Virial theorem
The virial theorem is a feature of systems with central forces.
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{ \mathcal{V} }= - \frac{1}{2} \overline{\sum_i \frac{dU}{dr}\cdot r_i}}
The overlines represent time averages. The right hand side is known as the virial of Clausius [1]. (Note: Herbert Goldstein uses Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} for the virial [2], however here we use T for temperature, thus we use as per Hansen and McDonald[3]).
References
- ↑ 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