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 :

Solution

Physics sir · 3 steps

Speed depends only on temperature, pressure depends on how many molecules hit the walls.

1. RMS speed. vᵣₘₛ = √(3RT/M) depends only on the temperature and the molar mass. Same gas at the same temperature gives the same vᵣₘₛ in both vessels, so A is true and D is false.

   PV = Nk_BT ⇒ P ∝ N (same V, T)

2. Pressure ratio. With V and T fixed, pressure is proportional to the number of molecules. So P₁ : P₂ = N₁ : N₂ = 1 : 4. B is true and C is false.
3. So. A and B are the correct statements, which is option (c).

The idea to keep. Temperature alone fixes how fast molecules move. The number of molecules fixes how often they hit the wall, and that sets the pressure.

Answer from the NTA final answer key. Solution by PrepWiser.