Question

The ratio of molecular weight of hydrogen to chlorine is $1:35$ at $300K$. Find the ratio of speed of sound of hydrogen to chlorine at the same temperature.

Answer 1

Velocity of sound in a gas is given by ,

$v=\sqrt{\gamma RT/M}$

Hence , velocity of sound in hydrogen is ,

$v_H=\sqrt{{\gamma }_{H}RT/M_H}$

And velocity of sound in chlorine is ,

$v_{Cl}=\sqrt{{\gamma }_{Cl}RT/M_{Cl}}$

Now , ${\gamma }_H={\gamma }_{Cl}$ ,because both are diatomic gases .

Therefore ,

$\frac{v_H}{v_{Cl}}=\sqrt{\frac{M_{Cl}}{M_H}}$

or $\frac{v_H}{v_{Cl}}=\sqrt{\frac{35}{1}}$

or $v_H:v_O=\sqrt{35}:\sqrt{1}$