoatomic gas. $\therefore$ Degrees of freedom, $f_1=3$ Oxygen is a diatomic gas. $\therefore$ Degrees of freedom, $f_2=54 \mathrm{~g}$ helium contains $N_1=N_A=6.023 \times 10^{23}$ number of molecules $32 \mathrm{~g}$ oxygen contains $N_2=N_A$ number of molecules. (As atomic mass of oxygen is $16 \mathrm{~g}$ ) $$\begin{aligned} \therefore \quad\frac{C_p}{C_V}& =\gamma\\ & =\frac{N_1\left(2+f_1\right)+N_2\left(2+f_2\right)}{N_1 f_1+N_2 f_2}\\ & =\frac{N_A(2+3)+N_A(2+5)}{3 N_A+5 N_A}\\ & =\frac{5+7}{3+5}=\frac{12}{8}=\frac{3}{2} \end{aligned}$$