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In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, energy (from
Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
:
ἐνέργεια In philosophy, potentiality and actuality are a pair of closely connected principles which Aristotle used to analyze motion, causality, ethics, and physiology in his ''Physics'', ''Metaphysics'', '' Nicomachean Ethics'', and ''De Anima''. Th ...
, ''enérgeia'', “activity”) is the
quantitative Quantitative may refer to: * Quantitative research, scientific investigation of quantitative properties * Quantitative analysis (disambiguation) * Quantitative verse, a metrical system in poetry * Statistics, also known as quantitative analysis ...
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 is 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 anima ...
or to a
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. The environment is ignored except for its effects on the ...
, recognizable in the performance of
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 ** Working animal, an animal t ...
and in the form of
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
and
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
. Energy is a
conserved quantity In mathematics, a conserved quantity of a dynamical system is a function of the dependent variables, the value of which remains constant along each trajectory of the system. Not all systems have conserved quantities, and conserved quantities are ...
—the law of
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
states that energy can be converted in form, but not created or destroyed. The unit of
measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
for energy in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI) is the
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
(J). Common forms of energy include the
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
of a moving object, the
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 potential energy include the gravitational potentia ...
stored by an object (for instance due to its position in 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 grass ...
), the
elastic energy Elastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Elastic energy occurs when objects are impermanently compressed, ...
stored in a solid object,
chemical energy Chemical energy is the energy of chemical substances that is released when they undergo a chemical reaction and transform into other substances. Some examples of storage media of chemical energy include batteries, Schmidt-Rohr, K. (2018). "How ...
associated with
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
s, the
radiant energy Radiant may refer to: Computers, software, and video games * Radiant (software), a content management system * GtkRadiant, a level editor created by id Software for their games * Radiant AI, a technology developed by Bethesda Softworks for '' ...
carried by
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
, and the
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
contained within a
thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...
. All living
organism In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells (cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and ...
s constantly take in and release energy. Due to
mass–energy equivalence In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physicis ...
, any object that has
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
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 or system of objects that is independent of the overall motion of the system. More precisely, i ...
) also has an equivalent amount of energy whose form is called
rest energy 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 or system of objects that is independent of the overall motion of the system. More precisely, ...
, 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. Human civilization requires energy to function, which it gets from
energy resource Energy development is the field of activities focused on obtaining sources of energy from natural resources. These activities include production of renewable, nuclear, and fossil fuel derived sources of energy, and for the recovery and reus ...
s such as
fossil fuel A fossil fuel is a hydrocarbon-containing material formed naturally in the Earth's crust from the remains of dead plants and animals that is extracted and burned as a fuel. The main fossil fuels are coal, oil, and natural gas. Fossil fuels m ...
s, nuclear fuel, or
renewable energy Renewable energy is energy that is collected from renewable resources that are naturally replenished on a human timescale. It includes sources such as sunlight, wind, the movement of water, and geothermal heat. Although most renewable energy ...
. The Earth's
climate Climate is the long-term weather pattern in an area, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years. Some of the meteorologic ...
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 syste ...
s processes are driven by the energy the planet receives from the Sun (although a small amount is also contributed by geothermal energy).


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 (systems), environment, is described by its boundaries, ...
can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways.
Kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
is determined by the movement of an object – or the
composite motion In deliberative procedure, compositing is the process of combining several 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 reasons. First, it c ...
of the components of an object – and
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 potential energy include the gravitational potentia ...
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 grass ...
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 Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
kinetic and potential energy within a system is referred to as
mechanical energy In Outline of physical science, physical sciences, mechanical energy is the sum of potential energy and kinetic energy. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, t ...
, 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 protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nucle ...
or the
weak force Weak may refer to: Songs * Weak (AJR song), "Weak" (AJR song), 2016 * Weak (Melanie C song), "Weak" (Melanie C song), 2011 * Weak (SWV song), "Weak" (SWV song), 1993 * Weak (Skunk Anansie song), "Weak" (Skunk Anansie song), 1995 * "Weak", a song ...
, among other examples.


