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| {{Unreferenced|date=December 2009}}
| | I would like to introduce myself to you, I am Jayson Simcox but I don't like when people use my full title. Credit authorising is where my primary earnings comes from. Some time ago she chose to reside in Alaska and her parents live nearby. Doing ballet is some thing she would by no means give up.<br><br>Here is my web site - clairvoyance ([http://www.edmposts.com/build-a-beautiful-organic-garden-using-these-ideas/ www.edmposts.com]) |
| 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 distribution#Distribution of the velocity vector|Maxwell-Boltzmann particle velocity distribution]]. Note that in the strictest sense ''thermal velocity'' is not a [[velocity]], since ''velocity'' usually describes a [[vector (geometric)|vector]] rather than simply a [[scalar (physics)|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.
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| Taking <math>k_B</math> to be the [[Boltzmann constant]], <math>T</math> is the temperature, and <math>m</math> is the mass of a particle, then we can write the different thermal velocities:
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| == In one dimension ==
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| If <math>v_{th}</math> is defined as the [[root mean square]] of the velocity in any one dimension (i.e. any single direction), then
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| :<math>v_{th}=\sqrt{\frac{k_BT}{m}}</math>. | |
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| If <math>v_{th}</math> is defined as the [[mean]] of the magnitude of the velocity in any one dimension (i.e. any single direction), then
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| :<math>v_{th}=\sqrt{\frac{2 k_BT}{\pi m}}</math>.
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| If <math>v_{th}</math> is defined as the <math>1/e</math> half-width of the thermal distribution or
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| if <math>v_{th}</math> is defined such that a particle with this speed has an energy of <math>k_B T</math>, then
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| :<math>v_{th}=\sqrt{\frac{2k_BT}{m}}</math>.
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| == In three dimensions ==
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| If <math>v_{th}</math> is defined as the most probable speed, then
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| :<math>v_{th}=\sqrt{\frac{2k_BT}{m}}</math>.
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| If <math>v_{th}</math> is defined as the root mean square of the total velocity (in three dimensions), then
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| :<math>v_{th}=\sqrt{\frac{3k_BT}{m}}</math>.
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| If <math>v_{th}</math> is defined as the mean of the magnitude of the velocity of the atoms or molecules, then
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| :<math>v_{th}=\sqrt{\frac{8k_B T}{m\pi}}</math>.
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| {{DEFAULTSORT:Thermal Velocity}}
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| [[Category:Thermodynamics]]
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| [[Category:Statistical mechanics]]
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| {{Physics-stub}}
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I would like to introduce myself to you, I am Jayson Simcox but I don't like when people use my full title. Credit authorising is where my primary earnings comes from. Some time ago she chose to reside in Alaska and her parents live nearby. Doing ballet is some thing she would by no means give up.
Here is my web site - clairvoyance (www.edmposts.com)