TheInfoList

In
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

, energy is the quantitative
property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, r ...
that must be transferred to a
body Body may refer to: In science * Physical body, an object in physics that represents a large amount, has mass or takes up space * Body (biology), the physical material of an organism * Body plan, the physical features shared by a group of animals ...
or
physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environment. The environment is ignored except ...
to perform
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...
on the body, or to
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 ...

it. Energy is a
conserved quantity In mathematics, a conserved quantity of a dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in a Manifold, geometrical space. ...
; the law of
conservation of 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 s ...
states that energy can be
converted Conversion or convert may refer to: Arts, entertainment, and media * Conversion (Doctor Who audio), "Conversion" (''Doctor Who'' audio), an episode of the audio drama ''Cyberman'' * Conversion (Stargate Atlantis), "Conversion" (''Stargate Atlantis ...
in form, but not created or destroyed. The unit of measurement in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
(SI) of energy is the
joule The joule ( ; symbol: J) is a derived unit of 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 ...

, which is the energy transferred to an object by the
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...

of moving it a distance of one
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English ...
against a
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

of one
newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...
. Common forms of energy include the
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 a moving object, the
potential energy In physics, potential energy is the energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...

stored by an object's position in a force
field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grassl ...
(
gravitational Gravity (), or gravitation, is a natural phenomenon by which all things with mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an ...

,
electric Electricity is the set of physics, physical Phenomenon, phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnet ...

or
magnetic Magnetism is a class of physical attributes that are mediated by s. s and the s of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. Magnetism is one aspect of the combined phenomenon of . The ...

), the
elastic energy Elastic energy is the mechanical potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of ...
stored by stretching solid objects, the
chemical energy Chemical energy is the energy of chemical substance A chemical substance is a form 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 th ...
released when a fuel
burns Matthew James Burns (born 31 October 1985), better known mononym A mononymous person is an individual who is known and addressed by a single name, or mononym. In some cases, that name has been selected by the individual, who may have originall ...
, the
radiant 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 succ ...
carried by light, and 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 are defined as types of energy transfer (as is ...
due to an object's
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 ...

.
Mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
and energy are closely related. Due to
mass–energy equivalence 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 ...
, any object that has mass when stationary (called
rest mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** ...
) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after
heating File:Pelletkessel in Wohnhaus.JPG, upHot water central heating unit, using wood as fuel A central heating system provides warmth to the number of spaces within a building and optionally also able to heat water heating, domestic hot water from one ...

an object, its increase in energy could in principle be measured as a small increase in mass, with a sensitive enough
scale Scale or scales may refer to: Mathematics * Scale (descriptive set theory)In the mathematical discipline of descriptive set theory, a scale is a certain kind of object defined on a set (mathematics), set of point (mathematics), points in some Poli ...

. Living
organism In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological ...

s require energy to stay alive, such as the energy humans get from food and oxygen. Human civilization requires energy to function, which it gets from
energy resource The energy industry is the totality of all of the industries involved in the production and sale of energy In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phý ...
s such as
fossil fuel A fossil fuel is a hydrocarbon In , a hydrocarbon is an consisting entirely of and . Hydrocarbons are examples of s. Hydrocarbons are generally colourless and hydrophobic with only weak odours. Because of their diverse molecular structure ...
s,
nuclear fuel Nuclear fuel is material used in nuclear power stations to produce heat to power turbines. Heat is created when nuclear fuel undergoes nuclear fission. Most nuclear fuels contain heavy fissile actinide elements that are capable of Fissile mate ...
, or
renewable energy Renewable energy is energy that is collected from renewable resource File:Global Vegetation.jpg, Global vegetation A renewable resource, also known as a flow resource, is a natural resource which will replenish to replace the portion resou ...
. The processes of Earth's
climate Climate is the long-term pattern of weather Weather is the state of the atmosphere An atmosphere (from the greek words ἀτμός ''(atmos)'', meaning 'vapour', and σφαῖρα ''(sphaira)'', meaning 'ball' or 'sphere') is a la ...

and
ecosystem An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...

are driven by the radiant energy Earth receives from the Sun and the
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 ...
contained within the earth.

# Forms

The total energy of a
system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purp ...

can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways.
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 ...
is determined by the
movement Movement may refer to: Common uses * Movement (clockwork), the internal mechanism of a timepiece * Motion (physics), commonly referred to as movement Arts, entertainment, and media Literature * Movement (short story), "Movement", a shor ...
of an object – or the
composite motionIn deliberative procedure, compositing is the process of combining several motion (democracy), motions into one composite motion.BBC News https://www.bbc.co.uk/news/uk-politics-34357018 The process of compositing motions may be desirable for two rea ...
of the components of an object – and
potential energy In physics, potential energy is the energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...

reflects the potential of an object to have motion, and generally is a function of the position of an object within a
field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grassl ...
or may be stored in the field itself. While these two categories are sufficient to describe all forms of energy, it is often convenient to refer to particular combinations of potential and kinetic energy as its own form. For example, the sum of translational and
rotational A rotation is a circular movement of an object around a center (or point) of rotation. The plane (geometry), geometric plane along which the rotation occurs is called the ''rotation plane'', and the imaginary line extending from the center an ...
kinetic and potential energy within a system is referred to as
mechanical energy In physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "p ...
, whereas nuclear energy refers to the combined potentials within an atomic nucleus from either the
nuclear force The nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1 ...

or the
weak force Weak may refer to: Songs * "Weak" (AJR song), 2016 * "Weak" (Melanie C song), 2011 * Weak (SWV song), "Weak" (SWV song), 1993 * Weak (Skunk Anansie song), "Weak" (Skunk Anansie song), 1995 * "Weak", a song by Seether from ''Seether: 2002-2013'' ...

