Two monoatomic ideal gases A and B of molecular masses $m_1$ and $m_2$ respectively, are enclosed in…
Two monoatomic ideal gases A and B of molecular masses $m_1$ and $m_2$ respectively, are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas A to that in gas B is given by
$\sqrt{\frac{m_2}{m_1}}$
$\frac{\frac{m_2}{m_1}}{\sqrt{\frac{m_2}{m_1}}}$
$\sqrt{\frac{m_1}{m_2}}$
$\frac{m_2}{m_1}$
Solution
The speed of sound in a gaseous medium is given by, $v=\sqrt{\frac{\gamma R T}{m}}$, where $y$ is the ratio of $\frac{C_P}{C_v}, R$ is the universal gas constant, $m$ is the molecular weight of the gas and $T$ is the temperature of the gas.
Therefore, $v \propto \frac{1}{\sqrt{m}}$
$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{m_2}{m_1}}$