Mean Free Path
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Mean free path
The average distance traveled between two similar events. The concept of mean free path is met in all fields of science and is classified by the events which take place. The concept is most useful in systems which can be treated statistically, and is most frequently used in the theoretical interpretation of transport phenomena in gases and solids, such as diffusion, viscosity, heat conduction, and electrical conduction. The types of mean free paths which are used most frequently are for elastic collisions of molecules in a gas, of electrons in a crystal, of phonons in a crystal, and of neutrons in a moderator. See Kinetic theory of matter
Mean Free Path
(l ), the mean length of the path traversed by a particle between two successive collisions with other particles. The concept of mean free path is used extensively in calculations of various transfer processes, such as viscosity, heat conduction, diffusion, and electrical conduction.
According to the kinetic theory of gases, molecules move uniformly and rectilinearly from collision to collision. If a molecule traverses an average path v in 1 sec, undergoing in the process v elastic collisions with similar molecules, then
ī = v/v = 1/nσ√2
where n is the number of molecules per unit volume (the density of the gas) and σ is the effective cross section of the molecule. As the density of the gas (its pressure) increases, the mean free path decreases, since the number of collisions v per sec increases. A rise in temperature or in the intensity of motion of the molecules leads to a certain decline in cr and consequently to an increase in σ. For ordinary molecular gases under normal conditions (at atmospheric pressure and 20°C), l ~ 10-5 cm, which is approximately 100 times greater than the average distance between molecules.
In many cases the concept of mean free path is also applicable to particles whose motion and interaction conform to the laws of quantum mechanics (such as conduction electrons in a solid, neutrons in weakly absorbing mediums, and photons in stars), but the calculation of the mean free path for such particles is more difficult.