Mean Free Path in Kinetic Theory
In kinetic theory the mean free path of a particle, such as a molecule, is the average distance the particle travels between collisions with other moving particles. The formula still holds for a particle with a high velocity relative to the velocities of an ensemble of identical particles with random locations. If, on the other hand, the velocities of the identical particles have a Maxwell distribution, the following relationship applies:
and it may be shown that the mean free path, in meters, is:
where kB is the Boltzmann constant in J/K, T is the temperature in K, p is pressure in Pascals, and d is the diameter of the gas particles in meters.
Following table lists some typical values for air at different pressures and at room temperature.
| Vacuum range | Pressure in hPa (mbar) | Molecules / cm3 | Molecules / m3 | Mean free path |
|---|---|---|---|---|
| Ambient pressure | 1013 | 2.7 × 1019 | 2.7 × 1025 | 68 nm |
| Low vacuum | 300 – 1 | 1019 – 1016 | 1025 – 1022 | 0.1 – 100 μm |
| Medium vacuum | 1 – 10−3 | 1016 – 1013 | 1022 – 1019 | 0.1 – 100 mm |
| High vacuum | 10−3 – 10−7 | 1013 – 109 | 1019 – 1015 | 10 cm – 1 km |
| Ultra high vacuum | 10−7 – 10−12 | 109 – 104 | 1015 – 1010 | 1 km – 105 km |
| Extremely high vacuum | <10−12 | <104 | <1010 | >105 km |
Read more about this topic: Mean Free Path
Famous quotes containing the words free, path, kinetic and/or theory:
“I doubt if a single individual could be found from the whole of mankind free from some form of insanity. The only difference is one of degree. A man who sees a gourd and takes it for his wife is called insane because this happens to very few people.”
—Desiderius Erasmus (c. 1466–1536)
“The sweetest and most inoffensive path of life leads through the avenues of science and learning; and whoever can either remove any obstructions in this way, or open up any new prospect, ought so far to be esteemed a benefactor to mankind.”
—David Hume (1711–1776)
“The poem has a social effect of some kind whether or not the poet wills it to have. It has kinetic force, it sets in motion ... [ellipsis in source] elements in the reader that would otherwise be stagnant.”
—Denise Levertov (b. 1923)
“The great tragedy of science—the slaying of a beautiful theory by an ugly fact.”
—Thomas Henry Huxley (1825–1895)