The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is

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$\sqrt{\frac{1}{7}}$

$\sqrt{\frac{2}{7}}$

$\frac{\sqrt{6}}{5}$

$\frac{\sqrt{3}}{5}$

answer is C.

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Detailed Solution

velocity of sound in gas v = $\sqrt{\frac{γRT}{M}} \Rightarrow v \propto \sqrt{\frac{γT}{M}}$

$\Rightarrow \frac{v_{N_{2}}}{v_{He}} = \sqrt{\frac{γ_{N_{2}}}{γ_{He}} \times \frac{M_{He}}{M_{N_{2}}}} = \sqrt{\frac{\frac{7}{5} R \times 4}{\frac{5}{3} R \times 28}} = \frac{\sqrt{3}}{5}$

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