# A box of 1.00m^3 is filled with nitrogen at 1.50 atm at 300K. The box has a hole of an area 0.010 mm^2.

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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.

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V1x = 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 V1x Δt distance. Let a = area of the wall. No. of particles colliding in time Δt = (1/2)nt(VtxΔt)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