Kinetic Theory Of Gases Question 22
Question: The absolute gas temperature at which the root mean square speed of helium molecules exceeds their most probable speed by 200 m/s is
Options:
A) 110.2 K
B) 90.2 K
C) 190.2 K
D) 100.2 K
Show Answer
Answer:
Correct Answer: C
Solution:
[c] If T be the required temperature, then, $ v _{rms}-v _{p}=200m/s $
$ \text{or }\sqrt{\frac{3RT}{M _{He}}}-\sqrt{\frac{2RT}{M _{He}}}=200m/s $
$ \text{or }\sqrt{T}[ \sqrt{3}-\sqrt{2} ]=\sqrt{\frac{M _{He}}{R}}( 200m/s ) $ Substituting $ M _{He}=4\times {{10}^{-3}}kg,,R=8.134,J/mol-K, $
$ T=190.2K. $
BETA
