In
physics, energy (from
Ancient Greek:
ἐνέργεια, ''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 that is
transferred to a
body or to a
physical system, recognizable in the performance of
work and in the form of
heat and
light. Energy is a
conserved quantity—the law of
conservation of energy states that energy can be
converted
Conversion or convert may refer to:
Arts, entertainment, and media
* "Conversion" (''Doctor Who'' audio), an episode of the audio drama ''Cyberman''
* "Conversion" (''Stargate Atlantis''), an episode of the television series
* "The Conversion" ...
in form, but not created or destroyed. The unit of
measurement for energy in the
International System of Units (SI) is the
joule (J).
Common forms of energy include the
kinetic energy of a moving object, the
potential energy stored by an object (for instance due to its position in a
field), the
elastic energy stored in a solid object,
chemical energy associated with
chemical reactions, the
radiant energy carried by
electromagnetic radiation, and the
internal energy contained within a
thermodynamic system. All living
organisms constantly take in and release energy.
Due to
mass–energy equivalence, any object that has
mass when stationary (called
rest mass) 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 resources such as
fossil fuels,
nuclear fuel, or
renewable energy. The Earth's
climate and
ecosystems 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 can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways.
Kinetic energy is determined by the
movement of an object – or the
composite motion of the components of an object – and
potential energy reflects the potential of an object to have motion, and generally is a function of the position of an object within a
field 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 kinetic and potential energy within a system is referred to as
mechanical energy, whereas nuclear energy refers to the combined potentials within an atomic nucleus from either the
nuclear force or the
weak force, 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''.
The ...
, activity, operation, which possibly appears for the first time in the work of
Aristotle 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 proposed the idea of the lat,
vis viva, 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, differs from ''vis viva'' only by a factor of two. Writing in the early 18th century,
Émilie du Châtelet proposed the concept of
conservation of energy in the marginalia of her French language translation of Newton's ''
Principia Mathematica'', which represented the first formulation of a conserved measurable quantity that was distinct from
momentum, 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, ...
described "
kinetic energy" in 1829 in its modern sense, and in 1853,
William Rankine coined the term "
potential energy". The law of
conservation of energy was also first postulated in the early 19th century, and applies to any
isolated system. It was argued for some years whether heat was a physical substance, dubbed the
caloric, or merely a physical quantity, such as
momentum. In 1845
James Prescott Joule 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) as the field of
thermodynamics. 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 princip ...
,
Josiah Willard Gibbs, and
Walther Nernst. It also led to a mathematical formulation of the concept of
entropy by Clausius and to the introduction of laws of
radiant energy by
Jožef Stefan. According to
Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.
Thus, since 1918, theorists have understood that the law of
conservation of energy is the direct mathematical consequence of the
translational symmetry 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 lost by the weight in descending was equal to the
internal energy gained by the water through
friction with the paddle.
In the
International System of Units (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 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,
calories,
British thermal units,
kilowatt-hours 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 ...
s, which require a conversion factor when expressed in SI units.
The SI unit of energy rate (energy per unit time) is the
watt, 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 work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a f ...
. Other energy units such as the
electronvolt,
food calorie or thermodynamic
kcal (based on the temperature change of water in a heating process), and
BTU 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. Several formulations of mechanics have been developed using energy as a core concept.
Work, a function of energy, is force times distance.
:
This says that the work (
) is equal to the
line integral of the
force F along a path ''C''; for details see the
mechanical work article. Work and thus energy is
frame dependent. For example, consider a ball being hit by a bat. In the center-of-mass reference frame, the bat does no work on the ball. But, in the reference frame of the person swinging the bat, considerable work is done on the ball.
The total energy of a system is sometimes called the
Hamiltonian, after
William Rowan Hamilton. The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems. These classical equations have remarkably direct analogs in nonrelativistic quantum mechanics.
