First slide

Law of equipartition of energy

Question

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

Moderate

A

1.4
B

1.54
C

1.59
D

1.62

Solution

For mixture of gases, $C_{v} = \frac{n_{1} C_{v_{1}} + n_{2} C_{v_{2}}}{n_{1} + n_{2}}$
where C = $\frac{f}{2} R, f is degree of freedom$
and $C_{p} = \frac{n_{1} C_{p 1} + n_{2} C_{p 2}}{n_{1} + n_{2}}$
where $C_{p} = (1 + \frac{f}{2}) R$
For helium, $n_{1} = 4, f = 3$
For oxygen, $n_{2} = \frac{1}{2}, f = 5$
$∴ \frac{C_{p}}{C_{v}} = \frac{4 \times \frac{5 R}{2} + \frac{1}{2} \times \frac{7 R}{2}}{4 \times \frac{3 R}{2} + \frac{1}{2} \times \frac{5 R}{2}} = \frac{47}{29}$
= 1.62

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