Thermal Velocity

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.

Definitions

Since the thermal velocity is only a "typical" velocity, a number of different definitions can be and are used.

Taking $k_\text$ to be the Boltzmann constant, $T$ the absolute temperature, and $m$ the mass of a particle, we can write the different thermal velocities:

In one dimension

If $v_\text$ is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then
$v_\text = \sqrt.$

If $v_\text$ is defined as the mean of the magnitude of the velocity in any one dimension (i.e. any single direction), then
$v_\text = \sqrt.$

In three dimensions

If $v_\text$ is defined as the most probable speed, then
$v_\text = \sqrt.$

If $v_\text$ is defined as the root mean square of the total velocity, then
$v_\text = \sqrt.$

If $v_\text$ is defined as the mean of the magnitude of the velocity of the atoms or molecules, then
$v_\text = \sqrt.$

All of these definitions are in the range
$v_\text = (1.6 \pm 0.2) \sqrt.$

Thermal velocity at room temperature

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

References

Thermodynamic properties
Statistical mechanics

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