Question

A box of 1.00m³ is filled with nitrogen at 1.50 atm at 300K. The box has a hole of an area 0.010 mm². How much time is required for the pressure to reduce by 0.10 atm, if the pressure outside is 1 atm.

Answer 1

V_1x = speed of molecule inside the box along x direction n₁ = number of molecules per unit volume In time Δt, particles moving along the wall will collide if they are within V_1x Δt distance. Let a = area of the wall. No. of particles colliding in time Δt = (1/2)n_t(V_txΔt)a (factor of 1/2 due to motion towards wall):

In general, gas is in equilibrium as the wall is very large as compared to hole.

No. of particles colliding in time Δt = (1/2)n₁ √(kT/m) Δt a. If particles collide along hole, they move out. Similarly outer particles colliding along hole will move in.

Net particle flow in time Δt = 1/2(n₁ - n₂) √(kT/m)Δt a as temperature is same in and out