Kinetic Theory Of Gases Question 40
Question: Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes are plotted as shown in figure. Choose the correct alternative
Options:
A) $ V _{1}=V _{2};V _{3}=V _{4}\text{ and }V _{2}>V _{3} $
B) $ V _{1}=V _{2};V _{3}=V _{4}\text{ and }V _{2}<V _{3} $
C) $ V _{1}=V _{2}=V _{3}=V _{4} $
D) $ V _{4}>V _{3}>V _{2}>V _{1} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] From ideal gas equation $ PV=\mu \text{RT} $
$ \Rightarrow $ Slope of P.F curve $ \frac{P}{T}=\frac{\mu R}{V} $
$ \Rightarrow $ $ Slope\propto \frac{1}{V} $ It means line of smaller slope represent greater volume of gas. For the given problem figure Point 1 and 2 are on the same line so they will represent same volume i.e. $ V _{1}=V _{2} $ Similarly point 3 and 4 are on the same line so they will represent same volume i.e. $ V _{3}=V _{4} $ Also slope of line 1-2 is less than 3-4. Hence $ (V _{1}=V _{2})>( V _{3}=V _{4} ) $
BETA
