Decompression function

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 [tex]L^3[/tex] 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:

[tex]
t_i = \frac{2 L - x_i}{\overline{v} \cos(a_i)}
[/tex]

where

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

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

where

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

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

Thanks