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  4. A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio Cp/Cv of the mixture is

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Q. A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $Cp/Cv$ of the mixture is

AIEEEAIEEE 2002Kinetic Theory

Solution:

Using $C_{v_{mix}} = \frac{n_0 C_{v_0} + n_H C_{v_H}}{n_0 + n_H}$ and $C_{p_{mix} }= \frac{n_0C_{p_0} + n_HC_{p_H}}{n_0 + n_H}$ Also $C_v = \frac{f}{2} R$ and $C_p = \left( 1 + \frac{n}{2} \right)R$ For oxygen, $n_0 = \frac{1}{2}$ and $f_0$ = 5 ; for helium $n_H$ = 4 and $f_H$ = 3, then $\frac{C_p}{C_v} = \frac{4 \times \frac{5}{2} R + \frac{1}{2} \times \frac{7}{2}R}{4 \times \frac{3}{2} R + \frac{1}{2} \times \frac{5}{2} R}$