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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.

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

Taking k B to be the Boltzmann constant, T is the temperature, and m is the mass of a particle, then we can write the different thermal velocities:

In one dimension

If v t h is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then

v t h = k B T m .

If v t h is defined as the mean of the magnitude of the velocity in any one dimension (i.e. any single direction), then

v t h = 2 k B T π m .

In three dimensions

If v t h is defined as the most probable speed, then

v t h = 2 k B T m .

If v t h is defined as the root mean square of the total velocity (in three dimensions), then

v t h = 3 k B T m .

If v t h is defined as the mean of the magnitude of the velocity of the atoms or molecules, then

v t h = 8 k B T m π .

By all of these definitions v t h falls in the range of

v t h = ( 1.6 ± 0.2 ) k B T m .

Thermal Velocity at Room Temperature

At 20 °C (293 Kelvin), the mean thermal velocity of common gasses is:

Molecular Hydrogen 1,754 m/sHelium 1,245 m/sWater vapor 585 m/sNitrogen 470 m/sAir 464 m/sArgon 394 m/sCarbon dioxide 375 m/s

References

Thermal velocity Wikipedia
(Text) CC BY-SA


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