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Thermal Energy |
Thermal energy is the sum of sensible heat and latent heat.
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According to the equipartition theorem, it is possible to define thermal energy. In a system of N molecules, each with f degrees of freedom, and if there are no other (non-quadratic) temperature-dependent forms of energy, then the total thermal energy of the system is:1

To note, Uthermal is almost never the total energy of a system; for instance, there can be static energy that doesn't change with temperature, such as bond energy or rest energy (E=mc2).
Thermal Energy comes from the movement of atoms and molecules in matter.
Thermal energy per particle is also called the average translational kinetic energy possessed by free particles given by equipartition of energy.2
Thermal energy is the difference between the internal energy of an object and the amount that it would have at absolute zero.citation needed It includes the quantity of kinetic energy due to the motion of the internal particles of an object, and is increased by heating and reduced by cooling.
In a monatomic ideal gas, the thermal energy is exactly given by the kinetic energy of the constituent particles.citation needed