Deflating tire, thermodynamics problem

[Melgibson]

Homework Statement

Find the size of the hole in the tire after it has taken 60minutes to become flat.

Homework Equations

Impulse = F*Deltat = DeltaN*Deltap (N=molecules, p=momentum) , P = F/A (A is area of hole), Equipartition for gas in 1-d -> 1/2kT = 1/2mv^2
Derivative of ideal gas law (assuming T and V are constant) = dPV=dNkT

The Attempt at a Solution

the general equation i came up with that describes the decrease in pressure as a function of time is P = e^-((Aroot(kT)/(2Vroot(m)) *t) + P(initial)) actually ill upload a typed image

Using a known volume of a tire i am trying to find the initial pressure but I am having trouble figuring out how to do it any help would be appreciated. Also I am not sure if i have made a mistake in deriving this equation

Ummm have i explained well enough? Is there more i need to include? Or is the answer not simple? I am sort of waiting for an update if someone could clarify it would be nice.

 

[Melgibson]

Oh i see where i made the mistake. After the integration there should be 1 constant on each side to be combined into another constant which is not P(initial). What a silly mistake. From there it is pretty straightforward.