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• o The distance which a particular gas molecule travels without colliding is known as mean
free path.

Expression for mean free path
• o Consider each molecule of gas is a sphere of diameter (d).The average speed of each
molecule is<v>.
• o Suppose the molecule suffers collision with any other molecule within the distance (d).
Any molecule which comes within the distance range of its diameter this molecule will have
collision with that molecule.
• o The volume within which a molecule suffer collision =<v>Δtπd2.
• o Let number of molecules per unit volume =n

• o Therefore the total number of collisions in time Δt =<v>Δtπd2xn
• o Rate of collision =<v>Δtπd2xn/Δt=<v>πd2n

• o Suppose time between collision τ =1/<v>πd2n
• o Average distance between collision = τ<v> = 1/πd2

• o 1/πd2n this value was modified and a factor was introduced.
• o Mean free path(l) = 1/√2 π d2n

Conclusion: - Mean free path depends inversely on:
• a) Number density (number of molecules per unit volume)
• b) Size of the molecule.

The volume swept by a molecule in time Δt in which any molecule will collide with it.