Kinetic Theory Of Gases Question 172
Question: A monoatomic ideal gas is expanded adiabatically to n times of its initial volume. The ratio of final rate of collision of molecules with the unit area of container walls to the initial rate will be
Options:
A) $ {{n}^{-4/3}} $
B) $ {{n}^{4/3}} $
C) $ {{n}^{2/3}} $
D) $ {{n}^{-2/3}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a]: Pressure is exerted by gas on container wall due to change in momentum during collision of gas molecules with container walls. i.e., $ P=N _{2}mv $ and also $ v\propto \sqrt{T} $ Hence, $ P\propto N\sqrt{T},,\text{i}\text{.e}\text{.,},\frac{N _{2}}{N _{1}}=\frac{P _{2}}{P _{1}},\sqrt{\frac{T _{1}}{T _{2}}}={{n}^{-4/3}} $
BETA
