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Q.
The ratio of the speed of sound in nitrogen gas to that in helium gas, at $300 \, K$ is
NTA AbhyasNTA Abhyas 2022
Solution:
Speed of sound in an ideal gas is given by
$v=\sqrt{\frac{\gamma R T}{M}}$
$\therefore v \propto \sqrt{\frac{\gamma }{M}}$ [ $T$ is same for both the gases]
$\gamma _{\text{N}_{2}} = \frac{7}{5}$ (Diatomic)
$\gamma _{\text{He}} = \frac{5}{3}$ (Monoatomic)
$ \therefore \frac{v_{ N _{2}}}{v_{ He }} =\sqrt{\frac{\gamma_{ N _{2}}}{\gamma_{ He }} \cdot \frac{M_{ He }}{M_{ N _{2}}}}=\sqrt{\frac{7 / 5}{5 / 3}\left(\frac{4}{28}\right)} $
$=\frac{\sqrt{3}}{5}$