The ratio of root mean square velocity to ave | vedclass

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Question

(A) The root mean square velocity $(V_{rms})$ is given by $V_{rms} = \sqrt{\frac{3RT}{M}}$.The average velocity $(V_{av})$ is given by $V_{av} = \sqrt

Vedclass · Accepted Answer

$1.086 : 1$

Vedclass · Answer

(A) The root mean square velocity $(V_{rms})$ is given by $V_{rms} = \sqrt{\frac{3RT}{M}}$.The average velocity $(V_{av})$ is given by $V_{av} = \sqrt{\frac{8RT}{\pi M}}$.The ratio $\frac{V_{rms}}{V_{av}}$ is calculated as $\sqrt{\frac{3RT}{M} 	imes \frac{\pi M}{8RT}} = \sqrt{\frac{3\pi}{8}}$.Substituting the value of $\pi \approx 3.14$,we get $\sqrt{\frac{3 	imes 3.14}{8}} = \sqrt{1.1775} \approx 1.086$.Thus,the ratio is $1.086 : 1$.

The ratio of root mean square velocity to average velocity of gas molecules at a particular temperature is

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