History

The word ''energy'' derives from the grc, ἐνέργεια,
energeia In philosophy, potentiality and actuality are a pair of closely connected principles which Aristotle used to analyze motion, causality, ethics, and physiology in his ''Physics'', ''Metaphysics'', '' Nicomachean Ethics'', and ''De Anima''. Th ...
, 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 and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
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 . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathem ...
proposed the idea of the lat,
vis viva ''Vis viva'' (from the Latin for "living force") is a historical term used for the first recorded description of what we now call kinetic energy in an early formulation of the principle of conservation of energy. Overview Proposed by Gottfried L ...
, 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, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
, 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 natural philosopher and mathematician from the early 1730s until her death due to complications during childbirth in 1749. ...
proposed the concept of
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
in the marginalia of her French language translation of Newton's ''
Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...
'', which represented the first formulation of a conserved measurable quantity that was distinct from
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
, and which would later be called "energy". In 1807, Thomas Young was possibly the first to use the term "energy" instead of ''vis viva'', in its modern sense.
Gustave-Gaspard Coriolis Gaspard-Gustave de Coriolis (; 21 May 1792 – 19 September 1843) was a French mathematician, mechanical engineer and scientist. He is best known for his work on the supplementary forces that are detected in a rotating frame of reference, le ...
described "
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
" 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 ( ...
coined the term "
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 potential energy include the gravitational potentia ...
". The law of
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
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 so far removed from other systems that it does not interact with them. # a thermodynamic system enclosed by rigid immovable walls through which neither m ...
. 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, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
. In 1845
James Prescott Joule James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist, mathematician and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). Th ...
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, Mathematical physics, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy (Glasgow), Professor of Natural Philoso ...
) as the field of
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
. 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 physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
,
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 t ...
, and Walther Nernst. 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 thermodynam ...
by Clausius and to the introduction of laws of
radiant energy Radiant may refer to: Computers, software, and video games * Radiant (software), a content management system * GtkRadiant, a level editor created by id Software for their games * Radiant AI, a technology developed by Bethesda Softworks for '' ...
by
Jožef Stefan Josef Stefan ( sl, Jožef Štefan; 24 March 1835 – 7 January 1893) was an ethnic Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire. Life and work Stefan was born in an outskirt village of St. Peter (Slovene: ; to ...
. According to
Noether's theorem Noether's theorem or Noether's first theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in ...
, 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 and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
is the direct mathematical consequence of the
translational symmetry In geometry, to translate a geometric figure is to move it from one place to another without rotating it. A translation "slides" a thing by . In physics and mathematics, continuous translational symmetry is the invariance of a system of equatio ...
of the quantity conjugate 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 held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
lost by the weight in descending was equal to the
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
gained by the water through
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...
with the paddle. In the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI), the unit of energy is the joule, named after Joule. It is a
derived unit SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate ...
. 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 ** Working animal, an animal t ...
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 10−7joules (100 nJ). It originated in the Centimetre–gram–second system of units (CGS). It has the symbol ''erg''. The erg is not an SI unit. Its name is derived from (), a Greek word meaning 'work' o ...
s,
calorie The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of on ...
s,
British thermal unit The British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United States customary units. The modern SI ...
s,
kilowatt-hour A kilowatt-hour (unit symbol: kW⋅h or kW h; commonly written as kWh) is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ). Kilowatt-hours are a common bil ...
s and
kilocalorie The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of on ...
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 the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
, 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 10−7joules (100 nJ). It originated in the Centimetre–gram–second system of units (CGS). It has the symbol ''erg''. The erg is not an SI unit. Its name is derived from (), a Greek word meaning 'work' o ...
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 Mechanical work, work or energy in the English Engineering Units, engineering and Foot–pound–second_system#force, gravitational systems in United States customary ...
. Other energy units such as the
electronvolt In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defi ...
,
food calorie The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of on ...
or thermodynamic
kcal The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of o ...
(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; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United States customary units. The modern SI u ...
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 is a function of the dependent variables, the value of which remains constant along each trajectory of the system. Not all systems have conserved quantities, and conserved quantities are ...
. 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 ** Working animal, an animal t ...
, 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, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''curvilinear integral'' are also used; ''contour integral'' is used as well, alt ...
of the
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
F along a path ''C''; for details see the
mechanical work In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...
article. Work and thus energy is
frame dependent In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both mathe ...
. 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 Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian ...
, after
William Rowan Hamilton Sir William Rowan Hamilton Doctor of Law, LL.D, Doctor of Civil Law, DCL, Royal Irish Academy, MRIA, Royal Astronomical Society#Fellow, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the ...
. 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 Lagrangian may refer to: Mathematics * Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier ** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...
, after Joseph-Louis Lagrange. This formalism is as fundamental as the Hamiltonian, and both can be used to derive the equations of motion or be derived from them. It was invented in the context of
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
, 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 symmetry of the action of a physical system with conservative forces has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in ...
(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 science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
,
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
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, an exothermic process () is a thermodynamic process or reaction that releases energy from the system to its surroundings, usually in the form of heat, but also in a form of light (e.g. a spark, flame, or flash), electricity (e ...
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 process. Constant pressure, constant temperature reactions are exergonic if and only if the Gibbs fr ...
if the final state is lower on the energy scale than the initial state; in the less common case of
endothermic In thermochemistry, an endothermic process () is any thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, H.P., Butler, L. J. (2015).''Principle of Modern Chemistry'', Brooks Cole. ...
reactions the situation is the reverse.
Chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
s are usually not possible unless the reactants surmount an energy barrier known as the
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
. 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 1 ...
. The activation energy necessary for a chemical reaction can be provided in the form of thermal energy.


