States of Matter - Result Question 68
68. The average velocity of gas molecules is $400 \mathrm{~m} \mathrm{~s}^{-1}$, find the rms velocity of the gas.
(2003, 2M)
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Answer:
Correct Answer: 68. ($435 \mathrm{~ms}^{-1}$)
Solution:
$\begin{aligned} & \dfrac{u_{\mathrm{av}}}{u_{\mathrm{mms}}}=\sqrt{\dfrac{8 R T}{\pi M}}: \sqrt{\dfrac{3 R T}{M}}=\sqrt{\dfrac{8}{3 \pi}} \\ & \Rightarrow \quad u_{\mathrm{mms}}=\sqrt{\dfrac{3 \pi}{8}} u_{\mathrm{av}}=\sqrt{\dfrac{3 \times 3.14}{8}} \times 400=434 \mathrm{~ms}^{-1} \ & \end{aligned}$
BETA