, among other examples.

# History

The word ''energy'' derives from the grc, ἐνέργεια,
energeia In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, l ...
, activity, operation, which possibly appears for the first time in the work of
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questio ...

in the 4th century BC. In contrast to the modern definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness and pleasure. In the late 17th century,
Gottfried Leibniz Gottfried Wilhelm (von) Leibniz ; see inscription of the engraving depicted in the " 1666–1676" section. ( – 14 November 1716) was a German polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, " ...
proposed the idea of the lat,
vis viva ''Vis viva'' (from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the ...
, or living force, which 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 theorized that thermal energy consisted of the motions of the constituent parts of matter, although it would be more than a century until this was generally accepted. The modern analog of this property,
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 ...
, differs from ''vis viva'' only by a factor of two. Writing in the early 18th century,
Émilie du Châtelet Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (; 17 December 1706 – 10 September 1749) was a French French (french: français(e), link=no) may refer to: * Something of, from, or related to France France (), officiall ...
proposed the concept of
conservation of 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 s ...
in the marginalia of her French language translation of Newton's ''
Principia Mathematica Image:Principia Mathematica 54-43.png, 500px, ✸54.43: "From this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2." – Volume I, 1st editionp. 379(p. 362 in 2nd edition; p. 360 in abridged v ...
'', which represented the first formulation of a conserved measurable quantity that was distinct from
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

, and which would later be called "energy". In 1807, was possibly the first to use the term "energy" instead of ''vis viva'', in its modern sense. Gustave-Gaspard Coriolis described "
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 ...
" in 1829 in its modern sense, and in 1853,
William Rankine William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a founding contributor, with Rudolf Clausius and William Thomson, 1 ...
coined the term "
potential energy In physics, potential energy is the energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...

". The law of
conservation of 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 s ...
was also first postulated in the early 19th century, and applies to any
isolated system In physical science, an isolated system is either of the following: # a physical system In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , i ...
. It was argued for some years whether heat was a physical substance, dubbed the caloric, or merely a physical quantity, such as
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

. In 1845
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 research The scientific method is an Empirical evidence, empirical m ...

discovered the link between mechanical work and the generation of heat. These developments led to the theory of conservation of energy, formalized largely by William Thomson (
Lord Kelvin William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of ...

) as the field of
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 ...

. Thermodynamics aided the rapid development of explanations of chemical processes by
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citize ...
,
Josiah Willard Gibbs Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in tr ...

, and
Walther Nernst Walther Hermann Nernst (25 June 1864 – 18 November 1941) was a German chemist known for his work in thermodynamics, physical chemistry, electrochemistry, and solid state physics. His formulation of the Nernst heat theorem helped pave the way f ...

. It also led to a mathematical formulation of the concept of
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

by Clausius and to the introduction of laws of
radiant 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 succ ...
by . According to
Noether's theorem Noether's theorem or Noether's first theorem states that every differentiable In calculus (a branch of mathematics), a differentiable function of one Real number, real variable is a function whose derivative exists at each point in its Domai ...
, the conservation of energy is a consequence of the fact that the laws of physics do not change over time. Thus, since 1918, theorists have understood that the law of
conservation of 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 s ...
is the direct mathematical consequence of the
translational symmetry In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space tha ...
of the quantity
conjugate Conjugation or conjugate may refer to: Linguistics * Grammatical conjugation, the modification of a verb from its basic form * Emotive conjugation or Russell's conjugation, the use of loaded language Mathematics * Complex conjugation, the change ...
to energy, namely time.

# Units of measure

In 1843, James Prescott Joule independently discovered the mechanical equivalent in a series of experiments. The most famous of them used the "Joule apparatus": a descending weight, attached to a string, caused rotation of a paddle immersed in water, practically insulated from heat transfer. It showed that the gravitational
potential energy In physics, potential energy is the energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...

lost by the weight in descending was equal to 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 ...
gained by the water through
friction Friction is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, st ...

International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
(SI), the unit of energy is the joule, named after Joule. It is a derived unit. It is equal to the energy expended (or
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...

done) in applying a force of one newton through a distance of one metre. However energy is also expressed in many other units not part of the SI, such as
erg The erg is a unit of energy equal to 10−7joule The joule ( ; symbol: J) is a SI derived unit, derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work (physics), work done on) an objec ...
s,
calorie The calorie is a unit of energy Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a di ...
s,
British Thermal Unit The British thermal unit (BTU or Btu) is a unit of 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 physica ...
s,
kilowatt-hour The kilowatt-hour ( SI symbol: kW⋅h or kW h; commonly written as kWh) is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, ...
s and
kilocalorie The calorie is a unit of energy Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a di ...
s, which require a conversion factor when expressed in SI units. The SI unit of energy rate (energy per unit time) is the
watt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...

