Physics: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.
Since the thermal velocity is only a "typical" velocity, a number of different definitions can be and are used.
Taking [math]\displaystyle{ k_\text{B} }[/math] to be the Boltzmann constant, [math]\displaystyle{ T }[/math] the absolute temperature, and [math]\displaystyle{ m }[/math] the mass of a particle, we can write the different thermal velocities:
In one dimension
If [math]\displaystyle{ v_\text{th} }[/math] is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then[1][2] [math]\displaystyle{ v_\text{th} = \sqrt{\frac{k_\text{B} T}{m}}. }[/math]
If [math]\displaystyle{ v_\text{th} }[/math] is defined as the mean of the magnitude of the velocity in any one dimension (i.e. any single direction), then [math]\displaystyle{ v_\text{th} = \sqrt{\frac{2 k_\text{B} T}{\pi m}}. }[/math]
In three dimensions
If [math]\displaystyle{ v_\text{th} }[/math] is defined as the most probable speed, then[2] [math]\displaystyle{ v_\text{th} = \sqrt{\frac{2k_\text{B} T}{m}}. }[/math]
If [math]\displaystyle{ v_\text{th} }[/math] is defined as the root mean square of the total velocity, then [math]\displaystyle{ v_\text{th} = \sqrt{\frac{3k_\text{B} T}{m}}. }[/math]
If [math]\displaystyle{ v_\text{th} }[/math] is defined as the mean of the magnitude of the velocity of the atoms or molecules, then [math]\displaystyle{ v_\text{th} = \sqrt{\frac{8k_\text{B} T}{\pi m}}. }[/math]
All of these definitions are in the range [math]\displaystyle{ v_\text{th} = (1.6 \pm 0.2) \sqrt{\frac{k_\text{B} T}{m}}. }[/math]
Thermal velocity at room temperature
At 20 °C (293.15 kelvins), the mean thermal velocity of common gasses in three dimensions is:[3]
| Gas | Thermal velocity |
|---|---|
| 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) |
References
- ↑ Baumjohann, Wolfgang; Treumann, Rudolf A. (2006). Basic Space Plasma Physics (Reprinted ed.). London: Imperial College Press. ISBN 978-1-86094-079-8.
- ↑ 2.0 2.1 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". https://www.pfeiffer-vacuum.com/en/know-how/introduction-to-vacuum-technology/fundamentals/thermal-velocity/.
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