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(C) For a gas mixture,the adiabatic index $\gamma_{	ext{mix}}$ is given by $\gamma_{	ext{mix}} = \frac{C_{p(	ext{mix})}}{C_{V(	ext{mix})}}$.Using

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$\frac{47}{29}$

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(C) For a gas mixture,the adiabatic index $\gamma_{	ext{mix}}$ is given by $\gamma_{	ext{mix}} = \frac{C_{p(	ext{mix})}}{C_{V(	ext{mix})}}$.Using the formula for mixture properties: $\gamma_{	ext{mix}} = \frac{n_1 C_{p1} + n_2 C_{p2}}{n_1 C_{V1} + n_2 C_{V2}}$.For oxygen $(O_2)$,which is diatomic: $n_1 = \frac{4 \ g}{32 \ g/mol} = \frac{1}{8} \ mol$. $C_{p1} = \frac{7}{2}R$,$C_{V1} = \frac{5}{2}R$.For helium (He),which is monatomic: $n_2 = \frac{4 \ g}{4 \ g/mol} = 1 \ mol$. $C_{p2} = \frac{5}{2}R$,$C_{V2} = \frac{3}{2}R$.Substituting these values into the formula:$\gamma_{	ext{mix}} = \frac{(\frac{1}{8} 	imes \frac{7}{2}R) + (1 	imes \frac{5}{2}R)}{(\frac{1}{8} 	imes \frac{5}{2}R) + (1 	imes \frac{3}{2}R)}$$\gamma_{	ext{mix}} = \frac{\frac{7}{16} + \frac{5}{2}}{\frac{5}{16} + \frac{3}{2}} = \frac{\frac{7+40}{16}}{\frac{5+24}{16}} = \frac{47}{29}$.

$A$ gaseous mixture consists of $4 \ g$ oxygen and $4 \ g$ of helium. The ratio $\frac{C_p}{C_V}$ of the mixture is ($C_p$ and $C_V$ are molar specific heats of the mixture at constant pressure and at constant volume respectively).

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