, which is a joule per second. Thus, one joule is one watt-second, and 3600 joules equal one watt-hour. The CGS energy unit is the
erg The erg is a unit of energy equal to 10−7joule The joule ( ; symbol: J) is a SI derived unit, derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work (physics), work done on) an objec ...
and the imperial and US customary unit is the
foot pound The foot-pound force (symbol: ft⋅lbf, ft⋅lbf, or ft⋅lb ) is a unit of work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work d ...
. Other energy units such as the
electronvolt 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 suc ...
,
food calorie The calorie is a unit of energy Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a di ...
or thermodynamic
kcal The calorie is a unit of energy Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a di ...
(based on the temperature change of water in a heating process), and
BTU The British thermal unit (BTU or Btu) is a unit of 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 ...
are used in specific areas of science and commerce.

# Scientific use

## Classical mechanics

In classical mechanics, energy is a conceptually and mathematically useful property, as it is a
conserved quantity In mathematics, a conserved quantity of a dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in a Manifold, geometrical space. ...
. Several formulations of mechanics have been developed using energy as a core concept.
Work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...

, a function of energy, is force times distance. : $W = \int_C \mathbf \cdot \mathrm \mathbf$ This says that the work ($W$) is equal to the
line integral In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
of the
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

F along a path ''C''; for details see the
mechanical work In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
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. The total energy of a system is sometimes called the Hamiltonian, after
William Rowan Hamilton Sir William Rowan Hamilton LL.D, DCL, MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician, Andrews Professor of Astronomy at Trinity College Dublin, Trinity College Dublin, and Dunsink Observatory#Directors, Royal Astronomer ...
. 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. Another energy-related concept is called the Lagrangian, after
Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangiaclassical mechanics, but is generally useful in modern physics. The Lagrangian is defined as the kinetic energy ''minus'' the potential energy. Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (such as systems with friction).
Noether's theorem Noether's theorem or Noether's first theorem states that every differentiable In calculus (a branch of mathematics), a differentiable function of one Real number, real variable is a function whose derivative exists at each point in its Domai ...
(1918) states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalisation of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian; for example, dissipative systems with continuous symmetries need not have a corresponding conservation law.

## Chemistry

In the context of
chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in the real world. T ...

,
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 ...
is an attribute of a substance as a consequence of its atomic, molecular, or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is usually accompanied by a decrease, and sometimes an increase, of the total energy of the substances involved. Some energy may be transferred between the surroundings and the reactants in the form of heat or light; thus the products of a reaction have sometimes more but usually less energy than the reactants. A reaction is said to be
exothermic 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 qu ...
or
exergonic An exergonic process is one which there is a positive flow of energy from the system to the surroundings. This is in contrast with an endergonic In chemical thermodynamics Chemical thermodynamics is the study of the interrelation of heat ...

if the final state is lower on the energy scale than the initial state; in the less common case of
endothermic In thermochemistry Thermochemistry is the study of the heat energy which is associated with chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substanc ...
reactions the situation is the reverse.
Chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...

s are usually not possible unless the reactants surmount an energy barrier known as the
activation energy In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...

. The ''speed'' of a chemical reaction (at a given temperature ''T'') is related to the activation energy ''E'' by the Boltzmann's population factor e−''E''/''kT''; that is, the probability of a molecule to have energy greater than or equal to ''E'' at a given temperature ''T''. This exponential dependence of a reaction rate on temperature is known as the
Arrhenius equation In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 ...
. The activation energy necessary for a chemical reaction can be provided in the form of thermal energy.

## Biology

In
biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechanisms, Development ...

, energy is an attribute of all biological systems, from the biosphere to the smallest living organism. Within an organism it is responsible for growth and development of a biological cell or
organelle In cell biology Cell biology (also cellular biology or cytology) is a branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, ...
of a biological organism. Energy used in
respiration Respiration may refer to: Biology * Cellular respiration, the process in which nutrients are converted into useful energy in a cell ** Anaerobic respiration, cellular respiration without oxygen ** Maintenance respiration, the amount of cellular ...
is mostly stored in molecular
oxygen Oxygen is the chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same ...

Schmidt-Rohr, K. (2020). "Oxygen Is the High-Energy Molecule Powering Complex Multicellular Life: Fundamental Corrections to Traditional Bioenergetics” ''ACS Omega'' 5: 2221–33. http://dx.doi.org/10.1021/acsomega.9b03352 and can be unlocked by reactions with molecules of substances such as
carbohydrate A carbohydrate () is a biomolecule , showing alpha helices, represented by ribbons. This poten was the first to have its suckture solved by X-ray crystallography by Max Perutz and Sir John Cowdery Kendrew in 1958, for which they received a ...
s (including sugars),
lipid In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechanis ...
s, and
protein Proteins are large biomolecule , showing alpha helices, represented by ribbons. This poten was the first to have its suckture solved by X-ray crystallography by Max Perutz and Sir John Cowdery Kendrew in 1958, for which they received a No ...

s stored by
cells Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Closed spaces * Monastic cell, a small room, hut, or cave in which a monk or religious recluse lives * Prison cell, a room used to hold peopl ...
. In human terms, the
human equivalentThe term human equivalent is used in a number of different contexts. This term can refer to human equivalents of various comparisons of animate and inanimate things. Animal models in chemistry and medicine Animal models are used to learn more abou ...
(H-e) (Human energy conversion) indicates, for a given amount of energy expenditure, the relative quantity of energy needed for human
metabolism Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life Life is a characteristic that distinguishes physical entities A bubble of exhaled gas in water In common usage and classical mechanics, a phys ...

