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.

mean free path

[′mēn ¦frē ′path]
(acoustics)
For sound waves in an enclosure, the average distance sound travels between successive reflections in the enclosure.
(physics)
The average distance traveled between two similar events, such as elastic collisions of molecules in a gas, of electrons or phonons in a crystal, or of neutrons in a moderator.
References in periodicals archive ?
The mean free path of air, [lambda], cannot be directly measured, but instead is determined from the kinetic theory relationship for viscosity,
3502 to determine a value for the mean free path of 94.
The values of the mean free path and the viscosity of air used in estimating the slip correction factor are summarized in Table 3 along with the value of the electronic charge.
This is due to the increase in mean free path with a decrease in system pressure, see Eq.
In this case it is the pressure effect on the mean free path of the gas that produces the change.
The mean free path of the gas, [lambda], is a function of pressure and temperature, although the uncertainty in temperature is neglected.
Recalling that the uncertainty contribution from temperature in the mean free path and flow rate has been neglected, the relative standard uncertainty in A, [u.
Conversely, the dependency of the pressure in the flow measurement and the mean free path resulted in a partial cancellation of the effect of pressure uncertainty.

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