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Energy transformation; In a typical lightning strike,500 megajoules of electric potential energy isconverted into the same amount of energy in otherforms, most notably light energy, sound energy andthermal energy.

EnergyFrom Wikipedia, the free encyclopedia

In physics, energy is a property of objects, transferableamong them via fundamental interactions, which can beconverted into different forms but not created or destroyed.The joule is the SI unit of energy, based on the amounttransferred to an object by the mechanical work of moving it1 metre against a force of 1 newton.[1]

Work and heat are two categories of processes ormechanisms that can transfer a given amount of energy. Thesecond law of thermodynamics limits the amount of workthat can be performed by energy that is obtained via a heatingprocess—some energy is always lost as waste heat. Themaximum amount that can go into work is called theavailable energy. Systems such as machines and living thingsoften require available energy, not just any energy.Mechanical and other forms of energy can be transformed inthe other direction into thermal energy without suchlimitations.

There are many forms of energy, but all these types must meet certain conditions such as being convertible toother kinds of energy, obeying conservation of energy, and causing a proportional change in mass in objects thatpossess it. Common energy forms include the kinetic energy of a moving object, the radiant energy carried bylight and other electromagnetic radiation, the potential energy stored by virtue of the position of an object in aforce field such as a gravitational, electric or magnetic field, and the thermal energy comprising the microscopickinetic and potential energies of the disordered motions of the particles making up matter. Some specific formsof potential energy include elastic energy due to the stretching or deformation of solid objects and chemicalenergy such as is released when a fuel burns. Any object that has mass when stationary, such as a piece ofordinary matter, is said to have rest mass, or an equivalent amount of energy whose form is called rest energy,though this isn't immediately apparent in everyday phenomena described by classical physics.

According to mass–energy equivalence, all forms of energy (not just rest energy) exhibit mass. For example,adding 25 kilowatt­hours (90 megajoules) of energy to an object in the form of heat (or any other form) increasesits mass by 1 microgram; if you had a sensitive enough mass balance or scale, this mass increase could bemeasured. Our Sun transforms nuclear potential energy to other forms of energy; its total mass does not decreasedue to that in itself (since it still contains the same total energy even if in different forms), but its mass doesdecrease when the energy escapes out to its surroundings, largely as radiant energy.

Although any energy in any single form can be transformed into another form, the law of conservation of energystates that the total energy of a system can only change if energy is transferred into or out of the system. Thismeans that it is impossible to create or destroy energy. The total energy of a system can be calculated by addingup all forms of energy in the system. Examples of energy transfer and transformation include generating ormaking use of electric energy, performing chemical reactions, or lifting an object. Lifting against gravityperforms work on the object and stores gravitational potential energy; if it falls, gravity does work on the objectwhich transforms the potential energy to the kinetic energy associated with its speed.

More broadly, living organisms require available energy to stay alive; humans get such energy from food alongwith the oxygen needed to metabolize it. Civilisation requires a supply of energy to function; energy resourcessuch as fossil fuels are a vital topic in economics and politics. Earth's climate and ecosystem are driven by theradiant energy Earth receives from the sun (as well as the geothermal energy contained within the earth), and are

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sensitive to changes in the amount received. The word "energy" is also used outside of physics in many ways,which can lead to ambiguity and inconsistency. The vernacular terminology is not consistent with technicalterminology. For example, while energy is always conserved (in the sense that the total energy does not changedespite energy transformations), energy can be converted into a form, e.g., thermal energy, that cannot be utilizedto perform work. When one talks about "conserving energy by driving less", one talks about conserving fossilfuels and preventing useful energy from being lost as heat. This usage of "conserve" differs from that of the lawof conservation of energy.[2]

Contents

1 Forms2 History3 Measurement and units4 Scientific use

4.1 Classical mechanics4.2 Chemistry4.3 Biology4.4 Earth sciences4.5 Cosmology4.6 Quantum mechanics4.7 Relativity

5 Transformation5.1 Conservation of energy and mass in transformation5.2 Reversible and non­reversible transformations

6 Conservation of energy7 Transfer between systems

7.1 Closed systems7.2 Open systems

8 Thermodynamics8.1 Internal energy8.2 First law of thermodynamics8.3 Equipartition of energy

9 See also10 Notes and references11 Further reading12 External links

Forms

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Thermal energy is energy ofmicroscopic constituents of matter,which may include both kinetic andpotential energy.

