The virial theorem relates gravitational potential energy to internal thermal energy. What is this relationship?

Answer

Gravitational potential energy must equal twice the internal thermal energy

The virial theorem provides the mathematical criterion for determining hydrostatic equilibrium, a state where a cloud is stable against collapse or expansion due to a perfect balance of forces. This theorem connects the total gravitational potential energy of the cloud system to its internal thermal energy, which is derived from the kinetic energy of the gas particles. For the system to be in equilibrium, the mathematical relationship mandates that the gravitational potential energy must be precisely twice the value of the internal thermal energy. If the gravitational energy exceeds this factor of two relationship, the cloud is supercritical, and gravity dominates, leading to collapse.

The virial theorem relates gravitational potential energy to internal thermal energy. What is this relationship?

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