Mean Free Path - Mean Free Path in Kinetic Theory

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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