Q 11-12-095JEE MainJEE Main 2022 (27 Jul, Shift 1)Easy
Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1 : 4$, then
A. The r.m.s. velocity of gas molecules in two vessels will be the same.
B. The ratio of pressure in these vessels will be $1 : 4$.
C. The ratio of pressure will be $1 : 1$.
D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $1 : 4$.
Answer: (C) A and B only
$v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}}$ depends only on the gas and its temperature, which are the same: A is true, D is false.
$P = \dfrac{Nk_BT}{V}$, so with equal $V$ and $T$, $P \propto N$: the ratio is $1 : 4$. B is true, C is false.
A and B only.
Solution by Sreeraj P, M.Sc Physics