Question

The constant $\gamma$ for oxygen as well as for hydrogen is $1.40$ . If the speed of sound in oxygen is $450m/s$ , what will be the speed of hydrogen at the same temperature and pressure?

Answer 1

Here value of adiabatic constant denoted by $\gamma$ has same value for hydrogen and oxygen both gases i.e. $1.4$.

Speed of sound in a gaseous medium is given by

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

Now velocity of sound in hydrogen

$v_H=\sqrt{\frac{1.4RT}{M_H}}$

Molecular mass of oxygen is $16$ and molecular mass of hydrogen is$1$. Now velocity of sound in oxygen is given by:

$v_O=\sqrt{\frac{1.4RT}{M_O}}$

$v_O=\sqrt{\frac{1.4RT}{16M_H}}$

Dividing the two equations we get

$\frac{v_H}{v_O}=\sqrt{\frac{1.4RT\times 16M_H}{M_H\times 1.4RT}}$

$\frac{v_H}{v_O}=\frac{4}{1}$

$v_H=4v_O$

$v_H=4\times 450$

$v_H=1800m/s$