Virial theorem - Revision history

Carl McBride: Correcte typos.

2011-05-18T14:43:14Z

Correcte typos.

← Older revision		Revision as of 16:43, 18 May 2011
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	:<math>\overline{ \mathcal{V} }= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math>		:<math>\overline{ \mathcal{V} }= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math>

	The overlines represent time averages. The right hand side is known as the virial of [[Rudolf Julius Emanuel Clausius \|Clausius]] <ref>[http://dx.doi.org/10.1080/14786447008640370 R. Clausius, "XVI. On a mechanical theorem applicable to heat" Philosophical Magazine '''40''' pp. 122-127 (1870)]</ref>. (Note: Herbert Goldstein uses <math>T</math> for the virial <ref>[http://www.aw-bc.com/catalog/academic/product/0,1144,0201657023,00.html Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002)] § 3.4</ref>, however here we use T for [[temperature]], thus we use <math>\mathcal{V}</math> as per Hansen and McDonald<ref>[http://www.sciencedirect.com/science/book/9780123705358 Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition)] Eq. 2.2.5</ref>).		The overlines represent time averages. The right hand side is known as the virial of [[Rudolf Julius Emanuel Clausius \|Clausius]] <ref>[http://dx.doi.org/10.1080/14786447008640370 R. Clausius "XVI. On a mechanical theorem applicable to heat", Philosophical Magazine '''40''' pp. 122-127 (1870)]</ref>. (Note: Herbert Goldstein uses <math>T</math> for the virial <ref>[http://www.aw-bc.com/catalog/academic/product/0,1144,0201657023,00.html Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002)] § 3.4</ref>, however here we use <math>T</math> for [[temperature]], thus we use <math>\mathcal{V}</math> as per Hansen and McDonald<ref>[http://www.sciencedirect.com/science/book/9780123705358 Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition)] Eq. 2.2.5</ref>).
	==See also==		==See also==
	*[[Virial pressure]]		*[[Virial pressure]]

Carl McBride: Added a see also section

2011-05-18T14:33:28Z

Added a see also section

← Older revision		Revision as of 16:33, 18 May 2011
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	The overlines represent time averages. The right hand side is known as the virial of [[Rudolf Julius Emanuel Clausius \|Clausius]] <ref>[http://dx.doi.org/10.1080/14786447008640370 R. Clausius, "XVI. On a mechanical theorem applicable to heat" Philosophical Magazine '''40''' pp. 122-127 (1870)]</ref>. (Note: Herbert Goldstein uses <math>T</math> for the virial <ref>[http://www.aw-bc.com/catalog/academic/product/0,1144,0201657023,00.html Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002)] § 3.4</ref>, however here we use T for [[temperature]], thus we use <math>\mathcal{V}</math> as per Hansen and McDonald<ref>[http://www.sciencedirect.com/science/book/9780123705358 Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition)] Eq. 2.2.5</ref>).		The overlines represent time averages. The right hand side is known as the virial of [[Rudolf Julius Emanuel Clausius \|Clausius]] <ref>[http://dx.doi.org/10.1080/14786447008640370 R. Clausius, "XVI. On a mechanical theorem applicable to heat" Philosophical Magazine '''40''' pp. 122-127 (1870)]</ref>. (Note: Herbert Goldstein uses <math>T</math> for the virial <ref>[http://www.aw-bc.com/catalog/academic/product/0,1144,0201657023,00.html Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002)] § 3.4</ref>, however here we use T for [[temperature]], thus we use <math>\mathcal{V}</math> as per Hansen and McDonald<ref>[http://www.sciencedirect.com/science/book/9780123705358 Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition)] Eq. 2.2.5</ref>).
			==See also==
			*[[Virial pressure]]
	==References==		==References==
	<references/>		<references/>

Carl McBride: Added a DOI (that does not seem to work yet)

2011-05-18T14:31:14Z

Added a DOI (that does not seem to work yet)

← Older revision		Revision as of 16:31, 18 May 2011
Line 3:		Line 3:
	:<math>\overline{ \mathcal{V} }= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math>		:<math>\overline{ \mathcal{V} }= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math>

	The overlines represent time averages. The right hand side is known as the virial of Clausius <ref>R. Clausius, " " Philosophical Magazine '''40''' pp. 122- (1870)</ref>. (Note: Herbert Goldstein uses <math>T</math> for the virial <ref>[http://www.aw-bc.com/catalog/academic/product/0,1144,0201657023,00.html Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002)] § 3.4</ref>, however here we use T for [[temperature]]).		The overlines represent time averages. The right hand side is known as the virial of [[Rudolf Julius Emanuel Clausius \|Clausius]] <ref>[http://dx.doi.org/10.1080/14786447008640370 R. Clausius, "XVI. On a mechanical theorem applicable to heat" Philosophical Magazine '''40''' pp. 122-127 (1870)]</ref>. (Note: Herbert Goldstein uses <math>T</math> for the virial <ref>[http://www.aw-bc.com/catalog/academic/product/0,1144,0201657023,00.html Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002)] § 3.4</ref>, however here we use T for [[temperature]], thus we use <math>\mathcal{V}</math> as per Hansen and McDonald<ref>[http://www.sciencedirect.com/science/book/9780123705358 Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition)] Eq. 2.2.5</ref>).
	==References==		==References==
	<references/>		<references/>

Carl McBride: Slight tidy

2011-05-18T14:14:41Z

Slight tidy

← Older revision		Revision as of 16:14, 18 May 2011
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	The '''virial theorem''' is a feature of systems with central forces.		The '''virial theorem''' is a feature of systems with central forces.