The total energy of a system can be subdivided and classified in various ways. For example, classical mechanicsdistinguishes between kinetic energy, which is determined by an object'smovement through space, and potential energy, which is a function of theposition of an object within a field. It may also be convenient todistinguish gravitational energy, thermal energy, several types of nuclearenergy (which utilize potentials from the nuclear force and the weakforce), electric energy (from the electric field), and magnetic energy(from the magnetic field), among others. Many of these classificationsoverlap; for instance, thermal energy usually consists partly of kinetic andpartly of potential energy. Some types of energy are a varying mix of bothpotential and kinetic energy. An example is mechanical energy which isthe sum of (usually macroscopic) kinetic and potential energy in a system.Elastic energy in materials is also dependent upon electrical potentialenergy (among atoms and molecules), as is chemical energy, which isstored and released from a reservoir of electrical potential energy betweenelectrons, and the molecules or atomic nuclei that attract them..The list isalso not necessarily complete. Whenever physical scientists discover that a certain phenomenon appears toviolate the law of energy conservation, new forms are typically added that account for the discrepancy.

Heat and work are special cases in that they are not properties of systems, but are instead properties of processesthat transfer energy. In general we cannot measure how much heat or work are present in an object, but ratheronly how much energy is transferred among objects in certain ways during the occurrence of a given process.Heat and work are measured as positive or negative depending on which side of the transfer we view them from.

Potential energies are often measured as positive or negative depending on whether they are greater or less thanthe energy of a specified base state or configuration such as two interacting bodies being infinitely far apart.Wave energies (such as radiant or sound energy), kinetic energy, and rest energy are each greater than or equal tozero because they are measured in comparison to a base state of zero energy: "no wave", "no motion", and "noinertia", respectively.

The distinctions between different kinds of energy is not always clear­cut. As Richard Feynman points out:

These notions of potential and kinetic energy depend on a notion of length scale. For example,one can speak of macroscopic potential and kinetic energy, which do not include thermalpotential and kinetic energy. Also what is called chemical potential energy is a macroscopicnotion, and closer examination shows that it is really the sum of the potential and kinetic energyon the atomic and subatomic scale. Similar remarks apply to nuclear "potential" energy andmost other forms of energy. This dependence on length scale is non­problematic if the variouslength scales are decoupled, as is often the case ... but confusion can arise when different lengthscales are coupled, for instance when friction converts macroscopic work into microscopicthermal energy.

Some examples of different kinds of energy:

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Thomas Young – the first to use theterm "energy" in the modern sense.

Forms of energyType of energy Description

Kinetic (≥0), that of the motion of a bodyPotential A category comprising many forms in this listMechanical The sum of (usually macroscopic) kinetic and potential energies

Mechanical wave (≥0), a form of mechanical energy propagated by a material's oscillationsChemical that contained in moleculesElectric that from electric fieldsMagnetic that from magnetic fieldsRadiant (≥0), that of electromagnetic radiation including lightNuclear that of binding nucleons to form the atomic nucleusIonization that of binding an electron to its atom or moleculeElastic that of deformation of a material (or its container) exhibiting a restorative force

Gravitational that from gravitational fieldsIntrinsic, the rest

energy (≥0) that equivalent to an object's rest mass

Thermal A microscopic, disordered equivalent of mechanical energy

Heat an amount of thermal energy being transferred (in a given process) in the direction ofdecreasing temperature

Mechanical work an amount of energy being transferred in a given process due to displacement in thedirection of an applied force

History

The word energy derives from the Ancient Greek:ἐνέργεια energeia "activity, operation",[3] which possibly appears for thefirst time in the work of Aristotle in the 4th century BC. In contrast to themodern 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 Latin:vis viva, or living force, which defined as the product of the mass of anobject and its velocity squared; he believed that total vis viva wasconserved. To account for slowing due to friction, Leibniz theorized thatthermal energy consisted of the random motion of the constituent parts ofmatter, a view shared by Isaac Newton, although it would be more than acentury until this was generally accepted. The modern analog of thisproperty, kinetic energy, differs from vis via only by a factor of two.