Biology

In
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
, 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 Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery ...
or
organelle In cell biology, an organelle is a specialized subunit, usually within a cell, that has a specific function. The name ''organelle'' comes from the idea that these structures are parts of cells, as organs are to the body, hence ''organelle,'' the ...
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 cellul ...
is stored in substances such as
carbohydrate In organic chemistry, a carbohydrate () is a biomolecule consisting of carbon (C), hydrogen (H) and oxygen (O) atoms, usually with a hydrogen–oxygen atom ratio of 2:1 (as in water) and thus with the empirical formula (where ''m'' may or ma ...
s (including sugars),
lipid Lipids are a broad group of naturally-occurring molecules which includes fats, waxes, sterols, fat-soluble vitamins (such as vitamins A, D, E and K), monoglycerides, diglycerides, phospholipids, and others. The functions of lipids include ...
s, and
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
s stored by cells. In human terms, the
human equivalent The 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-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run cell ...
, using as a standard an average human energy expenditure of 12,500 kJ per day and a
basal metabolic rate Basal metabolic rate (BMR) is the rate of food energy, energy expenditure per unit time by endotherm, endothermic animals at rest. It is reported in energy units per unit time ranging from watt (joule/second) to ml O2/min or joule per hour per kg b ...
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 light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities. Some of this chemical energy is stored i ...
, when carbon dioxide and water (two low-energy compounds) are converted into carbohydrates, lipids, proteins and oxygen. 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 pathways that breaks down molecules into smaller units that are either oxidized to release energy or used in other anabolic reactions. Catabolism breaks down large molecules (such as polysaccharides, lipids, ...
is triggered by
enzyme Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. A ...
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. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of on ...
(6–8 MJ) recommended for a human adult are taken as food molecules, mostly carbohydrates and fats, of which
glucose Glucose is a simple sugar with the molecular formula . Glucose is overall the most abundant monosaccharide, a subcategory of carbohydrates. Glucose is mainly made by plants and most algae during photosynthesis from water and carbon dioxide, using ...
(C6H12O6) and stearin (C57H110O6) are convenient examples. The food molecules are oxidized to
carbon dioxide Carbon dioxide (chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is transpar ...
and
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
in the
mitochondria A mitochondrion (; ) is an organelle found in the Cell (biology), cells of most Eukaryotes, such as animals, plants and Fungus, fungi. Mitochondria have a double lipid bilayer, membrane structure and use aerobic respiration to generate adenosi ...
C6H12O6 + 6O2 -> 6CO2 + 6H2O C57H110O6 + (81 1/2) O2 -> 57CO2 + 55H2O and some of the energy is used to convert ADP into ATP: The rest of the chemical energy of 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-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run cell ...
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. The reactants, products, and intermediates of an enzymatic reaction are known as metabolites, which are modified by a sequence of chemical reac ...
, 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 ** Working animal, an animal t ...
: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 most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
output (in case of a sprinter) and the
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
(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 a physical system using Power (physics), power to apply Force, forces and control Motion, movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to na ...
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 is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
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").Crystals 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. Simpler organisms can achieve higher energy efficiencies than more complex ones, but the complex organisms can occupy ecological niches 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. As an example, to take just the first step in the food chain: of the estimated 124.7 Pg/a of carbon that is carbon fixation, fixed by
photosynthesis Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities. Some of this chemical energy is stored i ...
, 64.3 Pg/a (52%) are used for the metabolism of green plants, i.e. reconverted into carbon dioxide and heat.


