JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Heat & Thermodynamics

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)

Solution

Statement A: The r.m.s. velocity

v_{rms} = \frac{3 R T}{M}

depends only on temperature and molecular mass, both of which are the same for both vessels — TRUE. Statement B: Using ideal gas law

P V = N k T

, with same

V

and

T

\frac{P _{1}}{P _{2}} = \frac{N _{1}}{N _{2}} = \frac{1}{4}

— TRUE. Statements C and D contradict A and B respectively — FALSE. Thus A and B are correct.

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Single correct option