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- Virial_theorem abstract "In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy, , of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, , where angle brackets represent the average over time of the enclosed quantity. Mathematically, the theorem stateswhere Fk represents the force on the kth particle, which is located at position rk. The word "virial" derives from vis, the Latin word for "force" or "energy", and was given its technical definition by Rudolf Clausius in 1870.The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; this average total kinetic energy is related to the temperature of the system by the equipartition theorem. However, the virial theorem does not depend on the notion of temperature and holds even for systems that are not in thermal equilibrium. The virial theorem has been generalized in various ways, most notably to a tensor form.If the force between any two particles of the system results from a potential energy V(r) = αr n that is proportional to some power n of the inter-particle distance r, the virial theorem takes the simple formThus, twice the average total kinetic energy equals n times the average total potential energy . Whereas V(r) represents the potential energy between two particles, VTOT represents the total potential energy of the system, i.e., the sum of the potential energy V(r) over all pairs of particles in the system. A common example of such a system is a star held together by its own gravity, where n equals −1.Although the virial theorem depends on averaging the total kinetic and potential energies, the presentation here postpones the averaging to the last step.".
- Virial_theorem wikiPageExternalLink 1978vtsa.book.
- Virial_theorem wikiPageExternalLink c2.
- Virial_theorem wikiPageExternalLink kmath572.htm.
- Virial_theorem wikiPageID "32664".
- Virial_theorem wikiPageRevisionID "593284425".
- Virial_theorem hasPhotoCollection Virial_theorem.
- Virial_theorem subject Category:Concepts_in_physics.
- Virial_theorem subject Category:Dynamics.
- Virial_theorem subject Category:Physics_theorems.
- Virial_theorem subject Category:Solid_mechanics.
- Virial_theorem type Abstraction100002137.
- Virial_theorem type Cognition100023271.
- Virial_theorem type Communication100033020.
- Virial_theorem type Concept105835747.
- Virial_theorem type Content105809192.
- Virial_theorem type FundamentalPhysicsConcepts.
- Virial_theorem type Idea105833840.
- Virial_theorem type Message106598915.
- Virial_theorem type PhysicsTheorems.
- Virial_theorem type Proposition106750804.
- Virial_theorem type PsychologicalFeature100023100.
- Virial_theorem type Statement106722453.
- Virial_theorem type Theorem106752293.
- Virial_theorem comment "In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy, , of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, , where angle brackets represent the average over time of the enclosed quantity. Mathematically, the theorem stateswhere Fk represents the force on the kth particle, which is located at position rk.".
- Virial_theorem label "Teorema de virial".
- Virial_theorem label "Teorema del viriale".
- Virial_theorem label "Teorema do virial".
- Virial_theorem label "Théorème du viriel".
- Virial_theorem label "Twierdzenie o wiriale".
- Virial_theorem label "Viriaaltheorema".
- Virial_theorem label "Virial theorem".
- Virial_theorem label "Virialsatz".
- Virial_theorem label "Вириал".
- Virial_theorem label "ビリアル定理".
- Virial_theorem label "维里定理".
- Virial_theorem sameAs Virialsatz.
- Virial_theorem sameAs Teorema_de_virial.
- Virial_theorem sameAs Théorème_du_viriel.
- Virial_theorem sameAs Teorema_del_viriale.
- Virial_theorem sameAs ビリアル定理.
- Virial_theorem sameAs 비리얼_정리.
- Virial_theorem sameAs Viriaaltheorema.
- Virial_theorem sameAs Twierdzenie_o_wiriale.
- Virial_theorem sameAs Teorema_do_virial.
- Virial_theorem sameAs m.0801t.
- Virial_theorem sameAs Q620602.
- Virial_theorem sameAs Q620602.
- Virial_theorem sameAs Virial_theorem.
- Virial_theorem wasDerivedFrom Virial_theorem?oldid=593284425.
- Virial_theorem isPrimaryTopicOf Virial_theorem.