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The term 'thermal energy' is used differently, and often loosely, in different contexts. It refers to several distinct physical concepts, such as the
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
, or as the
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant p ... , of a body of matter and radiation; or as
heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ... , defined as a type of energy transfer (as is
thermodynamic work In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is govern ...
); or as the characteristic energy of a degree of freedom, $k_T$, in a system that is described in terms of its microscopic particulate constituents, where $T$ denotes
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ... and $k_$ denotes the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathematics), c ...
.

# Relation to heat and internal energy

In
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ... , heat is
energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ... in transfer to or from a
thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, whic ...
, by mechanisms other than thermodynamic work or transfer of matter. Heat refers to a quantity transferred between systems, not to a property of any one system, or 'contained' within it. On the other hand, internal energy and enthalpy are properties of a single system. Heat and work depend on the way in which an energy transfer occurred, whereas internal energy is a property of the state of a system and can thus be understood without knowing how the energy got there. In a statistical mechanical account of an
ideal gas An ideal gas is a theoretical gas Gas is one of the four fundamental states of matter In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion ...
, in which the
molecule A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon ... s move independently between instantaneous collisions, the internal energy is the sum total of the gas's independent particles' kinetic energies, and it is this kinetic motion that is the source and the effect of the transfer of heat across a system's boundary. For a gas that does not have particle interactions except for instantaneous collisions, the term 'thermal energy' is effectively synonymous with '
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
'. In many
statistical physics Statistical physics is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), ...
texts, "thermal energy" refers to $kT$, the product of
Boltzmann's constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas ...
and the
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of ...
, also written as $k_\text T$. In a material, especially in condensed matter, such as a liquid or a solid, in which the constituent particles, such as molecules or ions, interact strongly with one another, the energies of such interactions contribute strongly to the internal energy of the body, but are not simply apparent in the temperature. The term 'thermal energy' is also applied to the energy carried by a heat flow, although this can also simply be called heat or quantity of heat.

# Historical context

In an 1847 lecture titled "On Matter, Living Force, and Heat",
James Prescott Joule James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, ... characterised various terms that are closely related to thermal energy and heat. He identified the terms
latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any su ...
and
sensible heatSensible heat is heat In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than Work (thermodynamics), thermodynamic work or Mass transfer, transfer of matter. The various mechanisms of energy tr ...
as forms of heat each affecting distinct physical phenomena, namely the
potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (phys ... and
kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
of particles, respectively. He described latent energy as the energy of interaction in a given configuration of particles, i.e. a form of potential energy, and the sensible heat as an energy affecting temperature measured by the
thermometer (mercury-in-glass thermometer) for measurement of room temperature. A thermometer is a device that temperature measurement, measures temperature or a temperature gradient A temperature gradient is a physical quantity that describes in which dir ... due to the thermal energy, which he called the living force.

# Useless thermal energy

If the minimum temperature of a system's environment is $T_\text$ and the system's entropy is $S$, then a part of the system's internal energy amounting to $S \cdot T_\text$ cannot be converted into useful work. This is the difference between the internal energy and the
Helmholtz free energy In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quan ...
.

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Geothermal energy Geothermal energy is the thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concepts, such as the internal energy of a system; heat or sensible heat, which a ...
*
Heat transfer Heat transfer is a discipline of thermal engineering Thermal engineering is a specialized sub-discipline of mechanical engineering Mechanical engineering is an engineering Engineering is the use of scientific method, scientific pri ... *
Ocean thermal energy conversion Ocean Thermal Energy Conversion (OTEC) uses the ocean thermal gradient between cooler deep and warmer shallow or surface seawaters to run a heat engine In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work ( ...
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Orders of magnitude (temperature) List of orders of magnitude for temperature Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, ...
*
Thermal energy storage Thermal energy storage (TES) is achieved with widely different technologies. Depending on the specific technology, it allows excess thermal energy to be stored and used hours, days, months later, at scales ranging from the individual process, b ...

# References

{{footer energy Thermodynamic properties Forms of energy