The ratio of the velocity of sound in hydroge | vedclass

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Question

(D) The velocity of sound in an ideal gas is given by $v = \sqrt{\frac{\gamma RT}{M}}$.For the same temperature $T$,the ratio of the velocity of sound

Vedclass · Accepted Answer

$\sqrt{42}: 5$

Vedclass · Answer

(D) The velocity of sound in an ideal gas is given by $v = \sqrt{\frac{\gamma RT}{M}}$.For the same temperature $T$,the ratio of the velocity of sound in hydrogen $(v_H)$ to helium $(v_{He})$ is:$\frac{v_H}{v_{He}} = \sqrt{\frac{\gamma_H R T / M_H}{\gamma_{He} R T / M_{He}}} = \sqrt{\frac{\gamma_H M_{He}}{\gamma_{He} M_H}}$.Given:$\gamma_H = 7/5$,$\gamma_{He} = 5/3$,$M_H = 2 	ext{ g/mol}$,$M_{He} = 4 	ext{ g/mol}$.Substituting these values:$\frac{v_H}{v_{He}} = \sqrt{\frac{(7/5) 	imes 4}{(5/3) 	imes 2}} = \sqrt{\frac{28/5}{10/3}} = \sqrt{\frac{28}{5} 	imes \frac{3}{10}} = \sqrt{\frac{84}{50}} = \sqrt{\frac{42}{25}} = \frac{\sqrt{42}}{5}$.Thus,the ratio is $\sqrt{42}: 5$.

The ratio of the velocity of sound in hydrogen gas $(\gamma = 7/5)$ to that in helium gas $(\gamma = 5/3)$ at the same temperature is

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