Compute the ratio of speed of sound in hydrogen gas to the rms speed of hydrogen molecules.
Compute the ratio of speed of sound in hydrogen gas to the rms speed of hydrogen molecules.
Solution
Sol. As hydrogen is a diatomic gas, $\gamma = \frac{7}{5}$
Speed of sound in hydrogen, $(v_{sound})_H = \sqrt{\frac{\gamma p}{\rho}}$
rms speed of hydrogen molecules, $(v_{rms})_H = \sqrt{\frac{3p}{\rho}}$
\therefore\ $\displaystyle\frac{(v_{sound})_H}{(v_{rms})_H} = \sqrt{\frac{\gamma}{3}} = \sqrt{\frac{\frac{7}{5}}{3}} = \sqrt{\frac{7}{15}}$
Answer: $\sqrt{7/15}$
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