Virial theorem: Difference between revisions

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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)] &sect; 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]]

Revision as of 15:14, 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 T for temperature).

References

Related reading