The virial theorem is applicable to the cores of stars, by establishing a relation between gravitational potential energy and thermal kinetic energy (i.e. temperature).

The meaning of VIRIAL is half the product of the stress due to the attraction or repulsion between two particles in space times the distance between them or in the case of more than two particles half the …

That's why the virial theorem refers to time averages of the kinetic and potential energy. But the basic idea is the same. And the proof is surprisingly simple. Here's how it goes. We consider a quantity …

The vir­ial the­o­rem re­lates the ex­pec­ta­tion ki­netic en­ergy of a quan­tum sys­tem to the po­ten­tial. That is of the­o­ret­i­cal in­ter­est, as well as im­por­tant for com­pu­ta­tional meth­ods like “den­sity func­tional the­ory.” …

Aug 8, 2024 · By the virial theorem, the second example shows that the increase in potential energy is twice the decrease in potential energy, so overall, the total energy is increased for higher orbits.

In fact, any system composed of electrons and nuclei, such as yourself, satisfies the conditions of the virial theorem. By far the most important force in systems composed of electrons and nuclei is the …

The virial theorem (from the Latin word ‘vis’, meaning ‘force’) is a relationship between the total gravitational and thermal energies of stars1that are in hydrostatic equilibrium.

Nov 1, 2025 · virial (not comparable) (mechanics) Of or pertaining to the interactive forces between molecules or particles.

Jun 6, 2020 · The virial theorem was established in 1870 by R. Clausius, and is a consequence of the equations of motion of a mechanical system on the condition that the motion of the system takes …

This is actually more reliable than what we got using the simple virial estimate, because we're thinking now about the central temperature instead of some \average" temperature.