Question

In a mixture of gases, the average number of degrees of freedom per molecule is $6$. The rms speed of the molecules of the gas is $c$. The velocity of sound in the gas is

• A. $\frac{c}{\sqrt{2}}$
• B. $\frac{3c}{4}$
• C. $\frac{2c}{3}$
• D. $\frac{c}{\sqrt{3}}$

Answer 1

Answer: (C)

$\frac{2c}{3}$

Velocity of sound $={\left(\frac{\gamma }{3}\right)}^{{}^1{/}_2}\times rmsspeedofmolecus$
$={\left(\frac{1+\frac{2}{f}}{3}\right)}^{{}^1{/}_2}\times c$ $(\because \gamma =1+\frac{2}{f})$
$={\left(\frac{1+\frac{2}{6}}{3}\right)}^{{}^1{/}_2}\times c$
$={\left(\frac{8}{6\times 3}\right)}^{{}^1{/}_2}\times c$
$={\left(\frac{4}{9}\right)}^{{}^1{/}_2}\times c$
$=\frac{2}{3}c$