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http://en.wikipedia.org/wiki/Energy

All text is available under the terms of the GNU Free Documentation License: http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License

# Energy

Energy is a fundamental concept of physics, with applications throughout the natural sciences.

Energy is subject to a strict local conservation law; that is, it can neither be created nor destroyed. It can only be exchanged between adjacent regions of 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.[1] [2] Conservation of energy is associated with the symmetry of the laws of physics, namely invariance with respect to time (via Noether's theorem).

• The total energy of a system can be subdivided and classified in various ways. For example, it is sometimes convenient to distinguish kinetic energy from potential energy. It may also be convenient to distinguish gravitational energy, electrical energy, thermal energy, and other forms. These classifications overlap; for instance thermal energy usually consists partly of kinetic and partly of potential energy.
• The transfer of energy can take various forms; familiar examples include work, heat flow, and advection, as discussed below.
• 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 technical terminology. For example, the important public-service announcement, "Please conserve energy" uses vernacular notions of "conservation" and "energy" which make sense in their own context but are utterly incompatible with the technical notions of "conservation" and "energy" (such as are used in the law of conservation of energy).[2].

In classical physics energy is considered a scalar quantity, having no direction in space. In special relativity energy is not a Lorentz scalar, but rather one component of the energy-momentum 4-vector, such that energy is associated with the timelike direction.[3] In other words, energy is invariant with respect to spacelike rotations, but not invariant with respect to boosts.

Lightning is a highly visible form of energy transfer.

## Etymology

Look up Energy in
Wiktionary, the free dictionary.

Energy comes from the Greek ενέργεια, where εν- means "in" and έργον "work". The compound εν-εργεια in Epic Greek meant "divine action" or "magical operation"; it was later used by Aristotle with the meaning of "activity, operation" or "vigour", and by Diodorus Siculus for "force of an engine."

## Definitions

Energy is so fundamental that it is not easily defined in terms of anything more fundamental.

For a general audience, rather than worrying about the details of a formal definition, it is far easier and far more useful to understand what energy does in various situations. This is called the "energy is as energy does" school of thought. This approach emphasizes examples of energy, the strict local conservation of energy, and the connection between energy and other quantities of interest. Thus, some textbooks[1] take the view that energy is primary and fundamental, and introduce it as a thing in itself, without relying on prior notions of force or work. Other textbooks first discuss work, and then introduce energy via equation (1) (below). That is appropriate for introductory purposes, but should not be carried too far. It is an approximation, neglecting the terms that appear in equation (2) (below).

In some quarters it is conventional to define "energy" as the capacity to do work. This definition is prevalent in textbooks, dictionaries, and other nontechnical references.[4] This notion of "energy" (or, rather, "available energy") is useful for some purposes, as discussed on the disambiguation page. However, it is not governed by a local conservation law, is not the physics energy, and is not the subject of this article. It is easy to find examples[2] where increasing the energy of a system decreases its capacity to do work. These examples, and others, eliminate any hope of finding a one-to-one correspondence between the physics energy and the "available energy" i.e. the capacity to do work.

## Historical perspective

Main articles: Timeline of thermodynamics, statistical mechanics, and random processes and History of Physics

The concept of energy, in the distant past, was used to explain easily observable phenomena, such as the effects observed on the properties of objects. It was generally construed that all changes could in fact be explained through some sort of energy. Soon the idea that energy could be stored in objects took its roots in scientific thought and the concept of energy came to embrace the idea of the potential for change as well as change itself. Such effects (both potential and realized) come in many different forms. While in spiritualism they were reflected in changes in a person, in physical sciences it is reflected in different forms of energy itself, for example, electrical energy stored in a battery, the chemical energy stored in a piece of food (along with the oxygen needed to burn it), the thermal energy of a water heater, or the kinetic energy of a moving train. In 1807, Thomas Young was the first to use the term "energy" instead of vis viva to refer to the product of the mass of an object and its velocity squared. Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, and in 1853, William Rankine coined the term "potential energy."

