Oxygen is enclosed at the temperature `0 ^@C` in a vessel with the characteristic dimension `l = 10 mm` (this is the linear dimension determining the character of a physical process in question). Find :
(a) the gas pressure below which the mean free path of the molecules `lamda gt l` ,
(b) the corresponding molecular concentration and the mean distanace between the molecules.

Explanation

(a) `lamda gt l` if `p lt (kT)/(sqrt(2) pi d^2 l)`
Now `(kT)/(sqrt(2) pi d^2 l)` for `O_2 of O is 0.7 Pa`
(b) The corresponding `n` is obtained by dividing by `kT` and is `1.84 xx 10^20` per `m^3 = 1.84^14 per c.c` and the correspending mean distance is `(l)/(n^(1//3))`.
=`(10^-2)/((0.184)^(1//3) xx 10^5) = 1.8 xx 10^- m ~~ 0.18 mu m`.