In 1807, Thomas Young was possibly the first to use the term "energy"instead of vis viva, in its modern sense.[4] Gustave­Gaspard Coriolisdescribed "kinetic energy" in 1829 in its modern sense, and in 1853,William Rankine coined the term "potential energy". The law ofconservation of energy, was also first postulated in the early 19th century, and applies to any isolated system. It

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A schematic diagram of a Calorimeter­ An instrument used by physicists tomeasure energy. In this example it isX­Rays.

was argued for some years whether heat was a physical substance, dubbed the caloric, or merely a physicalquantity, such as momentum. In 1845 James Prescott Joule discovered the link between mechanical work and thegeneration of heat.

These developments led to the theory of conservation of energy, formalized largely by William Thomson (LordKelvin) as the field of thermodynamics. Thermodynamics aided the rapid development of explanations ofchemical processes by Rudolf Clausius, Josiah Willard Gibbs, and Walther Nernst. It also led to a mathematicalformulation of the concept of entropy by Clausius and to the introduction of laws of radiant energy by JožefStefan. According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws ofphysics do not change over time.[5] Thus, since 1918, theorists have understood that the law of conservation ofenergy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy,namely time.

Measurement and units

Energy, like mass, is a scalar physical quantity. The joule is theInternational System of Units (SI) unit of measurement for energy. It is aderived unit of energy, work, or amount of heat. It is equal to the energyexpended (or work done) in applying a force of one newton through adistance of one metre. However energy is also expressed in many otherunits such as ergs, calories, British Thermal Units, kilowatt­hours andkilocalories for instance. There is always a conversion factor for these tothe SI unit; for instance; one kWh is equivalent to 3.6 million joules.[6]

The SI unit of power (energy per unit time) is the watt, which is simply ajoule per second. Thus, a joule is a watt­second, so 3600 joules equal awatt­hour. The CGS energy unit is the erg, and the imperial and UScustomary unit is the foot pound. Other energy units such as the electronvolt, food calorie or thermodynamic kcal (based on the temperature change of water in a heating process), andBTU are used in specific areas of science and commerce and have unit conversion factors relating them to thejoule.

Because energy is defined as the ability to do work on objects, there is no absolute measure of energy. Only thetransition of a system from one state into another can be defined and thus energy is measured in relative terms.The choice of a baseline or zero point is often arbitrary and can be made in whatever way is most convenient fora problem. For example in the case of measuring the energy deposited by X­rays as shown in the accompanyingdiagram, conventionally the technique most often employed is calorimetry. This is a thermodynamic techniquethat relies on the measurement of temperature using a thermometer or of intensity of radiation using a bolometer.

Energy density is a term used for the amount of useful energy stored in a given system or region of space per unitvolume. For fuels, the energy per unit volume is sometimes a useful parameter. In a few applications, comparing,for example, the effectiveness of hydrogen fuel to gasoline it turns out that hydrogen has a higher specific energythan does gasoline, but, even in liquid form, a much lower energy density.

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.

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Work, a form 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 themechanical work article. Work and thus energy is frame dependent. For example, consider a ball being hit by abat. In the center­of­mass reference frame, the bat does no work on the ball. But, in the reference frame of theperson 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 classicalequations 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.[7]

Another energy­related concept is called the Lagrangian, after Joseph­Louis Lagrange. This is even morefundamental than the Hamiltonian, and can be used to derive the equations of motion. It was invented in thecontext of classical mechanics, but is generally useful in modern physics. The Lagrangian is defined as thekinetic energy minus the potential energy. Usually, the Lagrange formalism is mathematically more convenientthan the Hamiltonian for non­conservative systems (such as systems with friction).

Noether's theorem (1918) states that any differentiable symmetry of the action of a physical system has acorresponding conservation law. Noether's theorem has become a fundamental tool of modern theoretical physicsand the calculus of variations. A generalisation of the seminal formulations on constants of motion in Lagrangianand Hamiltonian mechanics (1788 and 1833, respectively), it does not apply to systems that cannot be modeledwith a Lagrangian; for example, dissipative systems with continuous symmetries need not have a correspondingconservation law.