, using as a standard an average human energy expenditure of 12,500 kJ per day and a basal metabolic rate of 80 watts. For example, if our bodies run (on average) at 80 watts, then a light bulb running at 100 watts is running at 1.25 human equivalents (100 ÷ 80) i.e. 1.25 H-e. For a difficult task of only a few seconds' duration, a person can put out thousands of watts, many times the 746 watts in one official horsepower. For tasks lasting a few minutes, a fit human can generate perhaps 1,000 watts. For an activity that must be sustained for an hour, output drops to around 300; for an activity kept up all day, 150 watts is about the maximum. The human equivalent assists understanding of energy flows in physical and biological systems by expressing energy units in human terms: it provides a "feel" for the use of a given amount of energy. Sunlight's radiant energy is also captured by plants as ''chemical potential energy'' in
photosynthesis Photosynthesis is a process used by plants and other organisms to convert Conversion or convert may refer to: Arts, entertainment, and media * Conversion (Doctor Who audio), "Conversion" (''Doctor Who'' audio), an episode of the audio drama ' ...

, when carbon dioxide and water (two low-energy compounds) are converted into carbohydrates, lipids, proteins and high-energy compounds like oxygen and ATP. Carbohydrates, lipids, and proteins can release the energy of oxygen, which is utilized by living organisms as an
electron acceptor An electron acceptor is a chemical entity that accepts electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle phy ...
. Release of the energy stored during photosynthesis as heat or light may be triggered suddenly by a spark in a forest fire, or it may be made available more slowly for animal or human metabolism when organic molecules are ingested and
catabolism Catabolism () is the set of metabolic Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life Life is a characteristic that distinguishes physical entities that have biological processes, such as Cell ...

is triggered by
enzyme Enzymes () are proteins that act as biological catalysts (biocatalysts). Catalysts accelerate chemical reactions. The molecules upon which enzymes may act are called substrate (chemistry), substrates, and the enzyme converts the substrates in ...

action. All living creatures rely on an external source of energy to be able to grow and reproduce – radiant energy from the Sun in the case of green plants and chemical energy (in some form) in the case of animals. The daily 1500–2000
Calories The calorie is a unit of energy defined as the amount of heat needed to raise the temperature of a quantity of water by one degree. For historical reasons, two main definitions of calorie are in wide use. The small calorie or gram calorie (usual ...
(6–8 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 Glucose is a simple with the . Glucose is the most abundant , a subcategory of s. Glucose is mainly made by and most during from water and carbon dioxide, using energy from sunlight, where it is used to make in s, the most abundant carbohydr ...

(C6H12O6) and
stearin Stearin , or tristearin, or glyceryl tristearate is an odourless, white powder. It is a triglyceride derived from three units of stearic acid. Most triglycerides are derived from at least two and more commonly three different fatty acid fatty a ...

(C57H110O6) are convenient examples. The food molecules are oxidized to
carbon dioxide Carbon dioxide (chemical formula A chemical formula is a way of presenting information about the chemical proportions of s that constitute a particular or molecule, using symbols, numbers, and sometimes also other symbols, such as pare ...

and
water Water (chemical formula H2O) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known li ...
in the
mitochondria A mitochondrion (; ) is a double-membrane A membrane is a selective barrier; it allows some things to pass through but stops others. Such things may be molecules, ions, or other small particles. Biological membranes include cell membranes ...

C6H12O6 + 6O2 -> 6CO2 + 6H2O C57H110O6 + (81 1/2) O2 -> 57CO2 + 55H2O and some of the energy is used to convert into
ATP ATP may refer to: Companies and organizations * Association of Tennis Professionals * American Technical Publishers * ', a Danish pension * Armenia Tree Project * Association for Transpersonal Psychology * ATP architects engineers office * ATP ...

: The rest of the chemical energy of O2 and the carbohydrate or fat are converted into heat: the ATP is used as a sort of "energy currency", and some of the chemical energy it contains is used for other
metabolism Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life Life is a characteristic that distinguishes physical entities A bubble of exhaled gas in water In common usage and classical mechanics, a phys ...

when ATP reacts with OH groups and eventually splits into ADP and phosphate (at each stage of a
metabolic pathway In biochemistry, a metabolic pathway is a linked series of chemical reactions occurring within a cell (biology), cell. The reactants, products, and intermediates of an enzymatic reaction are known as metabolites, which are modified by a sequence ...
, some chemical energy is converted into heat). Only a tiny fraction of the original chemical energy is used for
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...

