Thermal velocity or thermal speed is a typical velocity of the thermal motion of particles that make up a gas, liquid, etc. Thus, indirectly, thermal velocity is a measure of temperature. Technically speaking, it is a measure of the width of the peak in the Maxwell–Boltzmann particle velocity distribution. Note that in the strictest sense thermal velocity is not a velocity, since velocity usually describes a vector rather than simply a scalar speed.
Since the thermal velocity is only a "typical" velocity, a number of different definitions can be and are used.
Taking to be the Boltzmann constant, the absolute temperature, and the mass of a particle, we can write the different thermal velocities:
In one dimension
If is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then
If is defined as the mean of the magnitude of the velocity in any one dimension (i.e. any single direction), then
In three dimensions
If is defined as the most probable speed, then
If is defined as the root mean square of the total velocity, then
If is defined as the mean of the magnitude of the velocity of the atoms or molecules, then
All of these definitions are in the range
Thermal velocity at room temperature
At 20 °C (293.15 kelvins), the mean thermal velocity of common gasses in three dimensions is:
|Hydrogen||1,754 m/s (5,750 ft/s)|
|Helium||1,245 m/s (4,080 ft/s)|
|Water vapor||585 m/s (1,920 ft/s)|
|Nitrogen||470 m/s (1,500 ft/s)|
|Air||464 m/s (1,520 ft/s)|
|Argon||394 m/s (1,290 ft/s)|
|Carbon dioxide||375 m/s (1,230 ft/s)|
- ^ Baumjohann, Wolfgang; Treumann, Rudolf A. (2006). Basic Space Plasma Physics (Reprinted ed.). London: Imperial College Press. ISBN 978-1-86094-079-8.
- ^ a b Gurnett, Donald A.; Bhattacharjee, Amitava (2017). Introduction to Plasma Physics: With Space, Laboratory and Astrophysical Applications (2nd ed.). Cambridge: Cambridge University Press. ISBN 978-1-107-02737-4.
- ^ "Thermal velocity". www.pfeiffer-vacuum.com. Retrieved 2023-05-28.