Chemistry

In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular oraggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kindsof structure, it is invariably accompanied by an increase or decrease of energy of the substances involved. Someenergy is transferred between the surroundings and the reactants of the reaction in the form of heat or light; thusthe products of a reaction may have more or less energy than the reactants. A reaction is said to be exergonic ifthe final state is lower on the energy scale than the initial state; in the case of endergonic reactions the situation isthe reverse. Chemical reactions are invariably not possible unless the reactants surmount an energy barrier knownas the activation energy. The speed of a chemical reaction (at given temperature T) is related to the activationenergy E, by the Boltzmann's population factor e−E/kT – that is the probability of molecule to have energy greaterthan or equal to E at the given temperature T. This exponential dependence of a reaction rate on temperature isknown as the Arrhenius equation.The activation energy necessary for a chemical reaction can be in the form ofthermal 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 an organelle of abiological organism. Energy is thus often said to be stored by cells in the structures of molecules of substancessuch as carbohydrates (including sugars), lipids, and proteins, which release energy when reacted with oxygen inrespiration. In human terms, the human equivalent (H­e) (Human energy conversion) indicates, for a givenamount of energy expenditure, the relative quantity of energy needed for human metabolism, assuming anaverage human energy expenditure of 12,500kJ per day and a basal metabolic rate of 80 watts. For example, ifour bodies run (on average) at 80 watts, then a light bulb running at 100 watts is running at 1.25 human

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Basic overview of energy and humanlife.

equivalents (100 ÷ 80) i.e. 1.25 H­e. For a difficult task of only a few seconds' duration, a person can put outthousands of watts, many times the 746 watts in one official horsepower. For tasks lasting a few minutes, a fithuman can generate perhaps 1,000 watts. For an activity that must be sustained for an hour, output drops toaround 300; for an activity kept up all day, 150 watts is about the maximum.[8] The human equivalent assistsunderstanding of energy flows in physical and biological systems by expressing energy units in human terms: itprovides a "feel" for the use of a given amount of energy[9]

Sunlight is also captured by plants as chemical potential energy inphotosynthesis, when carbon dioxide and water (two low­energycompounds) are converted into the high­energy compoundscarbohydrates, lipids, and proteins. Plants also release oxygen duringphotosynthesis, which is utilized by living organisms as an electronacceptor, to release the energy of carbohydrates, lipids, and proteins.Release of the energy stored during photosynthesis as heat or light may betriggered suddenly by a spark, in a forest fire, or it may be made availablemore slowly for animal or human metabolism, when these molecules areingested, and catabolism is triggered by enzyme action.

Any living organism relies on an external source of energy—radiationfrom the Sun in the case of green plants; chemical energy in some form inthe case of animals—to be able to grow and reproduce. The daily 1500–2000 Calories (6–8 MJ) recommended for a human adult are taken as a combination of oxygen and foodmolecules, the latter mostly carbohydrates and fats, of which glucose (C6H12O6) and stearin (C57H110O6) areconvenient examples. The food molecules are oxidised to carbon dioxide and water in the mitochondria

C6H12O6 + 6O2 → 6CO2 + 6H2O

C57H110O6 + 81.5O2 → 57CO2 + 55H2O

and some of the energy is used to convert ADP into ATP

ADP + HPO42− → ATP + H2O

The rest of the chemical energy in the carbohydrate or fat is converted into heat: the ATP is used as a sort of"energy currency", and some of the chemical energy it contains when split and reacted with water, is used forother metabolism (at each stage of a metabolic pathway, some chemical energy is converted into heat). Only atiny fraction of the original chemical energy is used for work:[10]

gain in kinetic energy of a sprinter during a 100 m race: 4 kJgain in gravitational potential energy of a 150 kg weight lifted through 2 metres: 3kJDaily 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 energythey receive (chemical energy or radiation), and it is true that most real machines manage higher efficiencies. Ingrowing organisms the energy that is converted to heat serves a vital purpose, as it allows the organism tissue tobe highly ordered with regard to the molecules it is built from. The second law of thermodynamics states thatenergy (and matter) tends to become more evenly spread out across the universe: to concentrate energy (ormatter) in one specific place, it is necessary to spread out a greater amount of energy (as heat) across theremainder of the universe ("the surroundings").[11] Simpler organisms can achieve higher energy efficiencies thanmore complex ones, but the complex organisms can occupy ecological niches that are not available to theirsimpler brethren. The conversion of a portion of the chemical energy to heat at each step in a metabolic pathway

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is the physical reason behind the pyramid of biomass observed in ecology: to take just the first step in the foodchain, of the estimated 124.7 Pg/a of carbon that is fixed by photosynthesis, 64.3 Pg/a (52%) are used for themetabolism of green plants,[12] i.e. reconverted into carbon dioxide and heat.

