What is the ratio of the velocity of sound in | vedclass

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(A) The velocity of sound in an ideal gas is given by the formula $V = \sqrt{\frac{\gamma RT}{M}}$.Since the temperature $T$ is the same for both gase

Vedclass · Accepted Answer

$\frac{\sqrt{42}}{5}$

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(A) The velocity of sound in an ideal gas is given by the formula $V = \sqrt{\frac{\gamma RT}{M}}$.Since the temperature $T$ is the same for both gases,the ratio of the velocity of sound in hydrogen $(V_H)$ to that in helium $(V_{He})$ is given by:$\frac{V_H}{V_{He}} = \sqrt{\frac{\gamma_H}{\gamma_{He}} \cdot \frac{M_{He}}{M_H}}$Substituting the given values $\gamma_H = \frac{7}{5}$,$\gamma_{He} = \frac{5}{3}$,$M_H = 2$,and $M_{He} = 4$:$\frac{V_H}{V_{He}} = \sqrt{\left(\frac{7/5}{5/3}\right) \cdot \left(\frac{4}{2}\right)}$$\frac{V_H}{V_{He}} = \sqrt{\left(\frac{7}{5} \cdot \frac{3}{5}\right) \cdot 2} = \sqrt{\frac{21}{25} \cdot 2} = \sqrt{\frac{42}{25}} = \frac{\sqrt{42}}{5}$.

What is the ratio of the velocity of sound in hydrogen $\left(\gamma=\frac{7}{5}\right)$ to that in helium $\left(\gamma=\frac{5}{3}\right)$ at the same temperature? (Molecular weight of hydrogen and helium is $2$ and $4$ respectively)

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