: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 Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, p ...
output (in case of a sprinter) and the
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...
(in case of a weightlifter).
:gain in kinetic energy of a sprinter during a 100 m race: 4 kJ :gain in gravitational potential energy of a 150 kg weight lifted through 2 metres: 3 kJ :Daily food intake of a normal adult: 6–8 MJ It would appear that living organisms are remarkably inefficient (in the physical sense) in their use of the energy they receive (chemical or radiant energy); most
machine A machine is any physical system with ordered structural and functional properties. It may represent human-made or naturally occurring device molecular machine A molecular machine, nanite, or nanomachine is a molecular component that produc ...

s manage higher efficiencies. 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 The second law of thermodynamics establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
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").
Crystal A crystal or crystalline solid is a solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformatio ...

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 The lattice energy is the energy change on formation of one mole of an ionic compound In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: ...
) to the surroundings.
Simpler organisms can achieve higher energy efficiencies than more complex ones, but the complex organisms can occupy
ecological niche In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms ...

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 Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms In biol ...
. As an example, to take just the first step in the
food chain A food chain is a linear network of links in a food web A food web is the natural interconnection of food chains and a graphical representation of what-eats-what in an ecological community. Another name for food web is Consumer-resource sy ...

: of the estimated 124.7 Pg/a of carbon that is
fixed Fixed may refer to: * Fixed (EP), ''Fixed'' (EP), EP by Nine Inch Nails * ''Fixed'', an upcoming 3D adult animated film directed by Genndy Tartakovsky * Fixed (typeface), a collection of monospace bitmap fonts that is distributed with the X Window ...
by
photosynthesis Photosynthesis is a process used by plants and other organisms to convert Conversion or convert may refer to: Arts, entertainment, and media * Conversion (Doctor Who audio), "Conversion" (''Doctor Who'' audio), an episode of the audio drama ' ...

, 64.3 Pg/a (52%) are used for the metabolism of green plants, i.e. reconverted into carbon dioxide and heat.

## Earth sciences

In
geology Geology (from the Ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek ...
,
continental drift Continental drift is the hypothesis that the Earth's continent A continent is one of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, up to seven regions are commonly reg ...
, ,
volcano A volcano is a rupture in the crust of a planetary-mass object A planet is an astronomical body orbit In physics, an orbit is the gravitationally curved trajectory of an physical body, object, such as the trajectory of a planet a ...

es, and
earthquake An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth Earth is the third planet from the Sun and the only astronomical object known ...

s are phenomena that can be explained in terms of energy transformations in the Earth's interior, while
meteorological Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting Weather forecasting is the application of science and technology to predict the ...
phenomena like wind, rain,
hail Hail is a form of solid precipitation In meteorology Meteorology is a branch of the (which include and ), with a major focus on . The study of meteorology dates back , though significant progress in meteorology did not begin until ...

, snow, lightning,
tornado A tornado is a violently rotating column of air File:Atmosphere gas proportions.svg, Composition of Earth's atmosphere by volume, excluding water vapor. Lower pie represents trace gases that together compose about 0.043391% of the atmos ...

es and
hurricanes A tropical cyclone is a rapidly rotating storm, storm system characterized by a Low-pressure area, low-pressure center, a closed low-level atmospheric circulation, Beaufort scale, strong winds, and a spiral arrangement of thunderstorms that ...
are all a result of energy transformations in our
atmosphere An atmosphere (from the greek words ἀτμός ''(atmos)'', meaning 'vapour', and σφαῖρα ''(sphaira)'', meaning 'ball' or 'sphere') is a layer or a set of layers of gases surrounding a planet or other material body, that is held in ...

solar energy Solar energy is Solar irradiance, radiant light and heat from the Sun that is harnessed using a range of technologies such as solar power to generate electricity, solar thermal energy including solar water heating, and solar architecture. It ...

. Sunlight is the main input to
Earth's energy budget Earth's energy budget accounts for the balance between the energy that Earth receives from the Sun,Earth's internal heat and other small effects, that are indeed taken into consideration, are thousand times smaller; see and the energy the Earth ...
which accounts for its temperature and climate stability. Sunlight may be stored as gravitational potential energy after it strikes the Earth, as (for example when) water evaporates from oceans and is deposited upon mountains (where, after being released at a hydroelectric dam, it can be used to drive turbines or generators to produce electricity). Sunlight also drives most weather phenomena, save a few exceptions, like those generated by volcanic events for example. An example of a solar-mediated weather event is a hurricane, which occurs when large unstable areas of warm ocean, heated over months, suddenly give up some of their thermal energy to power a few days of violent air movement. In a slower process,
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consi ...

of atoms in the core of the Earth releases heat. This thermal energy drives
plate tectonics upright=1.35, Diagram of the internal layering of Earth showing the lithosphere above the asthenosphere (not to scale) Plate tectonics (from the la, label=Late Latin Late Latin ( la, Latinitas serior) is the scholarly name for the written L ...
and may lift mountains, via
orogenesis Orogeny is the primary mechanism by which mountains are formed on continents. An orogeny is an event that takes place at a convergent plate margin when plate motion compresses the margin. This leads to both structural deformation Deformation ...
. This slow lifting represents a kind of gravitational potential energy storage of the thermal energy, which may later be transformed into active kinetic energy during landslides, after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a store that has been produced ultimately from the same radioactive heat sources. Thus, according to present understanding, familiar events such as landslides and earthquakes release energy that has been stored as potential energy in the Earth's gravitational field or elastic strain (mechanical potential energy) in rocks. Prior to this, they represent release of energy that has been stored in heavy atoms since the collapse of long-destroyed supernova stars (which created these atoms).

## Cosmology

In cosmology and astronomy the phenomena of
star A star is an astronomical object consisting of a luminous spheroid of plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark ...

s,
nova frame, Artist's conception of a white dwarf, right, accreting hydrogen from the Roche lobe of its larger companion star A nova (plural novae or novas) is a transient astronomical eventA transient astronomical event, often shortened by astronome ...

,
supernova A supernova ( plural: supernovae or supernovas, abbreviations: SN and SNe) is a powerful and luminous stellar explosion. This transient astronomical event occurs during the last stellar evolution, evolutionary stages of a massive star or when a ...

,
quasar A quasar (; also known as a quasi-stellar object, abbreviated QSO) is an extremely luminous active galactic nucleus An active galactic nucleus (AGN) is a compact region at the center of a galaxy A galaxy is a gravitation Gravity () ...

s and
gamma-ray burst In gamma-ray astronomy, gamma-ray bursts (GRBs) are immensely energetic explosions that have been observed in distant galaxies. They are the brightest and most energetic electromagnetic events known to occur in the universe. Bursts can last f ...
s are the universe's highest-output energy transformations of matter. All 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). The nuclear fusion of hydrogen in the Sun also releases another store of potential energy which was created at the time of the Big Bang. At that time, according to theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements. This meant that hydrogen represents a store of potential energy that can be released by fusion. Such a fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into sunlight.

## Quantum mechanics

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

## Relativity

When calculating kinetic energy (Mechanical work, work to accelerate a mass, massive body from zero speed to some finite speed) relativistically – using Lorentz transformations instead of Newtonian mechanics – Einstein discovered an unexpected by-product of these calculations to be an energy term which does not vanish at zero speed. He called it rest energy: energy which every massive body must possess even when being at rest. The amount of energy is directly proportional to the mass of the body: $E_0 = m_0 c^2 ,$ where *''m''0 is the Rest Mass, rest mass of the body, *''c'' is the speed of light in vacuum, *$E_0$ is the rest energy. For example, consider electron–positron annihilation, in which the rest energy of these two individual particles (equivalent to their rest mass) is converted to the radiant energy of the photons produced in the process. In this system the matter and antimatter (electrons and positrons) are destroyed and changed to non-matter (the photons). However, the total mass and total energy do not change during this interaction. The photons each have no rest mass but nonetheless have radiant energy which exhibits the same inertia as did the two original particles. This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from the radiant 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. Energy and mass are manifestations of one and the same underlying physical property of a system. This property is responsible for the inertia and strength of gravitational interaction of the system ("mass manifestations"), and is also responsible for the potential ability of the system to perform work or heating ("energy manifestations"), subject to the limitations of other physical laws. In classical physics, energy is 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). In other words, energy is invariant with respect to rotations of space, but not invariant with respect to rotations of spacetime (= Lorentz boost, boosts).

# Transformation

Energy may be energy transformation, transformed between different forms at various energy conversion efficiency, efficiencies. Items that transform between these forms are called transducers. Examples of transducers include a Battery (electric), battery (from
chemical energy Chemical energy is the energy of chemical substance A chemical substance is a form 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 th ...
to electric energy), a dam (from gravitational potential energy to
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 moving water (and the blades of a turbine) and ultimately to electric energy through an electric generator), and a heat engine (from heat to work). Examples of energy transformation include generating electric energy from heat energy via a steam turbine, or lifting an object against gravity using electrical energy driving a crane motor. Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object. If the object falls to the ground, gravity does mechanical work on the object which transforms the potential energy in the gravitational field to the kinetic energy released as heat on impact with the ground. Our Sun transforms nuclear potential energy to other forms of energy; its total mass does not decrease due to that itself (since it still contains the same total energy even in different forms) but its mass does decrease when the energy escapes out to its surroundings, largely as
radiant 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 succ ...
. There are strict limits to how efficiently heat can be converted into
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...

in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem (thermodynamics), Carnot's theorem and the
second law of thermodynamics The second law of thermodynamics establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

(equal energy spread among all available degrees of freedom (physics and chemistry), degrees of freedom) considerations. 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. Energy transformations in the universe over time are characterized by various kinds of potential energy, that has been available since the Big Bang, 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 nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of
supernova A supernova ( plural: supernovae or supernovas, abbreviations: SN and SNe) is a powerful and luminous stellar explosion. This transient astronomical event occurs during the last stellar evolution, evolutionary stages of a massive star or when a ...

e to "store" energy in the creation of heavy isotopes (such as uranium and thorium), and nuclear decay, a process in which energy is released that was originally stored in these heavy elements, before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a Chemical explosive, chemical explosion, chemical potential energy is transformed to kinetic energy, kinetic and
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 are defined as types of energy transfer (as is ...
in a very short time. Yet another example is that of a pendulum. At its highest points the
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 ...
is zero and the gravitational potential energy is at its maximum. At its lowest point the
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 ...
is at its maximum and is equal to the decrease in
potential energy In physics, potential energy is the energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...

. If one (unrealistically) assumes that there is no
friction Friction is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, st ...

or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever. Energy is also transferred from potential energy ($E_p$) to kinetic energy ($E_k$) and then back to potential energy constantly. This is referred to as conservation of energy. In this
isolated system In physical science, an isolated system is either of the following: # a physical system In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , i ...
, energy cannot be created or destroyed; therefore, the initial energy and the final energy will be equal to each other. This can be demonstrated by the following: The equation can then be simplified further since $E_p = mgh$ (mass times acceleration due to gravity times the height) and $E_k = \frac mv^2$ (half mass times velocity squared). Then the total amount of energy can be found by adding $E_p + E_k = E_\text$.

## Conservation of energy and mass in transformation

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula ''E'' = ''mc''², derived by Albert Einstein (1905) quantifies the relationship between relativistic mass and energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J.J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information). Part of the rest energy (equivalent to rest mass) of matter may be converted to other forms of energy (still exhibiting mass), but neither energy nor mass can be destroyed; rather, both remain constant during any process. However, since $c^2$ is extremely large relative to ordinary human scales, the conversion of an everyday amount of rest mass (for example, 1 kg) from rest energy to other forms of energy (such as kinetic energy, thermal energy, or the radiant energy carried by light and other radiation) can liberate tremendous amounts of energy (~$9\times 10^$ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of an everyday amount energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure on a weighing scale, unless the energy loss is very large. Examples of large transformations between rest energy (of matter) and other forms of energy (e.g., kinetic energy into particles with rest mass) are found in nuclear physics and particle physics. Often, however, the complete conversion of matter (such as atoms) to non-matter (such as photons) is forbidden by Conservation law, conservation laws.

## Reversible and non-reversible transformations

Thermodynamics divides energy transformation into two kinds: Reversible process (thermodynamics), reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy 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, quantum states of lower energy, present as possible excitations 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 thermal energy 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 with time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or as other kinds of increases in disorder). This has led to the hypothesis of 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 through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), continues to decrease.

# Conservation of energy

The fact that energy can be neither created nor destroyed is called the law of
conservation of 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 s ...
. In the form of the first law of thermodynamics, this states that a closed system's energy is constant unless energy is transferred in or out as
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...
or
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 ...

, and that no energy is lost in transfer. 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. 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. While heat can always be fully converted into work in a reversible isothermal expansion of an ideal gas, for cyclic processes of practical interest in heat engines the
second law of thermodynamics The second law of thermodynamics establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
states that the system doing work always loses some energy as waste heat. This creates a limit to the amount of heat energy that can do work in a cyclic process, a limit called the available energy. Mechanical and other forms of energy can be transformed in the other direction into
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 are defined as types of energy transfer (as is ...
without such limitations. The total energy of a system can be calculated by adding up all forms of energy in the system. Richard Feynman said during a 1961 lecture: Most kinds of energy (with gravitational energy being a notable exception) are 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.''The Laws of Thermodynamics''
including careful definitions of energy, free energy, et cetera.
This law is a fundamental principle of physics. As shown rigorously by
Noether's theorem Noether's theorem or Noether's first theorem states that every differentiable In calculus (a branch of mathematics), a differentiable function of one Real number, real variable is a function whose derivative exists at each point in its Domai ...
, the conservation of energy is a mathematical consequence of
translational symmetry In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space tha ...
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. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle – it is impossible to define the exact amount of energy during any definite time interval (though this is practically significant only for very short time intervals). The uncertainty principle should not be confused with energy conservation – rather it provides mathematical limits to which energy can in principle be defined and measured. Each of the basic forces of nature is associated with a different type of potential energy, and all types of potential energy (like all other types of energy) appear as system mass, whenever present. For example, a compressed spring will be slightly more massive than before it was compressed. Likewise, whenever energy is transferred between systems by any mechanism, an associated mass is transferred with it. In quantum mechanics energy is expressed using the Hamiltonian operator. On any time scales, the uncertainty in the energy is by : $\Delta E \Delta t \ge \frac$ which is similar in form to the Heisenberg 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 In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

. The exchange of virtual particles with real particles is responsible for the creation of all known fundamental forces (more accurately known as fundamental interactions). Virtual photons are also responsible for the electrostatic interaction between electric charges (which results in Coulomb's law), for Spontaneous fission, spontaneous radiative decay of excited atomic and nuclear states, for the Casimir force, for the Van der Waals force and some other observable phenomena.

# Energy transfer

## Closed systems

Energy transfer can be considered for the special case of systems which are closed system, closed to transfers of matter. The portion of the energy which is transferred by conservative forces over a distance is measured as the
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...
the source system does on the receiving system. The portion of the energy which does not do work during the transfer is called
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 ...

