Kinetic Theory Of Gases Question 148
Question: Let $ \overline{v},,v _{rms} $ and $ v _{p} $ respectively denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T, the mass of a molecule is m. Then
Options:
A) $ v _{p}<\overline{v}<v _{rms} $
B) The average kinetic energy of a molecule is $ \frac{3}{4}mv _{p}^{2} $
C) No molecule can have speed greater than $ \sqrt{2}v _{rms} $
D) No molecule can have speed less than $ v _{p}/\sqrt{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ v _{rms}=\sqrt{\frac{3RT}{M}},VP=\sqrt{\frac{2RT}{M}}=0.816,v _{rms} $ $ \overset{\to }{\mathop{v}},=\sqrt{\frac{8RT}{\pi M}}=0.92,v _{rms}\Rightarrow v _{P}<\overrightarrow{v}<v _{rms} $ Further $ E _{av}=\frac{1}{2}mv _{rms}^{2}=\frac{1}{2}m\frac{3}{2}v _{p}^{2}=\frac{3}{2}mv _{p}^{2} $
BETA
