Q30 of 31 Page 95

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.

Let be the speed of molecule inside the box along x direction and n’ be the no. of molecules per unit volume.


The particle moving along the wall will collide in time Δt when the particles are at a distance . Let A be the area of wall


Then, the no. of particle colliding in time Δt is


…(i)


The rms speed square towards x direction is equal to one third of speed


…(ii)


From kinetic theory of gases,


…(iii)


Using eqn.(ii)



∴ No. of particles colliding in time Δt is given by using eqn.(i)



If initial no. of molecules colliding along the wall =n’


Finally no. of molecules colliding along wall (Assume)


Net particle flow in time Δt


….(iv)


We know that by ideal gas equation


..(v)


Where μ =no. of moles of gas


And …(vi)


n= no. of molecules of gas


using eqn.(vi) and (v) we get



Let initial and final pressure of gas be p and p’ and let the pressure changes after time t’



In time t’ no. of particles gone out is given by





Putting all the values, we get




Therefore, time taken by pressure to reduce by 0.1atm is


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