# Decompression function

by intervoxel
Tags: decompression, function
 P: 135 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: $$t_i = \frac{2 L - x_i}{\overline{v} \cos(a_i)}$$ 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