Question

Two monoatomic ideal gases 1 and 2 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 1 to gas 2 is given by

• A. $\frac{m_1}{m_2}$
• B. $\sqrt{\frac{m_1}{m_2}}$
• C. $\frac{m_2}{m_1}$
• D. $\sqrt{\frac{m_2}{m_1}}$

Answer 1

The correct option is D $\sqrt{\frac{m_2}{m_1}}$

As we know that
$v=\sqrt{\frac{\gamma RT}{m}}$
So, $v$ is inversely proportional to $m$,
$\therefore \frac{v_1}{v_2}=\sqrt{\frac{m_2}{m_1}}$.