An ideal gas of molar mass `M` is enclosed in a vessel of volume of `V` whose thin walls are kept at a constant temperature `T`. At a moment `t = 0` a small hole of area `S` is opened, and the gas starts escaping into vacuum. Find the gas concentration `n` as a function of time `t` if at the initial moment `n (0) = n_0`.

Explanation

We can assume that all molecules, incident on the hole, leak out. Then,
`-dN = - d(nV) = (1)/(4) n lt v gt S dt`
or `dn = -n (dt)/(4 v//S lt v gt) = -n (dt)/(tau)`
Integrating `n = n_0 e^(-t//tau)`. Hence `lt v gt = sqrt((8 RT)/(pi M))`.