JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank Topic Test - Kinetic Theory of Gases

The pressure P, volume V and temperature T of a gas in the jar A and the other gas in the jar B at pressure 2P, volume \[\frac{V}{4}\] 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

Correct Answer: D

Solution :

[d] \[PV=NkT\Rightarrow \frac{{{N}_{A}}}{{{N}_{B}}}=\frac{{{P}_{A}}{{V}_{A}}}{{{P}_{B}}{{V}_{B}}}\times \frac{{{T}_{B}}}{{{T}_{A}}}\]

\[\Rightarrow \] \[\frac{{{N}_{A}}}{{{N}_{B}}}=\frac{P\times V\times \left( 2T \right)}{2P\times \frac{V}{4}\times T}=\frac{4}{1}\]