Lord Kelvin

The development of steam engines required engineers to develop concepts and formulas that would allow them to describe the mechanical and thermal efficiencies of their systems. Engineers such as Sadi Carnot and James Prescott Joule, mathematicians such as Émile Clapeyron and Hermann von Helmholtz , and amateurs such as Julius Robert von Mayer all contributed to the notion that the ability to perform certain tasks, called work, was somehow related to the amount of energy in the system. The nature of energy was elusive, however, and it was argued for some years whether energy was a substance (the caloric) or merely a physical quantity, such as momentum.

William Thomson (Lord Kelvin) amalgamated all of these laws into the laws of thermodynamics, which aided in the rapid development of explanations of chemical processes using the concept of energy by Rudolf Clausius, Josiah Willard Gibbs and Walther Nernst. It also led to a mathematical formulation of the concept of entropy by Ludwig Boltzmann, and to the introduction of laws of radiant energy by Jožef Stefan,

During a 1961 lecture[1] for undergraduate students at the California Institute of Technology, Richard Feynman, a celebrated physics teacher and Nobel Laureate, said this about the concept of energy:

—The Feynman Lectures on Physics, Vol. 1.

## Energy and contexts in science

The concepts of energy and its transformations are useful in explaining natural phenomena. The law of conservation of energy is equally useful. The direction of transformations explained with the help of energy is often influenced by entropy considerations also. It is very often used in almost all fields of science. The exact context of various natural phenomena and transformations varies from one natural science to another. Some examples are:

## Physics

### Energy transfer

Because energy is strictly and locally conserved, it is important to take note of the transfer of energy between the "system" and adjacent regions. A familiar example is mechanical work. In simple cases this contribution is:

ΔE = W             (1)

if there are no other energy-transfer processes involved. Here ΔE  is the amount of energy transferred, and W  represents the work done on the system.

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

ΔE = W + Q + A             (2)

where Q  represents the heat flow into the system, and A  represents advection[1] of energy.

In this context, advection means, literally, carrying energy across the boundary of the system. Putting new batteries into a flashlight is a familiar example of advection. It increases the energy content of the flashlight-system, but clearly cannot be categorized as work or heat-flow.

Note that these formulas speak only of the change in energy, and are entirely insensitive to the total amount of energy in the system. Indeed, in all of classical physics — everything but relativity — the absolute amount of energy is arbitrary and devoid of physical significance; only changes in energy appear in the classical equations of motion.

Energy transfers must uphold all the laws of physics, including the conservation laws among many others. A transfer that might be consistent with one law might be forbidden by another law.

### The Hamiltonian

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.[5]

### The Lagrangian

Another energy-related concept is called the Lagrangian, after Joseph Louis Lagrange. This is in some ways even more fundamental than the Hamiltonian, and can be used to derive the equations of motion.[specify] In simple cases the Lagrangian can be written as kinetic energy minus potential energy.

### Energy and Thermodynamics

According to the second law of thermodynamics, work can be totally converted into heat, but not vice versa. The first law of thermodynamics simply asserts that energy is conserved,[6] and that heat is included as a form of energy transfer. A commonly-used corollary of the first law is:

$\mathrm{d}E = T\mathrm{d}S - P\mathrm{d}V\,$,

where the last term on the RHS is identified as "work". This useful corollary is not entirely general, because it ignores advection, and because it depends on temperature. The most general statement of the first law — i.e. conservation of energy — is valid even in situations in which temperature is undefinable.

Energy is sometimes expressed as:

$\mathrm{d}E=\delta Q-\delta W\,$,

which is unsatisfactory[2] because there cannot exist any thermodynamic state functions W or Q that are meaningful on the RHS of that equation, except perhaps in trivial cases.

### Oscillators, phonons, and photons

The energy of a mechanical harmonic oscillator (a mass on a spring) is alternatively kinetic and potential. At two points in the cycle it is entirely kinetic, and alternatively at two other points entirely potential. Over the whole cycle, or over many cycles or over an ensemble of unsynchronized oscillators, the average energy is equally kinetic and potential.

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

In ideal gases, all of the energy is kinetic, making ideal gases an exception of a sort.

