On the basis of kinetic theory of gases, it is assumed that the molecules of a gas are continuously colliding against each other.
Molecules move in straight line with constant speeds between two successive collisions.
Thus path of a single molecule is a series of zig-zag paths of different lengths as shown in fig -.
These paths of different lengths are called free paths of the molecule
Mean Free Path is the average distance traversed by molecule between two successive collisions.
If s is the Total path travelled in Ncoll collisions, then mean free path
λ= s/Ncoll
Expression for mean free path :
Consider a gas containing n molecules per unit volume.
We assume that only one molecule which is under consideration is in motion while all others are at rest.
If σ is the diameter of each molecule then the moving molecule will collide with all these molecules where centers lie within a distance from its centre as shown in fig
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If v is the velocity of the moving molecule then in one second it will collide with all molecules with in a distance σ between the centres.
In one second it sweeps a volume πσ2v where any other molecule will collide with it.
If n is the total number of molecules per unit volume, then nπσ2v is number of collisions a molecule suffers in one second.
If v is the distance traversed by molecule in one second then mean free path is given by
λ = total distance traversed in one second /no. of collision suffered by the molecules
=v/πσ2vn
=1/πσ2n
This expression was derived with the assumption that all the molecules are at rest except the one which is colliding with the others.
However this assumption does not represent actual state of affair.
More exact statement can be derived considering that all molecules are moving with all possible velocities in all possible directions.
More exact relation found using distribution law of molecular speeds is
λ=1/(√2)πσ2n
its derivation is beyond our scope.
