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  • The ratio of the speed of sound in nitrogen gas to that in helium gas, at  is -

The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 \mathrm{K} is -
 

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

best_answer

Speed of sound in a gas is

\begin{aligned} V&=\sqrt{\frac{r k T}{M}}\\ or, \quad V& \propto \sqrt{\frac{\gamma}{M}}\\ \frac{V_{N_2}}{V_{\text {He }}}&=\sqrt{\frac{r_{N_2}}{r_{\text {He }}} \times \frac{M_{14}}{M_{H_2}}} \\& =\sqrt{\frac{7 / 5}{5 / 3} \times \frac{4}{28}} \\ & =\frac{\sqrt{3}}{5} \end{aligned}

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shivangi.bhatnagar

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