Two monoatomic ideal gases 1 and 2 of molecul | vedclass

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(B) The speed of sound $v$ in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$,where $\gamma$ is the adiabatic index,$R$ is the u

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$\sqrt{\frac{m_2}{m_1}}$

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(B) The speed of sound $v$ in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$,where $\gamma$ is the adiabatic index,$R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass.Since both gases are monoatomic,they have the same adiabatic index $\gamma = 5/3$.Given that both gases are at the same temperature $T$,the speed of sound is inversely proportional to the square root of the molar mass: $v \propto \frac{1}{\sqrt{M}}$.Therefore,the ratio of the speed of sound in gas $1$ $(v_1)$ to that in gas $2$ $(v_2)$ is $\frac{v_1}{v_2} = \sqrt{\frac{m_2}{m_1}}$.

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 that in gas $2$ is given by

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