A gaseous mixture consists of $16 g$ of helium and $16 g$ of oxygen, then the ratio $\frac{C_{p}}{C_{v}}$ of the mixture is

1.4

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1.54

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1.59

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1.62

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Solution

The correct option is D $1.62$
Hellium is monoatomic.
Oxygen is diatomic.
Degree of freedom of He, $f_{1} =$ 3
Degree of freedom of $O_{2}$ , $f_{2} =$ 5
$∴ \frac{C_{p}}{C_{v}}$ of mixture.
$\frac{C_{p}}{C_{v}} = \frac{[N_{1} (2 + f_{1}) + N_{2} (2 + f_{2})]}{N_{1} f_{1} + N_{2} f_{2}}$
Putting, $N_{1} = N_{2} = 16 g m,$ and $f_{1} = 3, f_{2} = 5$
we get, $\frac{C_{p}}{C_{v}} = \frac{3}{2} = 1.62$

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