Another energy-related concept is called the
Lagrangian, 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, 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 (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,
energy 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 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 ...
if the final state is lower on the energy scale than the initial state; in the less common case of
endothermic reactions the situation is the reverse.
Chemical reactions are usually not possible unless the reactants surmount an energy barrier known as the
activation energy. 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. The activation energy necessary for a chemical reaction can be provided in the form of thermal energy.
Biology
In
biology, 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 of a biological organism. Energy used in
respiration is stored in substances such as
carbohydrates (including sugars),
lipids, 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, res ...
s stored by
cells
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 w ...
. In human terms, the
human equivalent (H-e) (Human energy conversion) indicates, for a given amount of energy expenditure, the relative quantity of energy needed for human
metabolism, 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 energy expenditure per unit time by 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 body mass J/(h·kg). P ...
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, 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 is triggered by
enzyme 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 (6–8 MJ) recommended for a human adult are taken as food molecules, mostly carbohydrates and fats, of which
glucose (C
6H
12O
6) and
stearin (C
57H
110O
6) are convenient examples. The food molecules are oxidized to
carbon dioxide and
water in the
mitochondria
C6H12O6 + 6O2 -> 6CO2 + 6H2O
C57H110O6 + (81 1/2) O2 -> 57CO2 + 55H2O
and some of the energy is used to convert
ADP
Adp or ADP may refer to:
Aviation
* Aéroports de Paris, airport authority for the Parisian region in France
* Aeropuertos del Perú, airport operator for airports in northern Peru
* SLAF Anuradhapura, an airport in Sri Lanka
* Ampara Airp ...
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 when ATP reacts with OH groups and eventually splits into ADP and phosphate (at each stage of a
metabolic pathway, some chemical energy is converted into heat). Only a tiny fraction of the original chemical energy is used for
work:
[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 output (in case of a sprinter) and the force (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
machines 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 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
In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bin ...
) 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
fixed
Fixed may refer to:
* ''Fixed'' (EP), EP by Nine Inch Nails
* ''Fixed'', an upcoming 2D adult animated film directed by Genndy Tartakovsky
* Fixed (typeface), a collection of monospace bitmap fonts that is distributed with the X Window System
* F ...
by
photosynthesis, 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,
continental drift,
mountain ranges,
volcanoes, and
earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior, while
meteorological phenomena like wind, rain,
hail, snow, lightning,
tornadoes and
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
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
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
energy operator
In quantum mechanics, energy is defined in terms of the energy operator, acting on the wave function of the system as a consequence of time translation symmetry.
Definition
It is given by:
\hat = i\hbar\frac
It acts on the wave function (the ...
(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
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:
(where
is the
Planck constant and
the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or
photons.
Relativity
When calculating kinetic energy (
work to accelerate a
massive body from zero
speed to some finite speed) relativistically – using
Lorentz transformations
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...
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
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, ...
: 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:
where
*''m''
0 is the
rest mass of the body,
*''c'' is the
speed of light in vacuum,
*
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
Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specifi ...
– 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
Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation— ...
to time. In
special relativity energy is also a scalar (although not a
Lorentz scalar
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation
In physics, the Lorentz transformations are a six-parameter famil ...
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 (=
boosts).
Transformation
Energy may be
transformed between different forms at various
efficiencies. Items that transform between these forms are called
transducers. Examples of transducers include a
battery
Battery most often refers to:
* Electric battery, a device that provides electrical power
* Battery (crime), a crime involving unlawful physical contact
Battery may also refer to:
Energy source
*Automotive battery, a device to provide power t ...
(from
chemical energy to
electric energy), a dam (from
gravitational potential energy to
kinetic energy 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.
