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 MaxwellâÂÂBoltzmann 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:
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
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
At 20 ðC (293.15 kelvins), the mean thermal velocity of common gasses in three dimensions is: