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{{otheruses1|the physical quantity}}
[[Image:Lightning over Oradea Romania 2.jpg|thumb|right|258px|[[Lightning]] is the electric breakdown of air by strong electric fields, producing a [[plasma (physics)|plasma]], which causes an energy transfer from the electric field to [[heat]], mechanical energy (the random motion of air molecules caused by the heat), and light.]]

In [[physics]] and other [[science]]s, '''energy''' (from the [[Greek language|Greek]] ενεργός, ''energos'', "active, working")<ref>{{cite web |url=http://www.etymonline.com/index.php?term=energy |title=Energy |work=Online Etymology Dictionary |last=Harper |first=Douglas |accessmonthday=May 1|accessyear=2007}}</ref> is a [[scalar (physics)|scalar]] [[physical quantity]] that is a property of objects and systems which is conserved by nature. Energy is often defined as the ability to do [[work]]. 

Several different forms of energy, such as [[Kinetic energy|kinetic]], [[Potential energy|potential]], [[Thermal energy|thermal]], [[Chemical energy|chemical]], [[Nuclear energy|nuclear]], and [[Rest energy|mass]] have been defined to explain all known natural phenomena.

Energy is [[energy transformation|converted]] from one form to another, but it is never created or destroyed. This principle, the [[conservation of energy]], was first postulated in the early 19th century, and applies to any [[isolated system]]. According to [[Noether's theorem]], the conservation of energy is a consequence of the fact that the laws of physics do not change over time.<ref name="jphysics">{{cite book | last =Lofts| first =G| coauthors =O'Keeffe D; et al| title=Jacaranda Physics 1| publisher =John Willey & Sons Australia Ltd. | date =2004| location = Milton, Queensland, Australia| pages = 286| chapter=11 — Mechanical Interactions| edition=2| isbn=0 7016 3777 3}}</ref>

Although the total energy of a system does not change with time, its value may depend on the [[frame of reference]].  For example, a seated passenger in a moving airplane has zero kinetic energy relative to the airplane, but nonzero kinetic energy relative to the earth.

==History==
{{Main|History of energy|Timeline of thermodynamics, statistical mechanics, and random processes|History of physics|}}
[[Image:Thomas Young (scientist).jpg|thumb|right|[[Thomas Young (scientist)|Thomas Young]] - the first to use the term "energy" in the modern sense.]]
The concept of energy emerged out of the idea of [[vis viva]], which [[Gottfried Leibniz|Leibniz]] defined as the product of the mass of an object and its velocity squared; he believed that total vis viva was conserved. To account for slowing due to friction, Leibniz claimed that heat consisted of the random motion of the constituent parts of matter — a view shared by [[Isaac Newton]], although it would be more than a century until this was generally accepted.  In 1807, [[Thomas Young (scientist)|Thomas Young]] was the first to use the term "energy", instead of [[vis viva]], in its modern sense.<ref>{{cite book | last = Smith | first = Crosbie | title = The Science of Energy - a Cultural History of Energy Physics in Victorian Britain | publisher = The University of Chicago Press | year = 1998 | id = ISBN 0-226-76420-6}}</ref> [[Gustave-Gaspard Coriolis]] described "[[kinetic energy]]" in 1829 in its modern sense, and in 1853, [[William John Macquorn Rankine|William Rankine]] coined the term "[[potential energy]]."
It was argued for some years whether energy was a substance (the [[caloric theory|caloric]]) or merely a physical quantity, such as [[momentum]].

He amalgamated all of these laws into the laws of [[thermodynamics]], which aided in the rapid development of explanations of chemical processes using the concept of energy by [[Rudolf Clausius]], [[Josiah Willard Gibbs]] and [[Walther Nernst]]. It also led to a mathematical formulation of the concept of [[entropy]] by Clausius, and to the introduction of laws of [[radiant energy]] by [[Jožef Stefan]].

During a 1961 lecture<ref name="RPF1"/> for undergraduate students at the [[California Institute of Technology]], [[Richard Feynman]], a celebrated physics teacher and [[Nobel Laureate]], said this about the concept of energy:

{{cquote|There is a fact, or if you wish, a law, governing natural phenomena that are known to date. There is no known exception to this law &mdash; it is exact so far we know. The law is called [[conservation of energy]]; it states that there is a certain quantity, which we call energy that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity, which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same.| | |''The Feynman Lectures on Physics''<ref name=RPF1/>}}

Since 1918 it has been known that  the law of [[conservation of energy]] is the direct mathematical consequence of the [[translational symmetry]] of the quantity [[conjugate variables|conjugate]] to energy, namely [[time]]. That is, energy is conserved because the laws of physics do not distinguish between different moments of time (see [[Noether's theorem]]).

== Energy in various contexts since the beginning of the universe ==

The concept of energy and its transformations is extremely  useful in explaining and predicting most natural phenomena. The ''direction'' of transformations in energy (what kind of energy is transformed to what other kind) is often described by [[entropy]] (equal energy spread among all available [[degrees of freedom (physics and chemistry)|degrees of freedom]]) considerations, since in practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.  

The concept of energy is used often in all fields of science.

:In [[Chemistry#Energy|chemistry]], the energy differences between [[Chemical substance|substance]]s determine whether, and to what extent, it can be converted into another substance or react with other substances. 

:In [[biology]], [[chemical bond]]s are broken and made during [[Metabolism|metabolic processes]], and the associated changes in available energy are studied in the subfield of [[bioenergetics]]. Energy is often stored by [[Cell (biology)|cells]] in the form of substances such as [[carbohydrate]] molecules (including sugars) and [[lipid]]s, which release energy when reacted with [[oxygen]]. 

:In [[Earth science#earth's energy|geology and meteorology]],  [[continental drift]], [[mountain|mountain range]]s, [[volcano]]s, and [[earthquake]]s are phenomena that can be explained in terms of [[energy transformation]]s in the Earth's interior. <ref>[http://okfirst.ocs.ou.edu/train/meteorology/EnergyBudget.html Earth's Energy Budget<!-- Bot generated title -->]</ref> While meteorological phenomena like [[wind]], [[rain]], [[hail]], [[snow]], [[lightning]], [[tornado]]es and [[hurricanes]], are all a result of energy transformations brought about by [[solar energy]] on the planet Earth.

:In [[Physical cosmology#Energy of the cosmos|cosmology and astronomy]] the phenomena of [[star]]s, [[nova]], [[supernova]], [[quasar]]s and [[gamma ray burst]]s are the universe's highest-output [[energy transformation]]s of matter. All [[wikt:stellar|stellar]] phenomena (including solar activity) are driven by various kinds of energy transformations. Energy in such transformations is either from gravitational collapse of matter (usually molecular hydrogen) into various classes of astronomical objects (stars, black holes, etc.), or from nuclear fusion (of lighter elements, primarily hydrogen).

Energy transformations in the universe over time are characterized by various kinds of potential energy which has been available since the [[Big Bang]], later being "released" (transformed to more active types of energy such as kinetic or radiant energy), when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released which was originally "stored" in heavy isotopes (such as [[uranium]] and [[thorium]]), using the gravitational potential energy released from the gravitational collapse of supernovae, which created these elements before they were incorporated into the solar system and the Earth. Heat from such nuclear decay in the core of the Earth releases heat, which in turn may lift mountains via [[orogenesis]]. This lifting represents a kind of gravitational potential energy storage, which may be released to active kinetic energy in landslides, after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a store which has been produced ultimately from the same heat sources. Thus, according to present understanding, familiar events such as landslides and earthquakes release energy stored since the collapse of long-destroyed stars.

In another similar chain of transformations from the dawn of the universe, nuclear fussion of hydrogen in the Sun releases potential energy stored at the time of the Big Bang, when according to theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements. Energy from this fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the energy is transformed to sunlight. Such sunlight from our Sun may again be stored as gravitational potential energy after it strikes the Earth, when (for example) water evaporates from oceans and is deposited upon mountains (where, after being released at a hydroelectric dam, it can be used to drive turbine/generators to produce electricity). Sunlight also drives all weather phenomenon, including violent events triggered when large unstable areas of warm ocean, heated over months, give up some of their thermal energy suddently to power a few days of hurricanes. Sunlight is also is captured by plants as chemical potential energy, when carbon dioxide and water are converted into carbohydrates, lipids, and oxygen. This energy may be triggered suddenly by a spark in a forest fire; or may be available more slowly for animal or human metabolism, when these molecules are ingested, and [[catabolism]] is triggered by [[enzyme]] action. Through all of these tranformation chains, potential energy stored at the time of the Big Bang is later released by intermediate events, sometimes being stored in a number of ways over time between releases as more active energy. In all these events, one kind of energy is converted to other types of energy, including heat.

== Regarding applications of the concept of energy ==

Energy is subject to a strict [[conservation law|global conservation law]]; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.<ref> Berkeley Physics Course Volume 1. Charles Kittle, Walter D Knight and Malvin A Ruderman</ref>
* The total energy of a [[system]] can be subdivided and classified in various ways.  For example, it is sometimes convenient to distinguish [[potential energy]] (which is a function of coordinates only) from [[kinetic energy]] (which is a function of coordinate time [[derivative]]s only).  It may also be convenient to distinguish gravitational energy, electric energy, thermal energy, and other forms.  These classifications overlap;  for instance thermal energy usually consists partly of kinetic and partly of potential energy.
* The ''transfer'' of energy can take various forms;  familiar examples include work, heat flow, and advection, as discussed [[#Energy transfer|below]].
* The word "energy" is also used outside of physics in many ways, which can lead to [[Energy|ambiguity]] and inconsistency. The vernacular terminology is not consistent with technical terminology.  For example, the important public-service announcement, "Please conserve energy" uses vernacular notions of "conservation" and "energy" which make sense in their own context but are utterly incompatible with the technical notions of "conservation" and "energy" (such as are used in the law of conservation of energy).<ref name="thermo-laws"/>

In [[classical physics]] energy is considered a scalar quantity, the [[canonical conjugate]] to [[time]]. In [[special relativity]] energy is also a scalar (although not a [[Lorentz scalar]] but a time component of the [[energy-momentum]] [[4-vector]]).<ref name="MTW">{{cite book |author=Misner, Thorne, Wheeler |title=Gravitation |date=1973 |publisher=W. H. Freeman |location=San Francisco |id=ISBN 0716703440}}</ref>  In other words, energy is invariant with respect to rotations of [[space]], but not invariant with respect to rotations of [[space-time]] (= [[Lorentz boost|boosts]]).

===Energy transfer===

Because energy is strictly conserved and is also locally conserved (wherever it can be defined), it is important to remember that by definition of energy the transfer of energy between the "system" and adjacent regions is work.  A familiar example is ''[[mechanical work]]''.  In simple cases this is written as:

:<math>\Delta{}E = W</math>  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (1)

if there are no other energy-transfer processes involved.  Here <math>\Delta{}E</math>&nbsp; is the amount of energy transferred, and <math>W</math>&nbsp; represents the work done on the system.  

More generally, the energy transfer can be split into two categories:

:<math>\Delta{}E = W + Q </math> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (2)

where <math>Q</math>&nbsp; represents the heat flow into the system.

There are other ways in which an open system can gain or lose energy. If mass is counted as energy (as in many relativistic problems) then '''<math>E</math>''' must contain a term for mass lost or gained. In chemical systems, energy can be added to a system by means of adding substances with different chemical potentials, which potentials are then extracted (both of these process are illustrated by fueling an auto, a system which gains in energy thereby, without addition of either work or heat). These terms may be added to the above equation, or they can generally be subsumed into a quantity called "energy addition term <math>E</math>" which refers to ''any'' type of energy carried over the surface of a control volume or system volume. Examples may be seen above, and many others can be imagined (for example, the kinetic energy of a stream of particles entering a system, or energy from a laser beam adds to system energy, without either being either work-done or heat-added, in the classic senses). 

:<math>\Delta{}E = W + Q + E </math> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (3)

Where E in this general equation represents other additional advected energy terms not covered by work done on a system, or heat added to it.

Energy is also transferred from potential energy (<math>E_p</math>) to kinetic energy (<math>E_k</math>) and then back to potential energy constantly. This is referred to as conservation of energy. In this closed system, energy can not be created or destroyed, so the initial energy and the final energy will be equal to each other. This can be demonstrated by the following:

:'''<math>E_{pi} + E_{ki} = E_{pF} + E_{kF}'''</math>

The equation can then be simplified further since <math>E_p = mgh</math> (mass times acceleration due to gravity times the height) and <math>E_k = \frac{1}{2} mv^2</math> (half times mass times velocity squared). Then the total amount of energy can be found by adding <math>E_p + E_k = E_{total}</math>.

===Energy and the laws of motion===
===The Hamiltonian===

The total energy of a system is sometimes called the [[Hamilton's equations|Hamiltonian]], after [[William Rowan Hamilton]].  The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems.  These classical equations have remarkably direct analogs in
nonrelativistic quantum mechanics.<ref >[http://www.sustech.edu/OCWExternal/Akamai/18/18.013a/textbook/HTML/chapter16/section03.html The Hamiltonian] MIT OpenCourseWare website 18.013A  Chapter 16.3  Accessed February 2007</ref>

===The Lagrangian===

Another energy-related concept is called the [[Lagrangian]], after [[Joseph Louis Lagrange]]. This is even more fundamental than the Hamiltonian, and can be used to derive the equations of motion. In non-relativistic physics, the Lagrangian is the kinetic energy ''minus'' potential energy.

Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (like systems with friction).

===Energy and thermodynamics===
====Internal energy====
'''[[Internal energy]]''' – the sum of all microscopic forms of energy of a system.  It is related to the molecular structure and the degree of molecular activity and may be viewed as the sum of kinetic and potential energies of the molecules; it comprises the following types of energy:<ref>{{cite book | last = Cengel | first = Yungus, A. | coauthors = Boles, Michael | title = Thermodynamics - An Engineering Approach, 4th ed. | pages = 17-18 | publisher = McGraw-Hill | year = 2002 | id = ISBN 0-07-238332-1}}</ref>

<center>
{| border="1" cellpadding="2" style="border-collapse: collapse;"
! Type !! Composition of '''[[Internal Energy]]''' (U)
|-
! '''[[Sensible heat|Sensible energy]]'''
|width="700pt" align="left" | the portion of the [[internal energy]] of a system associated with kinetic energies (molecular translation, rotation, and vibration; electron translation and spin; and nuclear spin) of the molecules.
|-
! '''[[Latent heat|Latent energy]]'''
|width="700pt" align="left" | the internal energy associated with the [[phase (matter)|phase]] of a system.
|-
! '''[[Chemical energy]]'''
|width="700pt" align="left" |the internal energy associated with the different kinds of aggregration of [[atoms]] in [[matter]].
|-
! '''[[Nuclear energy]]'''
|width="700pt" align="left" |the tremendous amount of energy associated with the [[nuclear energy|strong bond]]s within the nucleus of the atom itself.
|-
! '''[[Fundamental interactions|Energy interaction]]s'''
|width="700pt" align="left" |those types of energies not stored in the system (e.g. [[heat transfer]], [[mass transfer]], and [[work (thermodynamics)|work]]), but which are recognized at the [[thermodynamic system|system boundary]] as they cross it, which represent gains or losses by a system during a process. 
|-
! '''[[Thermal energy]]'''
|width="700pt" align="left" |the sum of sensible and latent forms of internal energy.
|}
</center>

====The laws of thermodynamics====
According to the [[second law of thermodynamics]], work can be totally converted into heat, but not vice versa.This is a mathematical consequence of [[statistical mechanics]]. The [[first law of thermodynamics]] simply asserts that energy is conserved,<ref name="KK">{{cite book |author=Kittel and Kroemer|title=Thermal Physics |date=1980|publisher=W. H. Freeman |location=New York| id=ISBN 0-7167-1088-9}}</ref> and that heat is included as a form of energy transfer. A commonly-used corollary of the first law is that for a "system" subject only to [[pressure]] forces and heat transfer (e.g. a cylinder-full of gas), the differential change in energy of the system (with a ''gain'' in energy signified by a positive quantity) is given by:

:<math>\mathrm{d}E = T\mathrm{d}S - P\mathrm{d}V\,</math>,

where the first term on the right is the heat transfer into the system, defined in terms of [[temperature]] ''T'' and [[entropy]] ''S'' (in which entropy increases and the change d''S'' is positive when the system is heated); and the last term on the right hand side is identified as "work" done on the system, where pressure is ''P'' and volume ''V'' (the negative sign results since compressiong of the system is needed to do work on it, so that the volume change d''V'' is negative when work is done on the system). Although this equation is the standard text-book example of energy conservation in classical thermodynamics, it is highly specific, ignoring all chemical, electric, nuclear, and gravitational forces, effects such as [[advection]] of any form of energy other than heat, and because it contains a term that depends on temperature.  The most general statement of the first law — i.e. conservation of energy — is valid even in situations in which temperature is undefinable.

Energy is sometimes expressed as: 

:<math>\mathrm{d}E=\delta Q+\delta W\,</math>,

which is unsatisfactory<ref name="thermo-laws"/>  because there cannot exist any thermodynamic state functions ''W'' or ''Q'' that are meaningful on the right hand side of this equation, except perhaps in trivial cases. <!-- news to me. You can look up H's, standard enthalpies which are Q's at constant pressure), for all kinds of substances. These are used in many equations of the sort seen above, for what will happens to substances under varying conditions of volume (work done on the substance) and heat generation.-->

===Equipartition of energy===

The energy of a mechanical [[harmonic oscillator]] (a mass on a spring) is alternatively [[kinetic energy|kinetic]] and [[potential]].  At two points in the oscillation [[Cycle#physics|cycle]] it is entirely kinetic, and alternatively at two other points it is entirely potential.  Over the whole cycle, or over many cycles net energy is thus equally split between kinetic and potential. This is called [[equipartition principle]] - total energy of a system with many degrees of freedom is equally split among all these degrees of freedom.

This principle is vitally important to understanding the behavior of a quantity closely related to energy, called [[entropy]]. Entropy is a measure of evenness of a [[distribution (mathematics)|distribution]] of energy between parts of a system. This concept is also related to the [[second law of thermodynamics]] which basically states that when an isolated system is given more degrees of freedom (= is given new available [[energy state]]s which are the same as existing states), then energy spreads over '''all''' available degrees equally without distinction between  "new" and "old" degrees.

===Oscillators, phonons, and photons===

In an ensemble (connected collection) of unsynchronized oscillators, the average energy is spread equally between kinetic and potential types.

In a solid, '''[[thermal energy]]''' (often referred to loosely as heat content) can be accurately described by an ensemble of thermal phonons that act as mechanical oscillators.  In this model, thermal energy is equally kinetic and potential.

In an ideal gas, the interaction potential between particles is essentially the delta function which stores no energy: thus, all of the thermal energy is kinetic.

Because an electric oscillator (''LC'' circuit) is analogous to a mechanical oscillator, its energy must be, on average, equally kinetic and potential.  It is entirely arbitrary whether the magnetic energy is considered kinetic and the electric energy considered potential, or vice versa.  That is, either the inductor is analogous to the mass while the capacitor is analogous to the spring, or vice versa.  

#By extension of the previous line of thought, in free space the electromagnetic field can be considered an ensemble of oscillators, meaning that '''[[radiant energy|radiation energy]]''' can be considered equally potential and kinetic.  This model is useful, for example, when the electromagnetic Lagrangian is of primary interest and is interpreted in terms of potential and kinetic energy.

#On the other hand, in the key equation <math>m^2 c^4 = E^2 - p^2 c^2</math>, the contribution <math>mc^2</math> is called the rest energy, and all other contributions to the energy are called kinetic energy.  For a particle that has mass, this implies that the kinetic energy is <math>0.5 p^2/m</math> at speeds much smaller than ''c'', as can be proved by writing <math>E = mc^2 </math>&nbsp;√<math>(1 + p^2 m^{-2}c^{-2})</math> and expanding the square root to lowest order.  By this line of reasoning, the energy of a photon is entirely kinetic, because the photon is massless and has no rest energy.  This expression is useful, for example, when the energy-versus-momentum relationship is of primary interest.

The two analyses are entirely consistent.  The electric and magnetic degrees of freedom in item 1 are ''transverse'' to the direction of motion, while the speed in item 2 is ''along'' the direction of motion.  For non-relativistic particles these two notions of potential versus kinetic energy are numerically equal, so the ambiguity is harmless, but not so for relativistic particles.<!-- confusing -->

===Work and virtual work===

{{Main|Mechanics|Mechanical work|Thermodynamics|Quantum mechanics}}

Work is roughly force times distance.  But more precisely, it is

: <math> W = \int \mathbf{F} \cdot \mathrm{d}\mathbf{s}</math>

This says that the work (<math>W</math>) is equal to the integral (along a certain path) of the [[force]];  for details see the [[mechanical work]] article.

Work and thus energy is [[frame dependent]].  For example, consider a ball being hit by a bat.  In the center-of-mass reference frame, the bat does no work on the ball.  But, in the reference frame of the person swinging the bat, considerable work is done on the ball.

===Quantum mechanics===

In quantum mechanics energy is defined in terms of the [[Hamiltonian (quantum mechanics)|energy operator]]
as a time derivative of the [[wave function]]. The  [[Schrödinger equation]] equates energy operator to the full energy of a particle or a system. It thus can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of the [[wave function]] of quantum systems. The solution of this equation for bound system is discrete (a set of permitted states, each characterized by an [[energy level]]) which results in the concept of [[quanta]]. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic wave in vacuum, the resulting energy states are related to the frequency by the [[Planck]] equation <math>E = h\nu</math> (where <math>h</math> is the [[Planck's constant]] and <math>\nu</math> the frequency). In the case of electromagnetic wave these energy states are called quanta of [[light]] or [[photon]]s.

===Relativity===

When calculating kinetic energy (= [[Mechanical work|work]] to accelerate a [[mass]] from zero [[speed]] to some finite speed) relativistically - using [[Lorentz transformations]] instead of [[Newtonian mechanics]], Einstein discovered unexpected by-product of these calculations to be an energy term which does not vanish at zero speed. He called it [[rest mass energy]] - energy which every mass must possess even when being at rest. The amount of energy is directly proportional to the mass of body: 

:<math> E = m c^2 </math>,
where
:''m'' is the mass,
:''c'' is the [[speed of light]] in vacuum,
:''E'' is the rest mass energy.

For example, consider [[electron]]-[[positron]] annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its [[invariant mass]]) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process - the inverse process is called [[pair creation]] - in which the rest mass of particles is created from energy of two (or more) annihilating photons. 

In general relativity, the ''stress-energy tensor'' serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation.<ref name="MTW"/>

It is not uncommon to hear that energy is "equivalent" to mass. It would be more accurate to state that every energy has inertia and gravity equivalent, and because mass is a form of energy, then mass too has inertia and gravity associated with it.

==Measurement==
There is no absolute measure of energy, because energy is defined as the work that one system does (or can do) on another. Thus, only of the transition of a system from one state into another can be defined and thus measured.

===Methods===
The methods for the [[measurement]] of energy often deploy methods for the measurement of still more fundamental concepts of science, namely [[mass]], [[distance]], [[radiation]], [[temperature]], [[time]], [[electric charge]] and [[electric current]].
[[Image:X-ray microcalorimeter diagram.jpg|thumb|right|270px|A [[Calorimeter]] - An instrument used by physicists to measure energy]] Conventionally the technique most often employed is [[calorimetry]], a [[thermodynamic]] technique that relies on the measurement of temperature using a [[thermometer]] or of intensity of radiation using a [[bolometer]].

===Units===
{{Main|Units of energy}}
Throughout the history of science, energy has been expressed in several different units such as [[erg]]s and [[calorie]]s. At present, the accepted unit of measurement for energy is the [[SI]] unit of energy, the [[joule]].

==Forms of energy==
[[Image:Hot metalwork.jpg|right|200px|thumb|[[Heat]], a form of energy, is partly [[potential energy]] and partly [[kinetic energy]].]]

[[Classical mechanics]] distinguishes between [[potential energy]], which is a function of the position of an object, and [[kinetic energy]], which is a function of its [[motion (physics)|movement]]. Both position and movement are relative to a [[frame of reference]], which must be specified: this is often (and originally) an arbitrary fixed point on the surface of the Earth, the ''terrestrial'' frame of reference. Some introductory authors{{Fact|date=June 2007}} attempt to separate ''all'' forms of energy in either kinetic or potential: this is not incorrect, but neither is it clear that it is a real simplification, as Feynman points out:

{{quotation|These notions of potential and kinetic energy depend on a notion of length scale.  For example, one can speak of ''macroscopic'' potential and kinetic energy, which do not include thermal potential and kinetic energy.  Also what is called chemical potential energy (below) is a macroscopic notion, and closer examination shows that it is really the sum of the potential ''and kinetic'' energy on the atomic and subatomic scale.  Similar remarks apply to nuclear "potential" energy and most other forms of energy.  This dependence on length scale is non-problematic if the various length scales are decoupled, as is often the case ... but confusion can arise when different length scales are coupled, for instance when friction converts macroscopic work into microscopic thermal energy.}}

{| class="wikitable" align=right width=150px
|-
|+ Examples of the interconversion of energy
|-
! colspan=2 | Mechanical energy is converted
|-
! into
! by
|-
| '''[[Mechanical energy]]'''
| [[Lever]]
|-
| '''[[Thermal energy]]'''
| [[Brake]]s
|-
| '''[[Electric energy]]'''
| [[Dynamo]]
|-
| '''[[Electromagnetic radiation]]'''
| [[Synchrotron]]
|-
| '''[[Chemical energy]]'''
| [[Match]]es
|-
| '''[[Nuclear energy]]'''
| [[Particle accelerator]]
|-
|}

=== Potential energy ===
{{main|Potential energy}}
Potential energy, symbols ''E''<sub>p</sub>, ''V'' or ''Φ'', is defined as the work done ''against a given force'' (= work of ''given force'' with minus sign) in changing the position of an object with respect to a reference position (often taken to be infinite separation). If '''''F''''' is the [[force (physics)|force]] and '''''s''''' is the [[displacement (mathematics)|displacement]],
::<math>E_{\rm p} = -\int \mathbf{F}\cdot{\rm d}\mathbf{s}</math>
with the dot representing the [[scalar product]] of the two [[vector (spatial)|vector]]s.

The name "potential" energy originally signified the idea that the energy could readily be transferred as work—at least in an idealized system (reversible process, see below). This is not completely true for any real system, but is often a reasonable first approximation in classical mechanics.

The general equation above can be simplified in a number of common cases, notably when dealing with [[gravity]] or with [[elastic force]]s.

==== Gravitational potential energy ====
{{main|Gravitational potential energy}}
The [[gravitational force]] near the Earth's surface varies very little with the height, ''h'', and is equal to the [[mass]], ''m'', multiplied by the [[gravitational acceleration]], ''g''&nbsp;= 9.81&nbsp;m/s². In these cases, the gravitational potential energy is given by
::<math>E_{\rm p,g} = mgh</math>

A more general expression for the potential energy due to [[Newtonian gravitation]] between two bodies of masses ''m''<sub>1</sub> and ''m''<sub>2</sub>, useful in [[astronomy]], is
::<math>E_{\rm p,g} = -G{{m_1m_2}\over{r}}</math>,
where ''r'' is the separation between the two bodies and ''G'' is the [[gravitational constant]], 
6.6742(10)×10<sup>&minus;11</sup>&nbsp;m³kg<sup>&minus;1</sup>s<sup>&minus;2</sup>.<ref name="CODATA">{{CODATA}}</ref> In this case, the reference point is the infinite separation of the two bodies.

==== Elastic potential energy ====
[[Image:Bouncing ball strobe edit.jpg|thumb|right|350px|As a ball falls freely under the influence of [[gravity]], it accelerates downward, its initial [[potential energy]] converting into [[kinetic energy]]. On impact with a hard surface the ball deforms, converting the kinetic energy into [[elastic potential energy]].  As the ball springs back, the energy converts back firstly to kinetic energy and then as the ball re-gains height into potential energy.  Energy losses due to [[Elasticity (physics)|inelastic]] [[deformation]] and [[air resistance]] cause each successive bounce to be lower than the last.]]
{{main|Elastic potential energy}}
Elastic potential energy is defined as a work needed to compress (or expand) a spring.
The force, '''''F''''', in a [[spring (mechanics)|spring]] or any other system which obeys [[Hooke's law]] is proportional to the extension or compression, '''''x''''', 
::<math>F = -kx</math>
where ''k'' is the [[force constant]] of the particular spring (or system). In this case, the calculated work becomes
::<math>E_{\rm p,e} = {1\over 2}kx^2</math>.
Hooke's law is a good approximation for behaviour of [[chemical bond]]s under normal conditions, i.e. when they are not being broken or formed.

=== Kinetic energy ===

{{main|Kinetic energy}}
Kinetic energy, symbols ''E''<sub>k</sub>, ''T'' or ''K'', is the work required to accelerate an object to a given speed. Indeed, calculating this work one easily obtains the following:
 
::<math>E_{\rm k} = \int \mathbf{F} \cdot d \mathbf{x} = \int \mathbf{v} \cdot d \mathbf{p}=  {1\over 2}mv^2</math>
At speeds approaching the [[speed of light]], ''c'', this work must be calculated using [[Lorentz transformations]], which results in the following:
 
::<math> E_{\rm k} = m c^2\left(\frac{1}{\sqrt{1 - (v/c)^2}} - 1\right) </math>

This equation reduces to the one above it, at small (compared to '''c''') speed. A mathematical by-product of this work (which is immediately seen in the last equation) is that even at rest a mass has the amount of energy equal to:

::<math> E_{\rm rest} = mc^2 </math>

This energy is thus called [[rest mass energy]].

=== Thermal energy ===
{| class="wikitable" align=right width=150px
|-
|+ Examples of the interconversion of energy
|-
! colspan=2 | Thermal energy is converted
|-
! into
! by
|-
| '''[[Mechanical energy]]'''
| [[Steam turbine]]
|-
| '''[[Thermal energy]]'''
| [[Heat exchanger]]
|-
| '''[[Electric energy]]'''
| [[Thermocouple]]
|-
| '''[[Electromagnetic radiation]]'''
| [[Black body|Hot objects]]
|-
| '''[[Chemical energy]]'''
| [[Blast furnace]]
|-
| '''[[Nuclear energy]]'''
| [[Supernova]]
|-
|}

{{main|Thermal energy}}
The general definition of thermal energy, symbols ''q'' or ''Q'', is also problematic. A practical definition for small transfers of heat is
::<math>\Delta q = \int C_{\rm v}{\rm d}T</math>
where ''C''<sub>v</sub> is the [[heat capacity]] of the system. This definition will fail if the system undergoes a [[phase transition]]—e.g. if ice is melting to water—as in these cases the system can absorb heat without increasing its temperature. In more complex systems, it is preferable to use the concept of [[internal energy]] rather than that of thermal energy (see [[#Chemical energy|''Chemical energy'' below]]).

Despite the theoretical problems, the above definition is useful in the experimental measurement of energy changes. In a wide variety of situations, it is possible to use the energy released by a system to raise the temperature of another object, e.g. a bath of water. It is also possible to measure the amount of [[electric energy]] required to raise the temperature of the object by the same amount. The [[calorie]] was originally defined as the amount of energy required to raise the temperature of one gram of water by 1&nbsp;°C (approximately 4.1855&nbsp;J, although the definition later changed), and the [[British thermal unit]] was defined as the energy required to heat one [[gallon]] (UK) of water by 1&nbsp;[[degree Fahrenheit|°F]] (later fixed as 1055.06&nbsp;J).

=== Electric energy ===
{{main|Electromagnetism|Electricity}}
{| class="wikitable" align=right width=150px
|-
|+ Examples of the interconversion of energy
|-
! colspan=2 | Electric energy is converted
|-
! into
! by
|-
| '''[[Mechanical energy]]'''
| [[Electric motor]]
|-
| '''[[Thermal energy]]'''
| [[Resistor]]
|-
| '''[[Electric energy]]'''
| [[Transformer]]
|-
| '''[[Electromagnetic radiation]]'''
| [[Light-emitting diode]]
|-
| '''[[Chemical energy]]'''
| [[Electrolysis]]
|-
| '''[[Nuclear energy]]'''
| [[Synchrotron]]
|-
|}

The [[electric potential energy]] of given configuration of charges is defined as the [[work (thermodynamics)|work]] which must be done against the [[Coulomb force]] to rearrange charges from infinite separation to this configuration (or the work done by the Coulomb force separating the charges from this configuration to infinity). For two point-like charges ''Q''<sub>1</sub> and ''Q''<sub>2</sub> at a distance ''r'' this work, and hence electric potential energy is equal to:
::<math>E_{\rm p,e} = {1\over {4\pi\epsilon_0}}{{Q_1Q_2}\over{r}}</math>
where ε<sub>0</sub> is the [[electric constant]] of a vacuum, 10<sup>7</sup>/4π''c''<sub>0</sub>² or 8.854188…×10<sup>&minus;12</sup>&nbsp;F/m.<ref name="CODATA"/> If the charge is accumulated in a [[capacitor]] (of [[capacitance]] ''C''), the reference configuration is usually selected not to be infinite separation of charges, but vice versa - charges at an extremely close proximity to each other (so there is zero net charge on each plate of a capacitor). In this case the work and thus the electric potential energy becomes
::<math>E_{\rm p,e} = {{Q^2}\over{2C}}</math>

If an [[electric current]] passes through a [[resistor]], electric energy is converted to heat; if the current passes through an electric appliance, some of the electric energy will be converted into other forms of energy (although some will always be lost as heat). The amount of electric energy due to an electric current can be expressed in a number of different ways:
::<math>E = UQ = UIt = Pt = U^2t/R</math>
where ''U'' is the [[electric potential difference]] (in [[volt]]s), ''Q'' is the charge (in [[coulomb]]s), ''I'' is the current (in [[ampere]]s), ''t'' is the time for which the current flows (in seconds), ''P'' is the [[power (physics)|power]] (in [[watt]]s) and ''R'' is the [[electric resistance]] (in [[ohm]]s). The last of these expressions is important in the practical measurement of energy, as potential difference, resistance and time can all be measured with considerable accuracy.

==== Magnetic energy ====
There is no fundamental difference between magnetic energy and electric energy: the two phenomena are related by [[Maxwell's equations]]. The potential energy of a [[magnet]] of [[magnetic moment]] '''m''' in a [[magnetic field]] '''B''' is defined as the [[mechanical work|work]]  of magnetic force (actually of magnetic [[torque]]) on re-alignment of the vector of the magnetic dipole moment, and is equal:
::<math>E_{\rm p,m} = -m\cdot B</math>
while the energy stored in a [[inductor]] (of [[inductance]] ''L'') when current ''I'' is passing via it is

::<math>E_{\rm p,m} = {1\over 2}LI^2</math>.
This second expression forms the basis for [[superconducting magnetic energy storage]].

====Electromagnetic fields====

{| class="wikitable" align=right width=150px
|-
|+ Examples of the interconversion of energy
|-
! colspan=2 | Electromagnetic radiation is converted
|-
! into
! by
|-
| '''[[Mechanical energy]]'''
| [[Solar sail]]
|-
| '''[[Thermal energy]]'''
| [[Solar collector]]
|-
| '''[[Electric energy]]'''
| [[Solar cell]]
|-
| '''[[Electromagnetic radiation]]'''
| [[Non-linear optics]]
|-
| '''[[Chemical energy]]'''
| [[Photosynthesis]]
|-
| '''[[Nuclear energy]]'''
| [[Mössbauer spectroscopy]]
|-
|}

Calculating [[mechanical work|work]] needed to create an electric or magnetic field in unit volume (say, in a capacitor or an inductor) results in the electric and magnetic fields [[energy density|energy densities]]: 

::<math> u_e=\frac{\epsilon_0}{2} E^2 </math> 
and 
::<math> u_m=\frac{1}{2\mu_0} B^2 </math>,
in SI units.

Electromagnetic radiation, such as [[microwave]]s, [[visible light]] or [[gamma ray]]s, represents a flow of electromagnetic energy. Applying the above expressions to magnetic and electric components of electromagnetic field both the volumetric density and the flow of energy in e/m field can be calculated.   The resulting [[Poynting vector]], which is expressed as
::<math>\mathbf{S} = \frac{1}{\mu} \mathbf{E} \times \mathbf{B},</math>
in SI units, gives the density of the flow of energy and its direction.

The energy of electromagnetic radiation is quantized (has discrete [[energy levels]]). The spacing between these levels is equal to 

::<math>E = h\nu</math>

where ''h'' is the [[Planck constant]], 6.6260693(11)×10<sup>&minus;34</sup>&nbsp;Js,<ref name="CODATA"/> and ''ν'' is the [[frequency]] of the radiation.  This quantity of electromagnetic energy is usually called a photon. The photons which make up visible light have energies of 270–520&nbsp;yJ, equivalent to 160–310&nbsp;kJ/mol, the strength of weaker [[chemical bond]]s.

=== Chemical energy ===
{{main|Chemical thermodynamics}}
{| class="wikitable" align=right width=150px
|-
|+ Examples of the interconversion of energy
|-
! colspan=2 | Chemical energy is converted
|-
! into
! by
|-
| '''[[Mechanical energy]]'''
| [[Muscle]]
|-
| '''[[Thermal energy]]'''
| [[Fire]]
|-
| '''[[Electric energy]]'''
| [[Fuel cell]]
|-
| '''[[Electromagnetic radiation]]'''
| [[Glowworm]]s
|-
| '''[[Chemical energy]]'''
| [[Chemical reaction]]
|-
|}

[[Chemical energy]] is the energy due to associations of atoms in molecules and various other kinds of aggregrates of [[matter]]. It may be defined as a work done by electric forces during re-arrangement of electric charges, electrons and protons, in the process of aggregration.  If the chemical energy of a system decreases during a chemical reaction, it is transferred to the surroundings in some form of energy (often [[heat]]); on the other hand if the chemical energy of a system increases as a result of a [[chemical reaction]] - it is by converting another form of energy from the surroundings. For example,
:when two [[hydrogen]] atoms react to form a dihydrogen molecule, the chemical energy ''decreases'' by 724&nbsp;zJ (the [[bond energy]] of the H–H bond);
:when the electron is completely removed from a hydrogen atom, forming a hydrogen ion (in the gas phase), the chemical energy ''increases'' by 2.18&nbsp;aJ (the [[ionization energy]] of hydrogen).
It is common to quote the changes in chemical energy for one [[mole (unit)|mole]] of the substance in question: typical values for the change in molar chemical energy during a chemical reaction range from tens to hundreds of kJ/mol.

The chemical energy as defined above is also referred to by [[chemists]] as the [[internal energy]], ''U'': technically, this is measured by keeping the [[volume]] of the system constant. However, most practical chemistry is performed at constant pressure and, if the volume changes during the reaction (e.g. a gas is given off), a correction must be applied to take account of the work done by or on the atmosphere to obtain the [[enthalpy]], ''H'':
::&Delta;''H'' = &Delta;''U'' + ''p''&Delta;''V''
A second correction, for the change in [[entropy]], ''S'', must also be performed to determine whether a chemical reaction will take place or not, giving the [[Gibbs free energy]], ''G'':
::&Delta;''G'' = &Delta;''H'' &minus; ''T''&Delta;''S''
These corrections are sometimes negligible, but often not (especially in reactions involving gases).

Since the [[industrial revolution]], the [[combustion|burning]] of [[coal]], [[oil]], [[natural gas]] or products derived from them has been a socially significant transformation of chemical energy into other forms of energy. the energy "consumption" (one should really speak of "energy transformation") of a society or country is often quoted in reference to the average energy released by the [[combustion]] of these [[fossil fuel]]s:
:1&nbsp;[[tonne of coal equivalent]] (TCE) = 29&nbsp;GJ
:1&nbsp;[[tonne of oil equivalent]] (TOE) = 41.87&nbsp;GJ
On the same basis, a tank-full of [[gasoline]] (45&nbsp;litres, 12&nbsp;gallons) is equivalent to about 1.6&nbsp;GJ of chemical energy. Another chemically-based unit of measurement for energy is the "tonne of [[Trinitrotoluene|TNT]]", taken as 4.184&nbsp;GJ. Hence, burning a tonne of oil releases about ten times as much energy as the explosion of one&nbsp;tonne of TNT: fortunately, the energy is usually released in a slower, more controlled manner.

Simple examples of chemical energy are batteries and food. When you eat the food is digested and turned into chemical energy which can be transformed to kinetic energy.

===Nuclear energy===
{{main|Nuclear binding energy}}
{| class="wikitable" align=right width=150px
|-
|+ Examples of the interconversion of energy
|-
! colspan=2 | Nuclear binding energy is converted
|-
! into
! by
|-
| '''[[Mechanical energy]]'''
| [[Alpha radiation]]
|-
| '''[[Thermal energy]]'''
| [[Sun]]
|-
| '''[[Electric energy]]'''
| [[Beta radiation]]
|-
| '''[[Electromagnetic radiation]]'''
| [[Gamma radiation]]
|-
| '''[[Chemical energy]]'''
| [[Radioactive decay]]
|-
| '''[[Nuclear energy]]'''
| [[Nuclear isomerism]]
|-
|}

'''[[Nuclear Energy|Nuclear potential energy]]''', along with [[electric potential energy]], provides the energy released from [[nuclear fission]] and [[nuclear fusion]] processes. The result of both these processes are nuclei in which [[strong nuclear force]]s bind nuclear particles more strongly and closely. [[Weak nuclear force]]s (different from strong forces) provide the potential energy for certain kinds of radioactive decay, such as [[beta decay]]. The energy released in nuclear processes is so large that the relativistic change in mass (after the energy has been removed) can be as much as several parts per thousand. 

Nuclear particles ([[nucleon]]s) like protons and neutrons are ''not'' destroyed (law of conservation of [[baryon number]]) in fission and fusion processes. A few lighter particles may be created or destroyed (example: beta minus and beta plus decay, or electron capture decay), but these minor processes are not important to the immediate energy release in fission and fusion. Rather, fission and fusion release energy when collections of baryons become more tightly bound, and it is the energy associated with a fraction of the mass of the nucleons (but not the whole particles) which appears as the heat and electromagnetic radiation generated by nuclear reactions. This heat and radiation retains the "missing" mass, but the mass is missing only because it escapes in the form of heat and light, which retain the mass and conduct it out of the system where it is not measured. The energy from the [[Sun]], also called [[solar energy]], is an example of this form of energy conversion. In the [[Sun]], the process of hydrogen fusion converts about 4 million metric tons of solar matter per second into light, which is radiated into space, but during this process, the number of total protons and neutrons in the sun does not change. In this system, the light itself retains the inertial equivalent of this mass, and indeed the mass itself (as a system), which represents 4 million tons per second of electromagnetic radiation, moving into space. Each of the helium nuclei which are formed in the process are less massive than the four protons from they were formed, but (to a good approximation), no particles or atoms are destroyed in the process of turning the sun's nuclear potential energy into light.

===Surface energy===

If there is any kind of tension in a surface, such as a stretched sheet of rubber or material interfaces, it is possible to define '''surface energy'''. In particular, any meeting of dissimilar materials that don't mix will result in some kind of [[surface tension]], if there is freedom for the surfaces to move then, as seen in [[capillary surface]]s for example, the minimum energy will as usual be sought.

A [[minimal surface]], for example, represents the smallest possible energy that a surface can have if its energy is proportional to the area of the surface. For this reason, (open) soap films of small size are minimal surfaces (small size reduces gravity effects, and openness prevents pressure from building up. Note that a bubble is a minimum energy surface but not a [[minimal surface]] by definition).

==Transformations of energy==

{{Main|Energy conversion}}

One form of energy can often be readily transformed into another with the help of a device- for instance, a battery, from [[chemical energy]] to [[electric energy]]; a [[dam]]: [[gravitational potential energy]] to [[kinetic energy]] of moving [[water]] (and the blades of a [[turbine]]) and ultimately to [[electric energy]] through an [[electric generator]]. Similarly, in the case of a [[Chemical explosive|chemical explosion]], [[chemical potential]] energy is transformed to [[kinetic energy]] and [[thermal energy]] in a very short time. Yet another example is that of a [[pendulum]]. At its highest points the [[kinetic energy]] is zero and the [[gravitational potential energy]] is at maximum. At its lowest point the [[kinetic energy]] is at maximum and is equal to the decrease of [[potential energy]]. If one (unrealistically) assumes that there is no [[friction]], the conversion of energy between these processes is perfect, and the [[pendulum]] will continue swinging forever.

Energy can be converted into [[matter]] and vice versa.  The [[mass-energy equivalence]] formula ''E''&nbsp;=&nbsp;''mc''², derived independently by [[Albert Einstein]] and [[Henri Poincaré]],{{Fact|date=April 2007}} quantifies the relationship between mass and rest energy.  Since <math>c^2</math> is extremely large relative to ordinary human scales, the conversion of mass to other forms of energy can liberate tremendous amounts of energy, as can be seen in nuclear reactors and nuclear weapons.  Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (particles) are found in high energy [[nuclear physics]].

In nature, transformations of energy can be fundamentally classed into two kinds: those that are thermodynamically [[Reversible process (thermodynamics)|reversible]], and those that are thermodynamically [[Irreversibility|irreversible]]. A [[reversible process (thermodynamics)|reversible process in thermodynamics]] is one in which no energy is dissipated into empty quantum states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, however, quantum states of lower energy, present as possible exitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomization in a crystal). 

As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic [[heat death]] of the universe. In this [[heat death]] the energy of the universe does not change, but the fraction of energy which is available to do work, or be transformed to other usable forms of energy, grows less and less.<!-- This is contradictory as written, since energy is defined above as work that one system can do upon another, and now you're saying this goes to zero over time, yet without the total "energy" changing. You can't have it both ways. It either goes to zero, or it stays the same. -->

==Law of conservation of energy==

{{Main|Conservation of energy}}
Energy is subject to the ''law of conservation of energy''. According to this law, energy can neither be created (produced) nor destroyed itself. It can only be transformed. 

Most kinds of energy (with gravitational energy being a notable exception)[http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html] are also subject to strict local conservation laws, as well. In this case, energy can only be exchanged between adjacent regions of space, and all observers agree as to the volumetric density of energy in any given space. There is also a global law of conservation of energy, stating that the total energy of the universe cannot change; this is a corollary of the local law, but not vice versa.<ref name="RPF1">{{cite book |first=Richard |last=Feynman|title=The Feynman Lectures on Physics; Volume 1|date=1964|publisher=Addison Wesley|location=U.S.A| id=ISBN 0-201-02115-3}}</ref><ref name="thermo-laws">[http://www.av8n.com/physics/thermo-laws.htm ''The Laws of Thermodynamics''] including careful definitions of energy, free energy, et cetera.</ref>  [[Conservation of energy]] is the mathematical consequence of [[translational symmetry]] of [[time]] (that is, the indistinguishability of time intervals taken at different time)<ref>[http://ptolemy.eecs.berkeley.edu/eecs20/week9/timeinvariance.html Time Invariance<!-- Bot generated title -->]</ref> - see [[Noether's theorem]].

According to [[energy conservation]] law the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system.   

This law is a fundamental principle of physics. It follows from the [[translational symmetry]] of [[time]], a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. 

Because energy is quantity which is [[canonical conjugate]] to time, it is impossible to define exact amount of energy during any definite time interval - making it impossible to apply the law of conservation of energy.  This must not be considered a "violation" of the law.  We know the law still holds, because a succession of short time periods does not ''accumulate'' any violation of conservation of energy.

In [[quantum mechanics]] energy is expressed using the Hamiltonian [[operator]].  On
any time scales, the uncertainty in the energy is by 

: <math>\Delta E \Delta t \ge \frac {h} {2 \pi} </math>

which is similar in form to the [[Heisenberg Uncertainty Principle|uncertainty principle]] (but not really mathematically equivalent thereto, since ''H'' and ''t'' are not dynamically conjugate variables, neither in classical nor in quantum mechanics).

In [[particle physics]], this inequality permits a qualitative understanding of [[virtual particles]] which carry [[momentum]], exchange by which with real particles is responsible for creation of all known [[fundamental forces]] (more accurately known as [[fundamental interactions]]). [[Virtual photons]] (which are simply lowest quantum mechanical [[energy state]] of [[photon]]s) are also responsible for electrostatic interaction between [[electric charge]]s (which results in [[Coulomb law]]), for [[Spontaneous fission|spontaneous]] radiative decay of exited atomic and nuclear states, for the [[Casimir force]], for [[van der Waals force|van der Waals bond forces]] and some other observable phenomena.

== Energy and life ==
{{main|Bioenergetics}}
Any living organism relies on an external source of energy—radiation from the Sun in the case of green plants; chemical energy in some form in the case of animals—to be able to grow and reproduce. The daily 1500–2000&nbsp;[[kilocalorie|Calories]] (6–8&nbsp;MJ) recommended for a human adult are taken as a combination of oxygen and food molecules, the latter mostly carbohydrates and fats, of which [[glucose]] (C<sub>6</sub>H<sub>12</sub>O<sub>6</sub>) and [[stearin]] (C<sub>57</sub>H<sub>110</sub>O<sub>6</sub>) are convenient examples. The food molecules are oxidised to [[carbon dioxide]] and [[water (molecule)|water]] in the [[Mitochondrion|mitochondria]]
::C<sub>6</sub>H<sub>12</sub>O<sub>6</sub> + 6O<sub>2</sub> &rarr; 6CO<sub>2</sub> + 6H<sub>2</sub>O
::C<sub>57</sub>H<sub>110</sub>O<sub>6</sub> + 81.5O<sub>2</sub> &rarr; 57CO<sub>2</sub> + 55H<sub>2</sub>O
and some of the energy is used to convert [[Adenosine diphosphate|ADP]] into [[Adenosine triphosphate|ATP]]
::ADP + HPO<sub>4</sub><sup>2&minus;</sup> &rarr; ATP + H<sub>2</sub>O
The rest of the chemical energy in the carbohydrate or fat is converted into heat: the ATP is used as a sort of "energy currency", and some of the chemical energy it contains when split and reacted with water, is used for other [[metabolism]] (at each stage of a [[metabolic pathway]], some chemical energy is converted into heat). Only a tiny fraction of the original chemical energy is used for work:<ref>These examples are solely for illustration, as it is not the energy available for work which limits the performance of the athlete but the [[power (physics)|power]] output of the sprinter and the [[force (physics)|force]] of the weightlifter. A worker stacking shelves in a supermarket does more work (in the physical sense) than either of the athletes, but does it more slowly.</ref>
:gain in kinetic energy of a sprinter during a 100&nbsp;m race: 4&nbsp;kJ
:gain in gravitational potential energy of a 150&nbsp;kg weight lifted through 2&nbsp;metres: 3kJ
:Daily food intake of a normal adult: 6–8&nbsp;MJ 

It would appear that living organisms are remarkably [[Energy efficiency|inefficient (in the physical sense)]] in their use of the energy they receive (chemical energy or radiation), and it is true that most real [[machine]]s manage higher efficiencies. However, in growing organisms the energy that is converted to heat serves a vital purpose, as it allows the organism tissue to be highly ordered with regard to the molecules it is built from. The [[second law of thermodynamics]] states that energy (and matter) tends to become more evenly spread out across the universe: to concentrate energy (or matter) in one specific place, it is necessary to spread out a greater amount of energy (as heat) across the remainder of the universe ("the surroundings").<ref>[[Crystal]]s are another example of highly ordered systems that exist in nature: in this case too, the order is associated with the transfer of a large amount of heat (known as the [[lattice energy]]) to the surroundings.</ref> Simpler organisms can achieve higher energy efficiencies than more complex ones, but the complex organisms can occupy [[ecological niche]]s that are not available to their simpler brethren. The conversion of a portion of the chemical energy to heat at each step in a metabolic pathway is the physical reason behind the pyramid of biomass observed in [[ecology]]: to take just the first step in the [[food chain]], of the estimated 124.7&nbsp;Pg/a of carbon that is [[carbon fixation|fixed]] by [[photosynthesis]], 64.3&nbsp;Pg/a (52%) are used for the metabolism of green plants,<ref>Ito, Akihito; Oikawa, Takehisa (2004). "[http://www.terrapub.co.jp/e-library/kawahata/pdf/343.pdf Global Mapping of Terrestrial Primary Productivity and Light-Use Efficiency with a Process-Based Model.]" in Shiyomi, M. et al. (Eds.) ''Global Environmental Change in the Ocean and on Land.'' pp.&nbsp;343–58.</ref> i.e. reconverted into carbon dioxide and heat.

==See also==
{{Portal|Energy}}
{{Portal|Physics}}
<div style="-moz-column-count:3; column-count:3;">
* [[Activation energy]]
* [[American Museum of Science and Energy]] (AMSE)
* [[Americans for Balanced Energy Choices]] (ABEC)
* [[Enthalpy]]
* [[Energy conservation]]
* [[Entropy]]
* [[Interaction energy]]
* [[Internal energy]]
* [[List of energy topics]]
* [[Vacuum energy|Negative energy]]
* [[Orders of magnitude (energy)]]
* [[Power (physics)]]
* [[Renewable energy]]
* [[Solar radiation]]
* [[Thermodynamic free energy]]
* [[Thermodynamics]]
* [[Units of energy]]
* [[World energy resources and consumption]]
</div>

== Notes and references ==
<div class="references-small">
<references/>
</div>

==Further reading==
* {{cite book |first=G. N. |last=Alekseev|title=Energy and Entropy |date=1986 |publisher=Mir Publishers |location=Moscow }}
* {{cite book |author=Walding, Richard,&nbsp; Rapkins, Greg,&nbsp; Rossiter, Glenn |title=New Century Senior Physics |date=1999-11-01 |publisher=Oxford University Press |location=Melbourne, Australia |id=ISBN 0-19-551084-4}}

==External links==
{{sisterlinks|Energy}}
* [http://www.lightandmatter.com/html_books/2cl/ch01/ch01.html Conservation of Energy] - a chapter from an online textbook
*{{PDFlink|[http://physnet.org/home/modules/pdf_modules/m20.pdf ''Work, Power, Kinetic Energy'']|399&nbsp;[[Kibibyte|KiB]]<!-- application/pdf, 408788 bytes -->}} on [http://www.physnet.org Project PHYSNET]
* [http://www.physicsweb.org/article/world/15/7/2 What does energy really mean? From Physics World]
* [http://www.our-energy.com/en.html Compact description of various energy sources. Energy sources and ecology.]
* [http://www.energy.ca.gov/glossary/ Glossary of Energy Terms]
* [http://www.scribd.com/doc/1115/Energy-for-Kids/ Energy for kids]
*[http://www.arabianbusiness.com/energy/ Middle East Energy & Power News] — ''ArabianBusiness.com''
*[http://www.energyliteracy.org/compare.html Energy Source Comparisons] by [[Energy Literacy Advocates]]



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[[ast:Enerxía (física)]]
[[az:Enerji]]
[[bn:শক্তি]]
[[zh-min-nan:Lêng-liōng]]
[[bs:Energija]]
[[br:Energiezh]]
[[bg:Енергия]]
[[ca:Energia]]
[[cs:Energie]]
[[da:Energi]]
[[de:Energie]]
[[et:Energia]]
[[el:Ενέργεια]]
[[es:Energía (física)]]
[[eo:Energio]]
[[eu:Energia]]
[[fa:انرژی]]
[[fr:Énergie]]
[[gl:Enerxía]]
[[ko:에너지]]
[[hi:ऊर्जा]]
[[hr:Energija]]
[[io:Energio]]
[[id:Energi]]
[[ia:Energia]]
[[is:Orka]]
[[it:Energia]]
[[he:אנרגיה]]
[[ht:Enèji]]
[[ku:Wize]]
[[la:Energia]]
[[lv:Enerģija]]
[[lb:Energie]]
[[lt:Energija]]
[[ln:Molungé]]
[[hu:Energia]]
[[mk:Енергија]]
[[ml:ഊര്‍ജം]]
[[mr:ऊर्जा]]
[[ms:Tenaga]]
[[mn:Энерги]]
[[nah:Teōtl]]
[[nl:Energie]]
[[ja:エネルギー]]
[[no:Energi]]
[[nn:Energi]]
[[nov:Energie]]
[[oc:Energia]]
[[nds:Energie]]
[[pl:Energia (fizyka)]]
[[pt:Energia]]
[[ro:Energie]]
[[qu:Micha]]
[[ru:Энергия]]
[[sq:Energjia]]
[[simple:Energy]]
[[sk:Energia]]
[[sl:Energija]]
[[sr:Енергија]]
[[sh:Energija]]
[[fi:Energia]]
[[sv:Energi]]
[[ta:ஆற்றல்]]
[[th:พลังงาน]]
[[vi:Năng lượng]]
[[tg:Энергия]]
[[tr:Enerji]]
[[uk:Енергія]]
[[ur:توانائی]]
[[vec:Energia]]
[[wo:Kàttan]]
[[yi:ענערגיע]]
[[zh-yue:能量]]
[[bat-smg:Energėjė]]
[[zh:能量]]

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