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 |
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