Same gas is filled in two vessels of the same volume at the same… | JEE Main 2022 (27 Jul, Shift 1)

Q54JEE Main 2022 · 27 JUL · SHIFT 1Medium

Molecular Speeds & Maxwell Distribution

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 $1 : 4$ . Choose the correct answer from the options given below:

Show answer and solution

Answer: (c)

Same gas, same $T$ : $v_{rms} = \sqrt{\frac{3RT}{M}}$ is the same. A true, D false.
$PV = Nk_BT$ with same $V$ , $T$ : $P \propto N$ , so $P_1 : P_2 = 1 : 4$ . B true, C false.
So the answer is (c) A and B only.

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