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单词 virial theorem
释义
virial theorem

Physics
  • A result concerning systems consisting of a number of particles that relates the average kinetic energy over time to the average potential energy over time. If the potential between particles is proportional to the nth power of the distance between particles, then the virial theorem has the form that the average kinetic energy is (n/2) times the average potential energy. Thus, in the case of particles having an inverse-square law between them, the theorem states that the average kinetic potential energy is -½ the average potential energy. The virial theorem was first stated by Rudolf Clausius in 1870. It has been generalized to the special theory of relativity and quantum mechanics.


Astronomy
  • A way of estimating the total mass of an object such as a galaxy or a cluster of galaxies from the movement of its individual members. The theorem states that the average gravitational potential energy of the constituent objects is twice their average kinetic energy. Calculations with the virial theorem show that galaxies and clusters contain up to ten times as much mass as can be seen telescopically, providing strong evidence for the existence of large quantities of dark matter. A modified version of this theorem, called the cosmic virial theorem, applies on cosmological scales. It relates the statistics of galaxy motions and the correlation function (which describes the way galaxies cluster in space) to the average density of the Universe. Since the first two quantities are measurable, the density parameter can thus be estimated. The usual result obtained is around 0.2, indicating that there is dark matter on cosmological scales, but not enough to reach the critical density.


Chemistry
  • A theorem stating that, for a stable system composed of a number of particles, there is a specific relation between the average kinetic energy over time and the average potential energy over time. If there are no external forces to the system and all the forces inside it are inverse square forces, then the average kinetic energy is 2½ times the average potential energy. The virial theorem was first stated by Rudolf Clausius in 1870. A quantum-mechanical version was proved a few years after the discovery of quantum mechanics; this has been used extensively to discuss the roles of kinetic and potential energy in chemical bonding.


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