Earth sciences

In geology, continental drift, mountain ranges, volcanoes, and earthquakes are phenomena that can be explainedin terms of energy transformations in the Earth's interior.,[13] while meteorological phenomena like wind, rain,hail, snow, lightning, tornadoes and hurricanes, are all a result of energy transformations brought about by solarenergy on the atmosphere of the planet Earth.

Sunlight may be stored as gravitational potential energy after it strikes the Earth, as (for example) waterevaporates from oceans and is deposited upon mountains (where, after being released at a hydroelectric dam, itcan be used to drive turbines or generators to produce electricity). Sunlight also drives many weather phenomena,save those generated by volcanic events. An example of a solar­mediated weather event is a hurricane, whichoccurs when large unstable areas of warm ocean, heated over months, give up some of their thermal energysuddenly 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 drivesplate tectonics and may lift mountains, via orogenesis. This slow lifting represents a kind of gravitationalpotential energy storage of the thermal energy, which may be later released to active kinetic energy in landslides,after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a store that has beenproduced ultimately from the same radioactive heat sources. Thus, according to present understanding, familiarevents such as landslides and earthquakes release energy that has been stored as potential energy in the Earth'sgravitational field or elastic strain (mechanical potential energy) in rocks. Prior to this, they represent release ofenergy that has been stored in heavy atoms since the collapse of long­destroyed supernova stars created theseatoms.

Cosmology

In cosmology and astronomy the phenomena of stars, nova, supernova, quasars and gamma ray bursts are theuniverse's highest­output energy transformations of matter. All stellar phenomena (including solar activity) aredriven by various kinds of energy transformations. Energy in such transformations is either from gravitationalcollapse 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 Sunalso 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 intoheavier 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 cloudswhen 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 as a time derivative of the wavefunction. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Inresults can be considered as a definition of measurement of energy in quantum mechanics. The Schrödingerequation describes the space­ and time­dependence of slow changing (non­relativistic) wave function of quantumsystems. The solution of this equation for bound system is discrete (a set of permitted states, each characterizedby an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for anyoscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to thefrequency by Planck's relation: (where is the Planck's constant and the frequency). In the case ofelectromagnetic wave these energy states are called quanta of light or photons.

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Relativity

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

,

where

m is the mass,c is the speed of light in vacuum,E is the rest mass energy.

For example, consider electron–positron annihilation, in which the rest mass of individual particles is destroyed,but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy isassociated with mass), and this inertia and invariant mass is carried off by photons which individually aremassless, but as a system retain their mass. This is a reversible process ­ the inverse process is called paircreation ­ in which the rest mass of particles is created from energy of two (or more) annihilating photons. In thissystem the matter (electrons and positrons) is destroyed and changed to non­matter energy (the photons).However, the total system mass and energy do not change during this interaction.

In general relativity, the stress–energy tensor serves as the source term for the gravitational field, in roughanalogy to the way mass serves as the source term in the non­relativistic Newtonian approximation.[14]

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

In classical physics, energy is a scalar quantity, the canonical conjugate to time. In special relativity energy isalso a scalar (although not a Lorentz scalar but a time component of the energy–momentum 4­vector).[14] In otherwords, 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 theseforms are called transducers. Examples of transducers include a battery, from chemical energy to electric energy;a dam: gravitational potential energy to kinetic energy of moving water (and the blades of a turbine) andultimately to electric energy through an electric generator.

There are strict limits to how efficiently energy can be converted into other forms of energy via work, and heat asdescribed by Carnot's theorem and the second law of thermodynamics. These limits are especially evident whenan engine is used to perform work. However, some energy transformations can be quite efficient. The directionof transformations in energy (what kind of energy is transformed to what other kind) is often determined byentropy (equal energy spread among all available degrees of freedom) considerations. In practice all energytransformations are permitted on a small scale, but certain larger transformations are not permitted because it isstatistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

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Energy transformations in the universe over time are characterized by various kinds of potential energy that hasbeen available since the Big Bang, later being "released" (transformed to more active types of energy such askinetic or radiant energy), when a triggering mechanism is available. Familiar examples of such processesinclude nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such asuranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy releasedfrom the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before theywere incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fissionbombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potentialenergy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of apendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum.At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one(unrealistically) assumes that there is no friction or other losses, the conversion of energy between theseprocesses 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 energyconstantly. This is referred to as conservation of energy. In this closed system, energy cannot be created ordestroyed; therefore, the initial energy and the final energy will be equal to each other. This can be demonstratedby the following:

(4)

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 isalso equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount ofenergy, and likewise always appears associated with it, as described in mass­energy equivalence. The formulaE = mc², derived by Albert Einstein (1905) quantifies the relationship between rest­mass and rest­energy withinthe 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 Mass­energyequivalence#History for further information).

Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energyequivalence remains a constant for both the matter and the energy, during any process when they are convertedinto each other. However, since is extremely large relative to ordinary human scales, the conversion ofordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation)can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclearreactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why aloss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is verylarge. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are foundin high­energy nuclear physics.

Reversible and non­reversible 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 avolume, from which it cannot be recovered into more concentrated forms (fewer quantum states), withoutdegradation of even more energy. A reversible process is one in which this sort of dissipation does not happen.

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For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulumsystem described above. In processes where heat is generated, quantum states of lower energy, present aspossible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot berecovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy mustpartly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase insome other kind of heat­like increase in disorder in quantum states, in the universe (such as an expansion ofmatter, or a randomisation in a crystal).

As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heator other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death ofthe universe. In this heat death the energy of the universe does not change, but the fraction of energy which isavailable to do work through a heat engine, or be transformed to other usable forms of energy (through the use ofgenerators attached to heat engines), grows less and less.

Conservation of energy

According to conservation of energy, energy can neither be created (produced) nor destroyed by itself. It canonly be transformed. The total inflow of energy into a system must equal the total outflow of energy from thesystem, plus the change in the energy contained within the system. Energy is subject to a strict globalconservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whoseinteractions do not depend explicitly on time, it is found that the total energy of the system always remainsconstant.[15]

Richard Feynman said during a 1961 lecture:[16]

There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. Thereis no known exception to this law—it is exact so far as we know. The law is called the conservationof energy. It states that there is a certain quantity, which we call energy, that does not change inmanifold changes which nature undergoes. That is a most abstract idea, because it is a mathematicalprinciple; it says that there is a numerical quantity which does not change when something happens.It is not a description of a mechanism, or anything concrete; it is just a strange fact that we cancalculate some number and when we finish watching nature go through her tricks and calculate thenumber again, it is the same.

—The Feynman Lectures on Physics

Most kinds of energy (with gravitational energy being a notable exception)[17] are subject to strict localconservation laws as well. In this case, energy can only be exchanged between adjacent regions of space, and allobservers agree as to the volumetric density of energy in any given space. There is also a global law ofconservation of energy, stating that the total energy of the universe cannot change; this is a corollary of the locallaw, but not vice versa.[2][16]

This law is a fundamental principle of physics. As shown rigorously by Noether's theorem, the conservation ofenergy is a mathematical consequence of translational symmetry of time,[18] a property of most phenomenabelow 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 iscanonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertaintyprinciple ­ it is impossible to define the exact amount of energy during any definite time interval. The uncertaintyprinciple should not be confused with energy conservation ­ rather it provides mathematical limits to whichenergy can in principle be defined and measured.

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Each of the basic forces of nature is associated with a different type of potential energy, and all types of potentialenergy (like all other types of energy) appears as system mass, whenever present. For example, a compressedspring will be slightly more massive than before it was compressed. Likewise, whenever energy is transferredbetween 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 inthe energy is by

which is similar in form to the Heisenberg Uncertainty Principle (but not really mathematically equivalentthereto, since H and t are not dynamically conjugate variables, neither in classical nor in quantum mechanics).

In particle physics, this inequality permits a qualitative understanding of virtual particles which carry momentum,exchange by which and with real particles, is responsible for the creation of all known fundamental forces (moreaccurately known as fundamental interactions). Virtual photons (which are simply lowest quantum mechanicalenergy state of photons) are also responsible for electrostatic interaction between electric charges (which resultsin Coulomb law), for spontaneous radiative decay of exited atomic and nuclear states, for the Casimir force, forvan der Waals bond forces and some other observable phenomena.

