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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 the 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 the two vessels will be in the ratio of 1 : 4.

Asked in JEE Main 27th July 1st Shift 2022 · Number of molecules and number density

Answer: (3) A and B only

Step-by-step solution

The rms speed is vᵣₘₛ=√(3RT)/M: it depends only on the temperature and the molar mass.

Same gas and same temperature, so the rms speeds are equal. (A) is true and (D) is false.

At fixed volume and temperature, PV=Nk_BT gives P∝ N.

So the pressures are in the ratio 1:4. (B) is true and (C) is false.

The correct pair is A and B.

Why the other options are wrong

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