.Although heat is "wasted" energy for a specific energy transfer (see: waste heat), it can often be harnessed to do useful work in subsequent interactions. However, the maximum energy that can be "recycled" from such recovery processes is limited by the
second law of thermodynamics The second law of thermodynamics establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
.
Energy can be transferred between systems in a variety of ways. Examples include the transmission of electromagnetic energy via photons, physical collisions which transfer
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 ...
,The mechanism for most macroscopic physical collisions is actually Electromagnetism, electromagnetic, but it is very common to simplify the interaction by ignoring the mechanism of collision and just calculate the beginning and end result. and the conductive transfer of
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 are defined as types of energy transfer (as is ...
. Energy is strictly conserved and is also locally conserved wherever it can be defined. In thermodynamics, for closed systems, the process of energy transfer is described by the first law of thermodynamics, first law:There are several First law of thermodynamics#Description, sign conventions for this equation. Here, the signs in this equation follow the IUPAC convention. where $E$ is the amount of energy transferred, $W$  represents the work done on or by the system, and $Q$ represents the heat flow into or out of the system. As a simplification, the heat term, $Q$, can sometimes be ignored, especially for fast processes involving gases, which are poor conductors of heat, or when the thermal efficiency of the transfer is high. For such Adiabatic process, adiabatic processes, This simplified equation is the one used to define the
joule The joule ( ; symbol: J) is a derived unit of 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 ...

, for example.

## Open systems

Beyond the constraints of closed systems, Thermodynamic system#Open system, open systems can gain or lose energy in association with matter transfer (this process is illustrated by injection of an air-fuel mixture into a car engine, a system which gains in energy thereby, without addition of either work or heat). Denoting this energy by $E_$, one may write

# Thermodynamics

## Internal energy

Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to create the system. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometric aspects, as well as the motion of the particles, in form of kinetic energy. Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value, which is impossible to determine with thermodynamics alone.I. Klotz, R. Rosenberg, ''Chemical Thermodynamics – Basic Concepts and Methods'', 7th ed., Wiley (2008), p. 39

## First law of thermodynamics

The first law of thermodynamics asserts that the total energy of a system and its surroundings (but not necessarily thermodynamic free energy) is always conserved and that heat flow is a form of energy transfer. For homogeneous systems, with a well-defined temperature and pressure, 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) without chemical changes, the differential change in the internal energy of the system (with a ''gain'' in energy signified by a positive quantity) is given as :$\mathrmE = T\mathrmS - P\mathrmV\,$, where the first term on the right is the heat transferred into the system, expressed in terms of
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 ...

''T'' and
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

''S'' (in which entropy increases and its change d''S'' is positive when heat is added to the system), 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 compression of the system requires work to be done on it and so the volume change, d''V'', is negative when work is done on the system). This equation is highly specific, ignoring all chemical, electrical, nuclear, and gravitational forces, effects such as advection of any form of energy other than heat and ''PV''-work. The general formulation of the first law (i.e., conservation of energy) is valid even in situations in which the system is not homogeneous. For these cases the change in internal energy of a ''closed'' system is expressed in a general form by :$\mathrmE=\delta Q+\delta W$ where $\delta Q$ is the heat supplied to the system and $\delta W$ is the work applied to the system.

## Equipartition of energy

The energy of a mechanical harmonic oscillator (a mass on a spring) is alternately kinetic energy, kinetic and
potential energy In physics, potential energy is the energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...

. At two points in the oscillation Frequency, cycle it is entirely kinetic, and at two points it is entirely potential. Over a whole cycle, or over many cycles, average energy is equally split between kinetic and potential. This is an example of the equipartition principle: the total energy of a system with many degrees of freedom is equally split among all available degrees of freedom, on average. This principle is vitally important to understanding the behavior of a quantity closely related to energy, called
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

. Entropy is a measure of evenness of a distribution (mathematics), distribution of energy between parts of a system. When an isolated system is given more degrees of freedom (i.e., given new available energy states that are the same as existing states), then total energy spreads over all available degrees equally without distinction between "new" and "old" degrees. This mathematical result is part of the
second law of thermodynamics The second law of thermodynamics establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
. The second law of thermodynamics is simple only for systems which are near or in a physical equilibrium state. For non-equilibrium systems, the laws governing the systems' behavior are still debatable. One of the guiding principles for these systems is the principle of principle of maximum entropy, maximum entropy production. It states that nonequilibrium systems behave in such a way as to maximize their entropy production.

* Combustion * Index of energy articles * Index of wave articles * Orders of magnitude (energy) * Power station * Spaceflight#Transfer energy, Transfer energy

# References

* * ''The Biosphere'' (A ''Scientific American'' Book), San Francisco, W.H. Freeman and Co., 1970, . This book, originally a 1970 ''Scientific American'' issue, covers virtually every major concern and concept since debated regarding materials and
energy resource The energy industry is the totality of all of the industries involved in the production and sale of energy In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phý ...
s, population trends, and environmental degradation. * * ''Energy and Power'' (A ''Scientific American'' Book), San Francisco, W.H. Freeman and Co., 1971, . * * Santos, Gildo M. "Energy in Brazil: a historical overview," ''The Journal of Energy History'' (2018)
online
* *

## Journals

''The Journal of Energy History / Revue d'histoire de l'énergie'' (JEHRHE), 2018–