Virial theorem: Difference between revisions
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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 Clausius <ref>R. Clausius | 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== | |||
*[[Virial pressure]] | |||
==References== | ==References== | ||
<references/> | <references/> | ||
Latest revision as of 15:43, 18 May 2011
The virial theorem is a feature of systems with central forces.
The overlines represent time averages. The right hand side is known as the virial of Clausius [1]. (Note: Herbert Goldstein uses for the virial [2], however here we use for temperature, thus we use as per Hansen and McDonald[3]).
See also[edit]
References[edit]
- ↑ R. Clausius "XVI. On a mechanical theorem applicable to heat", Philosophical Magazine 40 pp. 122-127 (1870)
- ↑ Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002) § 3.4
- ↑ Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition) Eq. 2.2.5
- Related reading