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(B) For a mixture of gases,the adiabatic index $\gamma_{mix}$ is given by the formula:$\gamma_{mix} = \frac{n_1 C_{P1} + n_2 C_{P2}}{n_1 C_{V1} + n_2

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$2$

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(B) For a mixture of gases,the adiabatic index $\gamma_{mix}$ is given by the formula:$\gamma_{mix} = \frac{n_1 C_{P1} + n_2 C_{P2}}{n_1 C_{V1} + n_2 C_{V2}}$Alternatively,using the degrees of freedom $f$:$C_V = \frac{f}{2}R$ and $C_P = (\frac{f}{2} + 1)R$For Helium (monoatomic),$f_1 = 3$,so $C_{V1} = \frac{3}{2}R$ and $C_{P1} = \frac{5}{2}R$.For Hydrogen (diatomic),$f_2 = 5$,so $C_{V2} = \frac{5}{2}R$ and $C_{P2} = \frac{7}{2}R$.Given $n_1 = 2$ and $n_2 = n$,the mixture ratio is $\frac{C_P}{C_V} = \frac{3}{2}$.Using the relation $\frac{C_{P,mix}}{C_{V,mix}} = \frac{n_1 C_{P1} + n_2 C_{P2}}{n_1 C_{V1} + n_2 C_{V2}} = \frac{3}{2}$:$\frac{2(\frac{5}{2}R) + n(\frac{7}{2}R)}{2(\frac{3}{2}R) + n(\frac{5}{2}R)} = \frac{3}{2}$$\frac{5 + 3.5n}{3 + 2.5n} = \frac{3}{2}$$10 + 7n = 9 + 7.5n$$0.5n = 1$$n = 2$.

Two moles of helium are mixed with $n$ moles of hydrogen. If $\frac{C_P}{C_V} = \frac{3}{2}$ for the mixture,then the value of $n$ is:

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