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

1. By extension of the previous line of thought, in free space the electromagnetic field can be considered an ensemble of oscillators, meaning that radiation energy can be considered equally potential and kinetic. This model is useful, for example, when the electromagnetic Lagrangian is of primary interest and is interpreted in terms of potential and kinetic energy.
2. On the other hand, in the key equation m2c4 = E2p2c2, the contribution mc2 is called the rest energy, and all other contributions to the energy are called kinetic energy. For a particle that has mass, this implies that the kinetic energy is 0.5p2 / m at speeds much smaller than c, as can be proved by writing E = mc2 √(1 + p2m − 2c − 2) and expanding the square root to lowest order. By this line of reasoning, the energy of a photon is entirely kinetic, because the photon is massless and has no rest energy. This expression is useful, for example, when the energy-versus-momentum relationship is of primary interest.

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

### Work and virtual work

Main articles: Mechanics, Mechanical work, Thermodynamics, and Quantum mechanics

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

$W = \int \mathbf{F} \cdot \mathrm{d}\mathbf{s}$

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

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

### Quantum mechanics

The concept of quantized energy is a product of quantum mechanics. Any system can be described by the Schrodinger equation, and for bound systems the solution of this leads to certain permitted states, each characterized by an energy level. In the realm of wave mechanics energy is related to the frequency of the wave by the Planck equation E = hν (where h is the Planck's constant and ν the frequency).

### Relativity

According to special relativity, mass can make a large contribution to the energy.[3] This can be seen from the relativistic equation

m2c4 = E2p2c2,

where

m is the mass,
c is the speed of light,
E is the energy, and
p is the 3-dimensional momentum.

In this equation E does not correspond to the total energy, but only to the rest energy, that is, the energy when the momentum is zero. (Note that this equation has an elegant interpretation in terms of the dot product of the 4-momentum with itself.)

For example, consider electron-positron annihilation, in which mass is destroyed and the energy is carried off by massless photons. There are many similar processes. There are also processes that proceed in the other direction, such as pair creation, in which mass is created from other forms of energy.

In general relativity,[3] 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.

It is a common misconception to assert that energy is "equivalent" to mass. This is clearly not true, as can be seen from the equation above. They are equal when the momentum is zero, but they are not equal in general, and they are not equivalent. Neither the total energy E nor the rest energy mc² serves as the source term for the gravitational field in general relativity; the stress-energy tensor is considerably more complicated than that.

In the modern view, rest energy (aka mass) is included as one contribution to the energy E, although this contribution was not recognized until the 20th century[7].

It is a misconception to speak of "mass+energy" as a conserved quantity. That misconception presumably arises from trying to reconcile the conservation law with a pre-20th-century definition of energy. In the modern view, the rest energy (aka mass) is included in the definition of energy. Therefore the relevant conservation law is as simple as can be: E is conserved.

## Chemistry

Main articles: Chemical thermodynamics, Chemical kinetics, Thermochemistry, and Photochemistry

Atoms and molecules, the central concepts of chemistry, are made up of electrically charged electrons and protons, and therefore coulomb force is at work during the rearrangement of atoms (during formation or decomposition of molecules). The work of this force is what we call "chemical energy".

A chemical reaction invariably absorbs or releases heat or light. Usually there is some potential barrier between the two equilibrium states - initial state of reactants, and final state of products of chemical reaction (even when the final state is lower than the initial) - just by the definition of stable equilibrium (= local minimum of potential energy). Thus, chemical reactions usually require so called activation energy (in form of heat or light) to overcome this barrier and to proceed. A reaction is said to be exothermic if the final state is lower than in initial and endothermic otherwise.

Electrons in atoms and molecules obey rules of quantum mechanics which require quantization of energy of a bound system. The existence of energy levels allows identification of atoms and molecules by their spectral lines. This makes possible to identify the composition of remote objects - like stars and far galaxies - by analysing their radiation (see spectroscopy).

Emission spectrum of iron

These lines (so called because they appear as linear features in dispersion spectra (see example above), such as might be produced by a prism or diffraction grating) are the results of release or absorption of certain specific amount of energy involved in the transition of atoms or molecules from one state to another.

The speed of a chemical reaction (at given temperature T) is related to the activation energy E, by the Boltzmann's population factor e E / kT - that is the probability of molecule to have energy greater than or equal to E at the given temperature T. This exponential dependence of a reaction rate on temperature is known in chemistry as the Arrhenius equation.

