Q. The pressure is $P,$ volume $V$ and temperature $T$ of a gas in the jar $A$ and the other gas in the jar $B$ is at pressure $2P,$ volume $V/4$ and temperature $2T,$ then the ratio of the number of molecules in the jar $A$ and $B$ will be
A) $1\ :1$
B) $1\ :2$
C) $2\ :1$
D) $4\ :1$
Explanation
(d) $PV = NkT \Rightarrow \frac{N_{A}}{N_{B}} = \frac{P_{A}V_{A}}{P_{B}V_{B}} \times \frac{T_{B}}{T_{A}}$
$\Rightarrow \frac{N_{A}}{N_{B}} = \frac{P \times V \times (2T)}{2P \times \frac{V}{4} \times T} = \frac{4}{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.