Earth sciences

In Earth science#earth's energy, geology, continental drift, mountain, mountain ranges, volcanoes, and earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior, while metereology, meteorological phenomena like wind, rain, hail, snow, lightning, tornadoes and tropical cyclone, hurricanes are all a result of energy transformations in our atmosphere brought about by solar energy. Sunlight is the main input to Earth's energy budget 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 of atoms in the core of the Earth releases heat. This thermal energy drives plate tectonics and may lift mountains, via orogenesis. 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 Physical cosmology#Energy of the cosmos, cosmology and astronomy the phenomena of stars, nova, supernova, quasars and gamma-ray bursts are the universe's highest-output energy transformations 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). 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 the Planck 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 substances that is released when they undergo a chemical reaction and transform into other substances. Some examples of storage media of chemical energy include batteries, Schmidt-Rohr, K. (2018). "How ...
to electric energy), a dam (from gravitational potential energy to
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
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 Radiant may refer to: Computers, software, and video games * Radiant (software), a content management system * GtkRadiant, a level editor created by id Software for their games * Radiant AI, a technology developed by Bethesda Softworks for '' ...
. 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 ** Working animal, an animal t ...
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 is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
. 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 thermodynam ...
(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 supernovae 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 in a very short time. Yet another example is that of a pendulum. At its highest points the
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
is zero and the gravitational potential energy is at its maximum. At its lowest point the
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
is at its maximum and is equal to the decrease in
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 potential energy include the gravitational potentia ...
. If one (unrealistically) assumes that there is no
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...
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 so far removed from other systems that it does not interact with them. # a thermodynamic system enclosed by rigid immovable walls through which neither m ...
, 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 and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
. 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 ** Working animal, an animal t ...
or
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
, 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 is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
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 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 symmetry of the action of a physical system with conservative forces has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in ...
, the conservation of energy is a mathematical consequence of
translational symmetry In geometry, to translate a geometric figure is to move it from one place to another without rotating it. A translation "slides" a thing by . In physics and mathematics, continuous translational symmetry is the invariance of a system of equatio ...
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 Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
, 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, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
. 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 ** Working animal, an animal t ...
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, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
.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 is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
.
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, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
,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. tidal interactions, and the conductive transfer of thermal energy. 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 the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
, 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_\text, 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 ''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 thermodynam ...
''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 held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
. 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 thermodynam ...
. 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 is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
. 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.


See also

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


Notes


References


Further reading

* * ''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 Energy development is the field of activities focused on obtaining sources of energy from natural resources. These activities include production of renewable, nuclear, and fossil fuel derived sources of energy, and for the recovery and reus ...
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–


External links

*
Differences between Heat and Thermal energy
– BioCab {{Authority control Energy, Main topic articles Nature Universe Scalar physical quantities