## Biology

Main articles: Biological thermodynamics, Cellular respiration, Photosynthesis, and Chemosynthesis

Growth, development and metabolism are some of the central phenomena in the study of biology. They cannot be explained without invoking the energy concept. Indeed sustenance of life itself is critically dependent on energy transformations; living organisms survive because of exchange of energy within and without. In a living organism chemical bonds are constantly broken and made to make the exchange and transformation of energy possible. These chemical bonds are most often bonds in carbohydrates, including sugars. Other chemical bonds include bonds in chemical compounds that are important for metabolism, for example, those in a molecule of ATP or fats and oils.[8] These molecules, along with oxygen, are common stores of concentrated energy for the biological processes. One can therefore assert that transformation of energy from a more to a less concentrated form is the driving force of all biological processes or chemical processes that are responsible for the life of a biological organism. Molecular biology and biochemistry are in fact scientific studies concerning the making and breaking of chemical bonds in the molecules found in biological organisms.

As with other natural phenomena, the exchange of metabolic energy in biological organisms also increases the entropy of the universe. Nearly all energy transformations studied in biology are due to the chemical synthesis and decompositions ultimately brought about by the energy absorbed from photons in sunlight through insolation[9] and photosynthesis.[10] The total energy captured by photosynthesis in green plants from the solar radiation is about 2 x 1023 joules of energy per year.[11] This is about 4% of the total sunlight energy which reaches Earth.

The predator-prey relationships, food chains, are in effect energy transformations within ecosystems that are studied in ecology.

## Meteorology

A volcano is the release of stored energy from below the surface of Earth originating in radioactive decay and gravitational sorting in the Earth's core and mantle of energies left over from its formation

## Geology

Continental drift, mountain ranges, volcanos, and earthquakes are phenomena that are a result of energy transformations in the Earth's crust. Recent studies suggest that the Earth transforms about 6.18 x 10-12 J/s (joules per second) per kilogram. Given the Earth's mass of about 5.97 x 1024 kilograms, this means that the rate of energy transformations inside the Earth is about 37 x 1012 J/s (37 terawatts). This is only about 0.1% of the amount of energy Earth receives from Sun in the form of sunlight and radiates back into space in the form of IR blackbody radiation (~4 x 1016 J/s = 40 petawatts).

From the study of neutrinos radiated from the Earth (see KamLAND), scientists have recently estimated that about 24 terawatts (65%) of this rate of energy transformation is due to radioactive decay (principally of potassium 40, thorium 232 and uranium 238), and the remaining 13 terawatts is from the continuous gravitational sorting of the core and mantle of the earth, energies left over from the formation of the Earth, about 4.57 billion years ago (this sorting represents continuing gravitational collapse of the Earth into the maximally compact object which is consistent with its composition-- a process which releases gravitational potential energy). The magnitude of both of these energy sources decline over time, and based on half-life alone, it has been estimated that the current radioactive energy of the planet represents less than 1% of that which was available at the time the planet was formed.

As a result, geological forces of continental accretion, subduction and sea floor spreading, account for 90% of the Earth's energy. The remaining 10% of geological tectonic energy comes through hotspots produced by mantle plumes, resulting in shield volcanoes like Hawaii, geyser activity like Yellowstone or flood basalts like Iceland.

Tectonic process are driven by heat from the Earth's interior. The process is a simple heat engine which works via the upward buoyancy-induced motion of hot, low density magma after expansion by heat. The processes metamorphose weathered rocks, and (more importantly from the energy view) during orogeny periods, lift them up into mountain ranges. The potential energy represented by the mountain range's weight and height thus represents heat from the core of the Earth which has been partly transformed into gravitational potential energy. This potential energy may be suddenly released in landslides or tsunamis. Similarly, the energy release which drives an earthquake represents stresses in rocks that are mechanical potential energy which has been similarly stored from tectonic processes. An earthquake thus ultimately represents kinetic energy which is being released from elastic potential energy in rocks, which in turn has been stored from heat energy released by radioactive decay and gravitational collapse in the Earth's interior.

