MathType - Revision history

178.116.216.184 at 20:09, 6 December 2014

2014-12-06T20:09:33Z

← Older revision		Revision as of 22:09, 6 December 2014
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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]]~~.

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

	~~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:~~

	~~== In one dimension ==~~

	~~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~~

	:~~<math>v_{th}=\sqrt{\frac{k_BT}{m}}<~~/~~math>.~~

	~~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~~

	~~:<math>v_{th}=\sqrt{\frac{2 k_BT}{\pi m}}</math>~~.

	~~If <math>v_{th}</math> is defined as the <math>1/e<~~/~~math> half~~-~~width of the thermal distribution or~~

	~~if <math>v_{th}</math> is defined such that~~ a ~~particle with this speed has an energy of <math>k_B T</math>, then~~

	~~:<math>v_{th}=\sqrt{\frac{2k_BT}{m}}<~~/~~math>~~.

	~~== In three dimensions ==~~

	~~If <math>v_{th}</math> is defined as the most probable speed, then~~

	~~:<math>v_{th}=\sqrt{\frac{2k_BT}{m}}</math>~~.

	~~If <math>v_{th}</math> is defined as the root mean square of the total velocity (in three dimensions~~)~~, then~~

	~~:<math>v_{th}=\sqrt{\frac{3k_BT}{m}}</math>.~~

	~~If <math>v_{th}</math> is defined as the mean of the magnitude of the velocity of the atoms or molecules, then~~

	~~:<math>v_{th}=\sqrt{\frac{8k_B T}{m\pi}}</math>.~~



	~~{{DEFAULTSORT:Thermal Velocity}}~~
	~~[[Category:Thermodynamics]]~~
	~~[[Category:Statistical mechanics]]~~


	~~{{Physics-stub}}~~

en>BattyBot: fixed CS1 errors: dates & General fixes using AWB (9832)

2014-01-07T16:32:47Z

fixed CS1 errors: dates & General fixes using AWB (9832)

← Older revision		Revision as of 18:32, 7 January 2014
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	~~Hello and welcome~~. ~~My name~~ is ~~Numbers Wunder~~. ~~My family members lives~~ in ~~Minnesota and my family members enjoys it~~. ~~My working day occupation~~ is a ~~meter reader~~. ~~One~~ of the ~~things he loves most~~ is ~~ice skating but he~~ is ~~struggling to find time for it~~.<br><br>~~my webpage over~~ the ~~counter std test~~ [[~~http~~://~~www~~.~~blaze16~~.~~com~~/~~blog~~/~~255682 Click On this site~~]]		{{Unreferenced\|date=December 2009}}
			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]].

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

			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:

			== In one dimension ==

			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

			:<math>v_{th}=\sqrt{\frac{k_BT}{m}}</math>.

			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

			:<math>v_{th}=\sqrt{\frac{2 k_BT}{\pi m}}</math>.

			If <math>v_{th}</math> is defined as the <math>1/e</math> half-width of the thermal distribution or

			if <math>v_{th}</math> is defined such that a particle with this speed has an energy of <math>k_B T</math>, then

			:<math>v_{th}=\sqrt{\frac{2k_BT}{m}}</math>.

			== In three dimensions ==

			If <math>v_{th}</math> is defined as the most probable speed, then

			:<math>v_{th}=\sqrt{\frac{2k_BT}{m}}</math>.

			If <math>v_{th}</math> is defined as the root mean square of the total velocity (in three dimensions), then

			:<math>v_{th}=\sqrt{\frac{3k_BT}{m}}</math>.

			If <math>v_{th}</math> is defined as the mean of the magnitude of the velocity of the atoms or molecules, then

			:<math>v_{th}=\sqrt{\frac{8k_B T}{m\pi}}</math>.



			{{DEFAULTSORT:Thermal Velocity}}
			[[Category:Thermodynamics]]
			[[Category:Statistical mechanics]]


			{{Physics-stub}}

en>Jbarberoj at 22:29, 14 June 2012

2012-06-14T22:29:29Z

New page

Hello and welcome. My name is Numbers Wunder. My family members lives in Minnesota and my family members enjoys it. My working day occupation is a meter reader. One of the things he loves most is ice skating but he is struggling to find time for it.<br><br>my webpage over the counter std test [[http://www.blaze16.com/blog/255682 Click On this site]]