The average speed of a gas molecule is 400 , | vedclass

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(A) The average speed is given by $\overline{v} = \sqrt{\frac{8RT}{\pi M}}$ and the $rms$ speed is given by $u = \sqrt{\frac{3RT}{M}}$.Taking the rati

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$434$

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(A) The average speed is given by $\overline{v} = \sqrt{\frac{8RT}{\pi M}}$ and the $rms$ speed is given by $u = \sqrt{\frac{3RT}{M}}$.Taking the ratio: $\frac{u}{\overline{v}} = \sqrt{\frac{3RT}{M}} 	imes \sqrt{\frac{\pi M}{8RT}} = \sqrt{\frac{3\pi}{8}}$.Substituting the value of $\pi \approx 3.14$: $\frac{u}{\overline{v}} = \sqrt{\frac{3 	imes 3.14}{8}} = \sqrt{1.1775} \approx 1.085$.Therefore,$u = 1.085 	imes \overline{v} = 1.085 	imes 400 \, m/s = 434 \, m/s$.

The average speed of a gas molecule is $400 \, m/s$. Calculate its $rms$ speed at the same temperature in $m/s$.

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