The energy which is responsible for the geological processes of erosion and deposition is a result of the interaction of solar energy and gravity. An estimated 23% of the total insolation is used to drive the water cycle. When water vapour condenses to fall as rain, it dissolves small amounts of carbon dioxide, making a weak acid. This acid acting upon the metallic silicates that form most rocks produces chemical weathering, removing the metals, and leading to the production of rocks and sand, carried by wind and water downslope through gravity to be deposited at the edge of continents in the sea. Physical weathering of rocks is produced by the expansion of ice crystals, left by water in the joint planes of rocks. A geologic cycle is continued when these eroded rocks are later uplifted into mountains.

## Astronomy and cosmology

The phenomona 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).

Dark energy is believed to make up 70% of the universe

Light elements, primarily hydrogen and helium, were created in the Big Bang. These light elements were spread too fast and too thinly in the Big Bang process (see nucleosynthesis) to form the most stable medium-sized atomic nuclei, like iron and nickel. This fact allows for later energy release, as such intermediate-sized elements are formed in our era. The formation of such atoms powers the steady energy-releasing reactions in stars, and also contributes to sudden energy releases, such as in novae. Gravitational collapse of matter into black holes is also thought to power the very most energetic processes, generally seen at the centers of galaxies (see quasars and in general active galaxies).

Cosmologists are still unable to explain all cosmological phenomena purely on the basis of known conventional forms of energy, for example those related to the accelerating expansion of the universe, and therefore invoke a yet unexplored form of energy called dark energy[12] to account for certain cosmological observations.

## Measurement

There is no absolute measure of energy. Rather energy is measured in terms of the transition of a system from one state into another.

### Methods

The methods for the measurement of energy often deploy methods for the measurement of still more fundamental concepts of science, viz. mass, distance, radiation, temperature, time, electric charge and electric current.

A Calorimeter - An instrument used by physicists to measure energy

Conventionally the technique most often employed are calorimetry, in thermodynamics that relies on the measurement of temperature: a thermometer or a bolometer for measurement of intensity of a radiation.

### Units

Main article: Units of energy

Through the history of science energy has been expressed in several different units, e.g. ergs and calorie. At present, the accepted unit of measurement for energy is the SI unit of energy is the joule.

## Kinetic and potential energy: general remarks

Main articles: Kinetic energy, Potential energy, Electromagnetic radiation, Photon, and Thermal energy

Classical kinetic energy is due to motion of a body, or particles within it (subject to length-scale restrictions, as discussed below).

Classical potential energy is due to the position of an object relative to other objects. This form of energy can be positive or negative, depending on whether it is work done on an object by a force, or work done by the object against a force. Negative energy is a thus a mathematical construct in reference to another system. Each of the fundamental interactions of nature can be linked to a kind of potential energy.

These notions of potential and kinetic energy depend on a notion of length scale. For example, one can speak of macroscopic potential and kinetic energy, which do not include thermal potential and kinetic energy. Also what is called chemical potential energy (below) is a macroscopic notion, and closer examination shows that it is really the sum of the potential and kinetic energy on the atomic and subatomic scale. Similar remarks apply to nuclear "potential" energy and most other forms of energy. This dependence on length scale is non-problematic if the various length scales are decoupled, as is often the case ... but confusion can arise when different length scales are coupled, for instance when friction converts macroscopic work into microscopic thermal energy.[13]

## Forms of potential energy

Heat, a form of energy, is partly potential energy and partly kinetic energy.

In the context of natural sciences, energy can be in any of several different forms: thermal, chemical, electrical, radiant, nuclear etc. Some basic textbooks broadly groups all these forms of energy into two broad categories:[14] kinetic energy and potential energy. However, some forms of energy resist such easy classification, as is the case with light energy. Other familiar types of energy (such as heat in most circumstances) are a varying mix of both potential and kinetic energy.

### Gravitational potential energy

Gravitational potential energy is the work of gravitational force during rearrangement of mutual positions of interacting masses - say, when masses are moved apart (such as when a crate is lifted), or closer together (as when a meteorite falls to Earth). If the masses of the objects are considered to be point masses, this work (thus the gravitational potential energy) is equal to

$E_{pG} = - {GmM \over r}$

where

m and M are the two masses in question,
r is the distance between them,
G is the gravitational constant.

