En mécanique classique, le théorème du viriel est une relation générale qui s'applique à un système de plusieurs corps en interaction. Il relie les moyennes temporelles de ses énergies cinétique et potentielle. Il fut proposé en 1870 par Rudolf Clausius qui travaillait alors sur les fondements de la thermodynamique et cherchait à relier les notions de température et de chaleur aux mouvements des molécules de gaz.

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  • En mécanique classique, le théorème du viriel est une relation générale qui s'applique à un système de plusieurs corps en interaction. Il relie les moyennes temporelles de ses énergies cinétique et potentielle. Il fut proposé en 1870 par Rudolf Clausius qui travaillait alors sur les fondements de la thermodynamique et cherchait à relier les notions de température et de chaleur aux mouvements des molécules de gaz.
  • 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.
  • In meccanica classica, il teorema del viriale è una proposizione che lega la media temporale dell'energia cinetica e dell'energia potenziale di un sistema stabile di N particelle, e che ha importanti risvolti in diverse branche della fisica.La prima formulazione del teorema è dovuta a Rudolf Clausius, nel 1870. Il nome viriale deriva dal latino vis che significa forza o energia.
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  • En mécanique classique, le théorème du viriel est une relation générale qui s'applique à un système de plusieurs corps en interaction. Il relie les moyennes temporelles de ses énergies cinétique et potentielle. Il fut proposé en 1870 par Rudolf Clausius qui travaillait alors sur les fondements de la thermodynamique et cherchait à relier les notions de température et de chaleur aux mouvements des molécules de gaz.
  • In meccanica classica, il teorema del viriale è una proposizione che lega la media temporale dell'energia cinetica e dell'energia potenziale di un sistema stabile di N particelle, e che ha importanti risvolti in diverse branche della fisica.La prima formulazione del teorema è dovuta a Rudolf Clausius, nel 1870. Il nome viriale deriva dal latino vis che significa forza o energia.
  • 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.
rdfs:label
  • Théorème du viriel
  • Teorema de virial
  • Teorema de virial
  • Teorema del viriale
  • Teorema do virial
  • Twierdzenie o wiriale
  • Viriaaltheorema
  • Virial theorem
  • Virialsatz
  • Viriáltétel
  • Вириал
  • ビリアル定理
  • 비리얼 정리
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