Statistical mechanics - diatomic particles leaving and entering a box

[khfrekek92]

Homework Statement

A box of volume .5m^3 contains air pressure 3*10^5 n/m^2, and air composition of 80% N2 and 20% O2. There is a small hole of area 1*10^6 m^2 in one face. The exterior of the box has air of the same composition and temperature but pressure of 1*10^5. How long will it take for the pressure in the box to drop to 1.2*10^5 n/m^2?

Homework Equations

(dP/dt)=[16[pi]^3ak^2T^2NPx]/[V^2Im]

The Attempt at a Solution

After Using PV=NkT to getVdP +PdV=kTdN+Nkdt (then since pressure and temperature are constant) dP/dt=(kT/V)dN/dt
dNdt was a 10-dimensional integral which took quite awhile to solve for, and nw I am left with:
(dP/dt)=[16[pi]^3ak^2T^2NPx]/[V^2Im]
Now I need to solve for how long it will take to go from a pressure of 3*10^5 to 1.2*10^5. How do I do that using this above equation? What do I use for m or I? Do I need to take the integral? Thanks so much in advance!

 

[DA_BOMB26]

You're going to need to give more information on how you got your dN/dt function?