We have a jar filled with gas characterized by parameters $\mathrm{P}, \mathrm{V}, \mathrm{T}$ and another…
We have a jar filled with gas characterized by parameters $\mathrm{P}, \mathrm{V}, \mathrm{T}$ and another jar B filled with gas having parameters $2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}$, where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is
$1: 1$
$1: 2$
$2: 1$
$4: 1$
Solution
According to the gas equation, $\mathrm{PV}=\mathrm{Nk}_{\mathrm{B}} \mathrm{T}$ For the first gas, we have,
$\mathrm{PV}=\mathrm{N}_1 \mathrm{k}_{\mathrm{B}} \mathrm{T}$
For the second gas, we have,
(2P) $\left(\frac{\mathrm{V}}{4}\right)=\mathrm{N}_2 \mathrm{k}_{\mathrm{B}}(2 \mathrm{~T})$
$\mathrm{PV}=4 \mathrm{~N}_2 \mathrm{k}_{\mathrm{B}} \mathrm{T}$
From equations (i) and (ii)
$\mathrm{N}_1=4 \mathrm{~N}_2 \Rightarrow \frac{\mathrm{N}_1}{\mathrm{~N}_2}=4$