---

Mean Free Path

---

Quick
The mean distrance traveled by molecules between collisions.


Equation

λ  =  utmean  =

V 4πr2N

Nomenclature

symbol	description
λ	mean free path
u	velocity of molecule
tmean	mean time between collisions
V	volume
r	radius of molecule
N	number of molecules

Visualization

molecules can move around in the void

Details

For a simplified model this can be the speed of the molecule v multiplied by the average time between collisions t_mean. The mean free path is inversely proportional to the number of molecules per unit volume (N/V) and inversely proportional to the cross-sectional area πr² of a molecule. The more molecules there are and the larger the size of a molecule, the shorter the mean distance between collisions. The mean free path does not depend on the speed of the molecule.

The above equation can be expressed in terms of macroscopic properties of the gas, using the ideal-gas equation in the form of pV = NkT:

λ  =  utmean  =

kT 4πr2p

If the temperature is increased at constant pressure, the gas expands, the average distance between molecules increases, and the mean free path increases. If the pressure is increased at constant temperature, the gas compresses and the mean free path decreases.

A long mean free path permits high mobilities and high conductivities.