	:<math>\overline{T}= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math>		:<math>\overline{ \mathcal{V} }= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math>

	~~where <math>\overline{T}</math> is the kinetic energy.~~ The overlines represent time averages. The right hand side is known as the [[virial]] of Clausius (~~Ref. 2~~).		The overlines represent time averages. The right hand side is known as the virial of Clausius <ref>R. Clausius, " " Philosophical Magazine '''40''' pp. 122- (1870)</ref>. (Note: Herbert Goldstein uses <math>T</math> for the virial <ref>[http://www.aw-bc.com/catalog/academic/product/0,1144,0201657023,00.html Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002)] § 3.4</ref>, however here we use T for [[temperature]]).
	~~==Interesting reading==~~
	#[http://dx.~~doi~~.~~org~~/~~10.1063~~/1.~~1749227~~ J. C. ~~Slater~~ "~~The Virial and Molecular Structure~~"~~, Journal of Chemical Physics '''1''' pp. 687~~-~~691~~ (~~1933~~)]
	==References==		==References==
	~~# Section 3~~.~~4 of '''Classical Mechanics''' by Herbert Goldstein 2nd Edition (1980) Addison Wesley~~		<references/>
	#R. ~~Clausius,~~ " " ~~Philosophical Magazine~~ '''40''' pp. ~~122~~- (~~1870~~)		;Related reading
			*[http://dx.doi.org/10.1063/1.1749227 J. C. Slater "The Virial and Molecular Structure", Journal of Chemical Physics '''1''' pp. 687-691 (1933)]
	[[category: classical mechanics]]		[[category: classical mechanics]]

Dduque: link to virial

2008-02-06T14:09:03Z

link to virial

← Older revision		Revision as of 16:09, 6 February 2008
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	:<math>\overline{T}= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math>		:<math>\overline{T}= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math>

	where <math>\overline{T}</math> is the kinetic energy. The overlines represent time averages. The right hand side is known as the virial of Clausius (Ref. 2).		where <math>\overline{T}</math> is the kinetic energy. The overlines represent time averages. The right hand side is known as the [[virial]] of Clausius (Ref. 2).
	==Interesting reading==		==Interesting reading==
	#[http://dx.doi.org/10.1063/1.1749227 J. C. Slater "The Virial and Molecular Structure", Journal of Chemical Physics '''1''' pp. 687-691 (1933)]		#[http://dx.doi.org/10.1063/1.1749227 J. C. Slater "The Virial and Molecular Structure", Journal of Chemical Physics '''1''' pp. 687-691 (1933)]

Carl McBride at 13:40, 25 May 2007

2007-05-25T13:40:45Z

← Older revision		Revision as of 15:40, 25 May 2007
Line 4:		Line 4:

	where <math>\overline{T}</math> is the kinetic energy. The overlines represent time averages. The right hand side is known as the virial of Clausius (Ref. 2).		where <math>\overline{T}</math> is the kinetic energy. The overlines represent time averages. The right hand side is known as the virial of Clausius (Ref. 2).
			==Interesting reading==
			#[http://dx.doi.org/10.1063/1.1749227 J. C. Slater "The Virial and Molecular Structure", Journal of Chemical Physics '''1''' pp. 687-691 (1933)]
	==References==		==References==
	# Section 3.4 of '''Classical Mechanics''' by Herbert Goldstein 2nd Edition (1980) Addison Wesley		# Section 3.4 of '''Classical Mechanics''' by Herbert Goldstein 2nd Edition (1980) Addison Wesley

Carl McBride: New page: The '''virial theorem''' is a feature of systems with central forces. : $\overline{T}= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}$ where $\overline{T}$ i...

2007-03-26T12:42:02Z

New page: The '''virial theorem''' is a feature of systems with central forces. :<math>\overline{T}= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math> where <math>\overline{T}</math> i...

New page

The '''virial theorem''' is a feature of systems with central forces.

:<math>\overline{T}= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}</math>

where <math>\overline{T}</math> is the kinetic energy. The overlines represent time averages. The right hand side is known as the virial of Clausius (Ref. 2).
==References==
# Section 3.4 of '''Classical Mechanics''' by Herbert Goldstein 2nd Edition (1980) Addison Wesley
#R. Clausius, " " Philosophical Magazine '''40''' pp. 122- (1870)

[[category: classical mechanics]]