Thermal velocity

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The thermal velocity or thermal speed is a typical velocity of the thermal motion of particles which 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. If v_th is defined as the root mean square of the velocity in any one dimension, then

where k_B is the Boltzmann constant, T is the temperature, and m is the mass of a particle. If v_th is defined as the root mean square of the total velocity (in three dimensions), then

.

Still other people define the thermal speed so that a particle with this speed has an energy of k_BT, or

.

The mean of the magnitude of the velocity of the atoms or molecules is given by