Question

At room temperature, the velocity of sound in $O_2$ gas is $v$. Then, in a mixture of $H_2$ and $O_2$ gas, the speed of sound at the same temperature is

• A. less than $v$.
• B. more than $v$.
• C. equal to $v$.
• D. nothing can be said.

Answer 1

The correct option is B more than $v$.

Speed of sound in $O_2$ is
$v_{O_2}=\sqrt{\frac{\gamma RT}{M_{O_2}}}=v$
Speed of sound in mixture of $O_2$ and $H_2$ is
$v_{(H_2+O_2)}=\sqrt{\frac{\gamma RT}{(M_{H_2+O_2}{)}_{\text{mix}}}}$

As $(M_{O_2+H_2}{)}_{\text{mix}}<M_{O_2}$,
[since $M_{H_2}<M_{O_2}$]
so, $v_{H_2+O_2}>v_{O_2}$