There are strict limits to how efficiently heat can be converted into
work in a cyclic process, e.g. in a heat engine, as described by
Carnot's theorem and the
second law of thermodynamics. 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 (equal energy spread among all available
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 bomb
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions ( thermonuclear bomb), producing a nuclear explosion. Both bomb ...
s or in civil nuclear power generation. Similarly, in the case of a
chemical explosion,
chemical potential energy is transformed to
kinetic
Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to:
* Kinetic theory, describing a gas as particles in random motion
* Kinetic energy, the energy of an object that it possesses due to its motion
Art and ent ...
and
thermal energy in a very short time.
Yet another example is that of a
pendulum. At its highest points the
kinetic energy is zero and the
gravitational potential energy is at its maximum. At its lowest point the
kinetic energy is at its maximum and is equal to the decrease in
potential energy. If one (unrealistically) assumes that there is no
friction 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 (
) to kinetic energy (
) and then back to potential energy constantly. This is referred to as conservation of energy. In this
isolated system, 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
(mass times acceleration due to gravity times the height) and
(half mass times velocity squared). Then the total amount of energy can be found by adding
.
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
The word " mass" has two meanings in special relativity: '' invariant mass'' (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity ...
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
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 (~
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 laws
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of energy, conservation of linear momentum, ...
.
Reversible and non-reversible transformations
Thermodynamics divides energy transformation into two kinds:
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 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 or
heat, 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 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
In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir, reaching maximum entropy. When the surroundings are the reservoir, exergy is the p ...
. 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''](_blank)
including careful definitions of energy, free energy, et cetera.
This law is a fundamental principle of physics. As shown rigorously by
Noether's theorem, the conservation of energy is a mathematical consequence of
translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is
canonical conjugate
Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation— ...
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
:
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. 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
A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbat ...
are also responsible for the electrostatic interaction between
electric charges (which results in
Coulomb's law), for
spontaneous
Spontaneous may refer to:
* Spontaneous abortion
* Spontaneous bacterial peritonitis
* Spontaneous combustion
* Spontaneous declaration
* Spontaneous emission
* Spontaneous fission
* Spontaneous generation
* Spontaneous human combustion
* Spontan ...
radiative decay of excited atomic and nuclear states, for the
Casimir force
In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who pre ...
, 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
Closed may refer to:
Mathematics
* Closure (mathematics), a set, along with operations, for which applying those operations on members always results in a member of the set
* Closed set, a set which contains all its limit points
* Closed interval, ...
to transfers of matter. The portion of the energy which is transferred by
conservative forces over a distance is measured as the
work the source system does on the receiving system. The portion of the energy which does not do work during the transfer is called
heat.
[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.] 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,
[The mechanism for most macroscopic physical collisions is actually 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:
[There are several sign conventions for this equation. Here, the signs in this equation follow the IUPAC convention.]
where
is the amount of energy transferred,
represents the work done on or by the system, and
represents the heat flow into or out of the system. As a simplification, the heat term,
, 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 processes,
This simplified equation is the one used to define the
joule, for example.
Open systems
Beyond the constraints of closed systems,
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
, 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
:
,
where the first term on the right is the heat transferred into the system, expressed in terms of
temperature ''T'' and
entropy ''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
:
where
is the heat supplied to the system and
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
Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to:
* Kinetic theory, describing a gas as particles in random motion
* Kinetic energy, the energy of an object that it possesses due to its motion
Art and ent ...
and
potential energy. At two points in the oscillation
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
In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. T ...
: 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 measure of evenness of a
distribution Distribution may refer to:
Mathematics
* Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations
*Probability distribution, the probability of a particular value or value range of a vari ...
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 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
maximum entropy production. It states that nonequilibrium systems behave in such a way as to maximize their entropy production.
See also
*
Combustion
*
Energy democracy Energy democracy is a concept developed within the environmental justice movement that pairs the renewable energy transition with efforts to democratize the production and management of energy resources— including the social ownership of energy i ...
*
Index of energy articles
*
Index of wave articles
*
Orders of magnitude (energy)
*
Power station
*
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 resources,
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
Main topic articles
Nature
Universe
Scalar physical quantities