How does decompression affect the number of particles in a confined gas?

[intervoxel]

Hi,
I'm trying to assemble a function describing the decompression of an ideal gas in a infinitely long box of side L. The gas is initially confined in a volume L^3 at one end.

So far I got the following formula which gives the time the i-th particle takes to reach the barrier at x=L:

<br /> t_i = \frac{2 L - x_i}{\overline{v} \cos(a_i)}<br />

where

x_i is a random variable between 0 and L
a_i is a random variable between 0 and \pi /2
\overline{v} is the average speed of a gas particle

What I need is n(t) = f(N, L, \overline{v},t)

where

N is the total number of particles
n(t) is the the number of particles in the original volume L^3 after time t

Please, help. I'm stuck a long time in this.

Thanks

 

[fresh_42]

I do not see a mechanism which could change $n(t)$. Also it might be reasonable to work with a ball instead of a cube. As given, the problem is insufficiently explained.