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:
“The improved American highway system ... isolated the American-in-transit. On his speedway ... he had no contact with the towns which he by-passed. If he stopped for food or gas, he was served no local fare or local fuel, but had one of Howard Johnson’s nationally branded ice cream flavors, and so many gallons of Exxon. This vast ocean of superhighways was nearly as free of culture as the sea traversed by the Mayflower Pilgrims.”
—Daniel J. Boorstin (b. 1914)
“Although personally I am quite content with existing explosives, I feel we must not stand in the path of improvement.”
—Winston Churchill (1874–1965)
“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)
“There never comes a point where a theory can be said to be true. The most that one can claim for any theory is that it has shared the successes of all its rivals and that it has passed at least one test which they have failed.”
—A.J. (Alfred Jules)