Write short note on mean free path.

Explanation

It is the average distance travelled by a gas molecule between two successive collisions.
Expression for mean free path
Consider a gas in a container having n molecule per unit volume. Let d be diameter of molecule A. molecule A will collide with molecules B and C which lies at distance d. IF the molecule moves a distance L, then this molecule makes collisions with all the molecules lying in cylinder of volume `pi d^2 L`
Total number of collisions suffered =`pi r^2 L`
Mean free path of a molecule
`pi=("Total distance travelled")/("number of collisions suffered")=L/(pi rd^2L)implies pi =1/(pi rd^2)`
This relation is derived by assuming that all molecules of the gas except one molecule under consideration are at rest. But ,all molecules are in motion
`pi =1/(sqrt2 pi d^2) ` As `n= N/V`
`pi=1/(sqrt2 pi N/V d^2)`
As `PV=nKT implies N/V=P/(kT)`
So, `pi =(kT)/(sqrt2 pi d^2 p)`. This is expression for mean free path