In a mixture of gases, the average number of degrees of freedom per molecules is 6. The rms speed of the…
In a mixture of gases, the average number of degrees of freedom per molecules is 6. The rms speed of the molecule of the gas is $c$. The velocity of sound in the gas is
$\frac{c}{\sqrt{3}}$
$\frac{c}{\sqrt{2}}$
$\frac{2c}{3}$
$\frac{3c}{4}$
Solution
The rms speed of the molecule of gas, $v_{\text{rms}} = \sqrt{\frac{3RT}{M}} = c$ ...(i)
As we know that, $\gamma = 1 + \frac{2}{f} = \frac{4}{3}$
Velocity of sound in air,
$v_{\text{sound}} = \sqrt{\frac{\gamma RT}{M}} = \sqrt{\frac{4RT}{3M}}$ ...(ii)
From Eqs. (i) and (ii), we get
$v_{\text{sound}} = \frac{2}{3}c$