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#REDIRECT [[Internal energy]]
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'''Thermal energy''' is a form of energy that manifests itself as an increase of [[temperature]]. It is also the sum of [[sensible heat]] and [[latent heat]].

==Definitions==

The thermal energy of a single particle in a thermal bath is:

<math>U_{thermal} = f \cdot \tfrac{1}{2} kT.</math>

where f refers to the degrees of freedom, T refers to the temperature, and k to [[Boltzmann's constant]]. For example, a monatomic particle in an ideal gas has three degrees of freedom, and thus,

<math>U_{thermal, monatomic} = \tfrac{3}{2} kT.</math>

The total thermal energy is the sum of the thermal energies of all particles in the system. Thus, for a system of N particles,

<math>U_{thermal} = N \cdot f \cdot \tfrac{1}{2} kT.</math>

Note that ''U<sub>thermal</sub>'' is rarely the total energy of a system; for instance, there can be static energy that doesn't change with temperature, such as [[potential energy]], [[bond energy]] or rest energy (E=mc<sup>2</sup>).

==History of the term==

The term was first used explicitly by [[James Prescott Joule|James Joule]], who studied the relationship between heat, work, and temperature. He observed that if he did mechanical work on a fluid such as water, by agitating the fluid, its temperature increased. He proposed that the mechanical work he was doing on the system was converted to "thermal energy." Specifically, he found that 4200 joules of energy were needed to raise the temperature of a kilogram of water by one degree Celsius.

==Thermal energy in an ideal gas==

Thermal energy is most easily defined in the context of an [[ideal gas]]. In a [[monatomic]] [[ideal gas]], the thermal energy is exactly given by the kinetic energy of the constituent particles.{{Citation needed|date=July 2007}}

==Other definitions==

Thermal energy per particle is also called the average translational kinetic energy possessed by free particles given by equipartition of energy.<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/eqpar.html#c2 Thermal energy] – Hyperphysics</ref>

Thermal energy is the difference between the [[internal energy]] of an object and the amount that it would have at [[absolute zero]].{{Citation needed|date=July 2007}} 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]].

==See also==
{{col-start}}
{{col-break}}
*[[Geothermal power]]
*[[Enthalpy]]
*[[Entropy]]
*[[Heat transfer]]
*[[Ocean thermal energy conversion]]
*[[Radiation]]
*[[Thermal efficiency]]
*[[Thermal science]]
{{col-end}}

==References==
{{reflist}}

[[Category:Thermodynamics]]

[[ar:طاقة حرارية]]
[[az:İstilik enerjisi]]
[[be-x-old:Цеплавая энэргія]]
[[bg:Топлинна енергия]]
[[ca:Energia tèrmica]]
[[da:Varmeenergi]]
[[de:Thermische Energie]]
[[el:Θερμική ενέργεια]]
[[es:Energía térmica]]
[[eu:Energia termiko]]
[[fr:Énergie thermique]]
[[gl:Enerxía térmica]]
[[it:Energia termica]]
[[he:אנרגיה תרמית]]
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[[lb:Thermesch Energie]]
[[no:Termisk energi]]
[[pl:Energia termiczna]]
[[pt:Energia térmica]]
[[ro:Energie termică]]
[[ru:Тепловая энергия]]
[[simple:Thermal energy]]
[[sv:Termisk energi]]
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[[uk:Теплова енергія]]
[[zh:热能]]

Revision as of 19:43, 11 October 2009

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