Kinetic Theory Of Gases Question 19
Question: The velocity of sound in air is $ 332m{{s}^{-1}} $ at NTP. Find the rms speed of air molecules at NTP. $ ( \gamma =1.41 ) $
Options:
A) $ 484m{{s}^{-1}} $
B) $ 418m{{s}^{-1}} $
C) $ 248m{{s}^{-1}} $
D) $ 382m{{s}^{-1}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Velocity of sound in a gas is $ v\sqrt{\frac{\gamma P}{\rho }}; $ rms speed $ C=\sqrt{\frac{3P}{\rho }} $ Dividing $ \frac{C}{v}=\sqrt{\frac{3}{\gamma }}\Rightarrow C=v\sqrt{\frac{3}{\gamma }} $
$ =332\times \sqrt{\frac{3}{1.41}}=484m/s $
BETA