Transfer between systems

Closed systems

Energy transfer usually refers to movements of energy between systems which are closed to transfers of matter.The portion of the energy which is transferred by conservative forces over a distance is measured as the work thesource system does on the receiving system. The portion of the energy which does not do work doing during thetransfer is called heat.[19] Energy can be transferred between systems in a variety of ways. Examples include thetransmission of electromagnetic energy via photons, physical collisions which transfer kinetic energy,[20] and theconductive transfer of thermal energy.

Energy is strictly conserved and is also locally conserved wherever it can be defined. Mathematically, the processof energy transfer is described by the first law of thermodynamics:

(1)

where is the amount of energy transferred, represents the work done on the system, and represents theheat flow into the system.[21] As a simplification, the heat term, , is sometimes ignored, especially when thethermal efficiency of the transfer is high.

(2)

This simplified equation is the one used to define the joule, for example.

Open systems

There are other ways in which an open system can gain or lose energy. In chemical systems, energy can be addedto a system by means of adding substances with different chemical potentials, which potentials are then extracted(both of these process are illustrated by fueling an auto, a system which gains in energy thereby, without additionof either work or heat). These terms may be added to the above equation, or they can generally be subsumed intoa quantity called "energy addition term " which refers to any type of energy carried over the surface of a

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control volume or system volume. Examples may be seen above, and many others can be imagined (for example,the kinetic energy of a stream of particles entering a system, or energy from a laser beam adds to system energy,without either being either work­done or heat­added, in the classic senses).

(3)

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

Thermodynamics

Internal energy

Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to create thesystem. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometricaspects, as well as the motion of the particles, in form of kinetic energy. Thermodynamics is chiefly concernedwith changes in internal energy and not its absolute value, which is impossible to determine withthermodynamics alone.[22]

First law of thermodynamics

The first law of thermodynamics asserts that energy (but not necessarily thermodynamic free energy) is alwaysconserved[23] and that heat flow is a form of energy transfer. For homogeneous systems, with a well­definedtemperature and pressure, a commonly used corollary of the first law is that, for a system subject only to pressureforces and heat transfer (e.g., a cylinder­full of gas), 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 andentropy S (in which entropy increases and the change dS is positive when the system is heated), and the last termon the right hand side is identified as work done on the system, where pressure is P and volume V (the negativesign results since compression of the system requires work to be done on it and so the volume change, dV, isnegative when work is done on the system).

This equation is highly specific, ignoring all chemical, electrical, nuclear, and gravitational forces, effects such asadvection of any form of energy other than heat and pV­work. 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 thechange 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 alternatively kinetic and potential. At twopoints in the oscillation cycle it is entirely kinetic, and alternatively at two other points it is entirely potential.Over the whole cycle, or over many cycles, net energy is thus equally split between kinetic and potential. This iscalled equipartition principle; total energy of a system with many degrees of freedom is equally split among allavailable degrees of freedom.

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This principle is vitally important to understanding the behaviour of a quantity closely related to energy, calledentropy. Entropy is a measure of evenness of a distribution of energy between parts of a system. When anisolated system is given more degrees of freedom (i.e., given new available energy states that are the same asexisting states), then total energy spreads over all available degrees equally without distinction between "new"and "old" degrees. This mathematical result is called the second law of thermodynamics.

See also

CombustionIndex of energy articlesIndex of wave articlesOrders of magnitude (energy)

Notes and references

1. ^ Energy units are usually defined in terms of the work they can do. However, because work is an indirect measurementof energy, (One example of the difficulties involved: if you use the first law of thermodynamics to define energy as thework an object can do, you must perform a perfectly reversible process, which is impossible in a finite time.) manyexperts emphasize understanding how energy behaves, specifically the conservation of energy, rather than trying toexplain what energy "is". "The Feynman Lectures on Physics Vol I."(http://www.colorado.edu/physics/phys1110/phys1110_fa10/Feynman_energy.pdf). Retrieved 3 Apr 2014.

2. ^ a b The Laws of Thermodynamics (http://www.av8n.com/physics/thermo­laws.htm) including careful definitions ofenergy, free energy, et cetera.

3. ^ Harper, Douglas. "Energy" (http://www.etymonline.com/index.php?term=energy). Online Etymology Dictionary.Retrieved May 1, 2007.

4. ^ Smith, Crosbie (1998). The Science of Energy – a Cultural History of Energy Physics in Victorian Britain. TheUniversity of Chicago Press. ISBN 0­226­76420­6.

