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12.Kinetic Theory of Gases
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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
A
$1.59$
B
$1.62$
C
$1.4$
D
$1.54$
Solution
For mixture of gases, $C_{v}=\frac{n_{1} C_{v_{1}}+n_{2} C_{v_{2}}}{n_{1}+n_{2}}$
Twhere $C=\frac{f}{2} R, f$ is degree of freedom and $C_{p}=\frac{n_{1} C_{P_{1}}+n_{2} C_{R_{3}}}{n_{1}+n_{2}}$
where $C_{p}=\left(1+\frac{f}{2}\right) R$
For helium, $n_{1}=4, f=3$
For oxygen, $n_{2}=\frac{1}{2}, f=5$
$\therefore \frac{C_{p}}{C_{v}}=\frac{4 \times \frac{5 R}{2}+\frac{1}{2} \times \frac{7 R}{2}}{4 \times \frac{3 R}{2}+\frac{1}{2} \times \frac{5 R}{2}}=\frac{47}{29}$
$=1.62$
Standard 11
Physics
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