Two monoatomic ideal gases A and B of molecul | vedclass

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(A) The speed of sound in a gaseous medium is given by the formula $v = \sqrt{\frac{\gamma R T}{M}}$,where $\gamma$ is the adiabatic index (ratio of s

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

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(A) The speed of sound in a gaseous medium is given by the formula $v = \sqrt{\frac{\gamma R T}{M}}$,where $\gamma$ is the adiabatic index (ratio of specific heats $C_P/C_V$),$R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molecular mass of the gas.Since both gases are monoatomic,the value of $\gamma$ is the same for both $(\gamma = 5/3)$.Given that both gases are at the same temperature $T$,the variables $\gamma, R,$ and $T$ are constant for both gases.Therefore,the speed of sound is inversely proportional to the square root of the molecular mass: $v \propto \frac{1}{\sqrt{M}}$.The ratio of the speed of sound in gas $A$ $(v_1)$ to that in gas $B$ $(v_2)$ is given by: $\frac{v_1}{v_2} = \sqrt{\frac{m_2}{m_1}}$.

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

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