Kinetic Theory Of Gases Question 140
Question: Inside a cylinder closed at both ends is a movable piston. On one side of the piston is a mass m of a gas, and on the other side a mass 2m of the same gas. What fraction of volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? The temperature is the same throughout.
Options:
A) 1/4
B) 1/2
C) 2/3
D) 1/3
Show Answer
Answer:
Correct Answer: C
Solution:
[c] At equilibrium, pressure is same, temp. and molecular weight do not change (given). Using ideal gas eq. $ P _{1}V _{1}=n _{1}RT _{1} $ From above, $ \frac{V}{m} $ is constant, $ \frac{V _{1}}{V _{2}}=\frac{m _{1}}{m _{2}}; $ Add 1 on both sides, we get $ \frac{V _{1}+V _{2}}{V _{2}}=\frac{m _{1}+m _{2}}{m _{2}} $
$ \Rightarrow $ $ \frac{V _{2}}{V _{1}+V _{2}}=\frac{m _{2}}{m _{1}+m _{2}}=\frac{2m}{m+2m}=\frac{2}{3} $
BETA