### Electric potential energy

Electric potential energy is the ability of electric forces to do work during rearrangement of positions of charges (as for example when electric charge flows in a circuit), and this kind of potential also includes the common chemical potential energies (energy required to break chemical bonds, or obtained from forming them). Chemical potentials can be seen directly in the electrical potentials of electrochemical cell (grouped in batteries), and fuel cells. The energy released in lightning, from burning a litre of fuel oil, or from using an amount of electrical power from an electrical-wiring system, are all common examples of extracting work from motion of charge, which is stored beforehand as electromagnetic potential energy. Quantitatively, electromagnetic potential energy is:

$E_{pE} = {q Q \over 4\pi\epsilon_0 r}$

where

q and Q are the electric charges on the objects in question,
r is the distance between them,
ε0 is the electric constant of a vacuum.

In use of electrical energy from an electrical wiring system, or from a chemical battery, the electric potential energy available per amount of electric charge moved (which in turn is given by electric current multiplied by time), is represented by the electrical potential difference (measured in volts) between the conductors. Thus, when one ampere flows for one second across a potential of one volt, one joule of energy is made available from the electrical potential. The force which provides for the work that is done, is provided to the charge by an electrical field.

### Magnetic potential energy

Energy can also be stored in a magnetic field. Such fields are intrinsic properties of certain particles, but they also often result from relative motion of electric charges in an electrical current; for example, superconducting magnetic energy storage works via the mechanism of magnetic potential energy. Magnetic potential energy is closely related to electric potential energy, since both types of potential are mediated by the electromagnetic field. High power application of magnetic potential energy is perhaps most familar as the type of energy storage which allows transfer of power within an electrical transformer.

### Thermal potential energy

Potential thermal energy is the part of thermal energy which is not made up of kinetic thermal energy, and is thus stored as electric potential energy. This potential electrical part of thermal energy is stored in "deformation" of atomic bonds during thermal motion of atoms (as atoms oscillate around their position of equilibrium, they not only have kinetic energy of motion, but also a potential energy of displacement from equilibrium). This type of potential energy is a significant portion (about half) of thermal energy for strongly-bonded systems (solids and liquids), with the rest of thermal energy in such systems being the kinetic energy of the atoms. However, the potential part of thermal energy is a smaller fraction of thermal energy in gasses, which carry more than half of their thermal energy as various kinds of kinetic energies of the gas atoms.

### Chemical potential energy

Potential chemical energy of an object is the energy which may potentially be liberated as a result of transformations of chemical substances it is composed of.

The change in chemical potential energy in the course of a chemical transformation depends on the parameters like temperature, pressure and concentration. It is equal to the difference between the energy content of the product substances and that of the reactants. Energy is involved in breaking or making of chemical bonds. Some energy can be released as a result of rearrangement of bonds between atoms of a chemical substance (or a mixture thereof) only if the energy in the reactant chemical substances is more than that in product substances.

This change in energy is rigorously the change in internal energy. It can be calculated using the formula

ΔUo = Σ(ΔUfoproducts) - Σ(ΔUforeactants).

Where ΔUforeactants is the internal energy of formation of the reactant molecules that can be calculated from the bond energies of the various chemical bonds of the molecules under consideration and ΔUfoproducts is the internal energy of formation of the product molecules. The internal energy change of a process is equal to the heat change if it is measured under conditions of constant volume, as in a closed rigid container such as a bomb calorimeter. Under conditions of constant pressure, as in reactions in vessels open to the atmosphere, the heat change measured is not always the same as the internal energy change, since pressure-volume work releases or absorbs heat and energy. (The heat change at constant pressure is called the enthalpy change, in this case the enthalpy of formation).

The mixture of a hydrocarbon fuel and oxygen is an example: the hydrocarbon and oxygen molecules contain more energy in their C-H, C-C, and O-O bonds compared to the O-H and C-O bonds of the products of combustion (water and carbon dioxide). All chemical bonds represent missing energy; it takes energy to break ALL of them. Still, energy storage in chemical systems may be accomplished by making and breaking bonds: if net energy used in breaking bonds during a reaction is exceeded by energy released in making new bonds, energy will be released.

