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