Kinetic Theory Of Gases Question 23
Question: N (< 100) molecules of a gas have velocities 1, 2, 3,…….. N km/s respectively. Then ratio of rms speed and average speed is
Options:
A) 1
B) $ \frac{\sqrt{( 2N+1 )( N+1 )}}{6N} $
C) $ \frac{\sqrt{( 2N+1 )( N+1 )}}{6} $
D) $ 2\sqrt{\frac{2N+1}{6( N+1 )}} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ V _{rms}=\sqrt{\frac{1^{2}+2^{2}+….+N^{2}}{N}} $
$ =\sqrt{\frac{N( N+1 )( 2N+1 )}{6N}} $
$ V _{mean}=\frac{1+2+….N}{N}=\frac{N( N+1 )}{2N} $
BETA
