FREE PATH LENGTH.
We all know that the odors propagate very slowly, though the velocity of gas molecules is rather high (about 500 meters per second). In fact, gas molecules don’t move freely all the time. From time to time, they collide with each other, and that changes both the direction and speed of the their motion. The mean free path L is an important cinematic characteristic of molecular motion.
Any particle of a gas with diameter d will collide with other particles, if the distance between their centers is less than d. For this reason, we can consider one particle with the radius d propagating in the presence of point molecules of gas. In the time interval t, this particle will collide with all the molecules of a gas inside the cylinder of the volume
(pd 2)nvt, where n is the concentration of gas molecules, and v is the mean speed of the particle considered. The mean free path equals the height of the cylinder vt, which contains on the average only a single molecule. For this reason the mean free path can be written as:L =1/(pd 2n)
Precise calculations of free path length were done by J.Maxwell (1860):
L =0.707/(pd 2n)
We can see that precise formula is very close to the one achieved by us from the elementary model consideration.