5. ^ Lofts, G; O'Keeffe D; et al. (2004). "11 — Mechanical Interactions". Jacaranda Physics 1 (2 ed.). Milton,Queensland, Australia: John Willey & Sons Australia Ltd. p. 286. ISBN 0­7016­3777­3.

6. ^ Ristinen, Robert A., and Kraushaar, Jack J. Energy and the Environment. New York: John Wiley & Sons, Inc., 2006.7. ^ The Hamiltonian (http://classic­

web.archive.org/web/20071011135413/http://www.sustech.edu/OCWExternal/Akamai/18/18.013a/textbook/HTML/chapter16/section03.html) MIT OpenCourseWare website 18.013A Chapter 16.3 Accessed February 2007

8. ^ "Retrieved on May­29­09" (http://www.uic.edu/aa/college/gallery400/notions/human%20energy.htm). Uic.edu.Retrieved 2010­12­12.

9. ^ Bicycle calculator ­ speed, weight, wattage etc. [1] (http://bikecalculator.com/).10. ^ 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 of the sprinter and the force of the weightlifter. A worker stacking shelves in asupermarket does more work (in the physical sense) than either of the athletes, but does it more slowly.

11. ^ Crystals are another example of highly ordered systems that exist in nature: in this case too, the order is associatedwith the transfer of a large amount of heat (known as the lattice energy) to the surroundings.

12. ^ Ito, Akihito; Oikawa, Takehisa (2004). "Global Mapping of Terrestrial Primary Productivity and Light­UseEfficiency with a Process­Based Model. (http://www.terrapub.co.jp/e­library/kawahata/pdf/343.pdf)" in Shiyomi, M. etal. (Eds.) Global Environmental Change in the Ocean and on Land. pp. 343–58.

13. ^ "Earth's Energy Budget" (http://okfirst.ocs.ou.edu/train/meteorology/EnergyBudget.html). Okfirst.ocs.ou.edu.

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Further reading

Alekseev, G. N. (1986). Energy and Entropy. Moscow: Mir Publishers.Crowell, Benjamin (2011) [2003]. Light and Matter (http://www.lightandmatter.com/html_books/lm/ch11/ch11.html).Fullerton, California: Light and Matter.Ross, John S. (23 April 2002). "Work, Power, Kinetic Energy"(http://www.physnet.org/modules/pdf_modules/m20.pdf). Project PHYSNET. Michigan State University.Smil, Vaclav (2008). Energy in nature and society: general energetics of complex systems. Cambridge, USA: MITPress. ISBN 0­262­19565­8.Walding, Richard, Rapkins, Greg, Rossiter, Glenn (1999­11­01). New Century Senior Physics. Melbourne, Australia:Oxford University Press. ISBN 0­19­551084­4.

External links

Energy (https://www.dmoz.org/Science/Technology/Energy) at DMOZ

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Categories: Energy (physics) Energy State functions

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Retrieved 2010­12­12.

14. ^ a b Misner, Thorne, Wheeler (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0­7167­0344­0.15. ^ Berkeley Physics Course Volume 1. Charles Kittel, Walter D Knight and Malvin A Ruderman

16. ^ a b Feynman, Richard (1964). The Feynman Lectures on Physics; Volume 1. U.S.A: Addison Wesley. ISBN 0­201­02115­3.

17. ^ "E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws"(http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html). Physics.ucla.edu. 1918­07­16. Retrieved2010­12­12.

18. ^ "Time Invariance" (http://ptolemy.eecs.berkeley.edu/eecs20/week9/timeinvariance.html). Ptolemy.eecs.berkeley.edu.Retrieved 2010­12­12.

19. ^ Although heat is "wasted" energy for a specific energy transfer,(see: waste heat) it can often be harnessed to do usefulwork in subsequent interactions. However, the maximum energy that can be "recycled" from such recovery processes islimited by the second law of thermodynamics.

20. ^ The mechanism for most macroscopic physical collisions is actually electromagnetic, but it is very common tosimplify the interaction by ignoring the mechanism of collision and just calculate the beginning and end result.

21. ^ The signs in this equation follow the IUPAC convention.22. ^ I. Klotz, R. Rosenberg, Chemical Thermodynamics ­ Basic Concepts and Methods, 7th ed., Wiley (2008), p.3923. ^ Kittel and Kroemer (1980). Thermal Physics. New York: W. H. Freeman. ISBN 0­7167­1088­9.