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

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$1.5$

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(B) For a mixture of gases,the adiabatic index $\gamma_{mix}$ is given by $\gamma_{mix} = \frac{C_{P,mix}}{C_{V,mix}} = \frac{n_1 C_{P1} + n_2 C_{P2}}{n_1 C_{V1} + n_2 C_{V2}}$.Helium is a monoatomic gas,so $n_1 = 1$,$C_{V1} = \frac{3}{2}R$,and $C_{P1} = \frac{5}{2}R$.Hydrogen is a diatomic gas,so $n_2 = 1$,$C_{V2} = \frac{5}{2}R$,and $C_{P2} = \frac{7}{2}R$.Substituting these values:$C_{V,mix} = \frac{1(\frac{3}{2}R) + 1(\frac{5}{2}R)}{1+1} = \frac{8R/2}{2} = 2R$.$C_{P,mix} = \frac{1(\frac{5}{2}R) + 1(\frac{7}{2}R)}{1+1} = \frac{12R/2}{2} = 3R$.Therefore,$\gamma_{mix} = \frac{3R}{2R} = 1.5$.

The ratio of specific heat of a mixture of one mole of helium and one mole of hydrogen gas will be

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