The chemical potential energy of a fuel appears as its heat of combustion. Food is similar to hydrocarbon fuel and carboydrate fuels, and when it is oxidized, its caloric content is similar (though not assessed in the same way as a hydrocarbon fuel-- see food energy).

Some chemical fuels or explosives (for example, nitroglycerine) do not require a second reactant substance to release their potential chemical energy, but even in these cases, the source of the energy released is the difference in the net difference in total strengths of the chemical bonds between the products and the reactants.

Another common form of chemical potential exists in batteries, but here again bonds are broken, and a standard chemical reaction occurs in which electrons are transferred from one atom to another, along an electrical potential (voltage gradient).

In chemical thermodynamics the term used for the chemical potential energy is chemical potential and for chemical transformation an equation most often used is Gibbs-Duhem equation

$\sum_iN_i\mathrm{d}\mu_i = - S\mathrm{d}T + V\mathrm{d}P \,$

### Elastic potential energy

Potential elastic energy is the energy stored in the elastic intermolecular bonds. Elastic energy is actually of several types: it is sometimes a kind of electric potential energy (as in metal springs), and in these cases energy is released as charged atoms which have been compressed are allowed to move apart. However, in other cases (such as compressed ideal gas) the potential energy is not stored as electric, but rather is stored as a kinetic energy of moving atoms.

In the ideal case of a metal spring described by Hooke's Law, the stored elastic energy is equal to:

$\!E_{pE} = {\frac{1}{2} k x^2}$

where

k is the spring constant, dependent on the individual spring,
x is the deformation of the object.

### Nuclear potential energy

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

Nuclear particles like protons and neutrons are not destroyed(law of conservation of energy) in fission and fusion processes (except in beta minus and beta plus decay or electron capture decay), but collections of them have less mass than if they were individually free, and this mass difference is liberated as heat and radiation in nuclear reactions (the heat and radiation have the missing mass, but it often escapes from the system, where it is not measured). The energy from the Sun, also called solar energy, is an example of this form of energy conversion. In the Sun, the process of hydrogen fusion converts about 4 million metric tons of solar matter per second into light, which is radiated into space. In this system, the light itself retains the mass and represents 4 million tons per second of electromagnetic field, moving into space.

## Transformations of energy

Main article: Energy conversion

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

Energy can be converted into matter and vice versa. The equation E=mc2, derived independently by Albert Einstein and Henri Poincaré quantifies the relationship between mass and rest energy. Since c2 is very large relative to ordinary human scales, the conversion of mass to other forms of energy can liberate tremendous amounts of energy, as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why loss of energy from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (particles) are found in high energy nuclear physics.

## Law of conservation of energy

Main article: Conservation of energy

Energy is subject to the law of conservation of energy. According to this law it can neither be created (produced) nor destroyed. It can only be transformed. This law is the mathematical consequence of translational symmetry of time (=indistinguishability of time intervals taken at different time) [15] - see Noether's theorem.

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

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

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

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

$\Delta E \Delta t \ge \frac {h} {4 \pi}$

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

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

• Activation energy
• Enthalpy
• Energy: world resources and consumption
• Free energy
• Interaction energy
• Internal energy
• Negative energy
• Orders of magnitude (energy)
• Power (physics)
• Renewable energy
• Thermodynamic entropy
• Thermodynamics
• Units of energy measurements

## Notes and references

1. ^ a b c Feynman, Richard (1964). The Feynman Lectures on Physics; Volume 1. U.S.A: Addison Wesley. ISBN 0-201-02115-3.
2. ^ a b c d The Laws of Thermodynamics including careful definitions of energy, free energy, et cetera.
3. ^ a b c Misner, Thorne, Wheeler (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0716703440.
4. ^ Parker, Cybil P. (1993). Encyclopedia of Physics. U.S.A: McGraw-Hill, Inc.. ISBN 0-07-051400-3.
5. ^ The Hamiltonian MIT OpenCourseWare website 18.013A Chapter 16.3 Accessed February 2007
6. ^ Kittel and Kroemer (1980). Thermal Physics. New York: W. H. Freeman. ISBN 0-7167-1088-9.
7. ^ http://forums.hypography.com/astronomy-cosmology/2363-massless-energy-nothing.html
8. ^ http://crab.rutgers.edu/~peterpal/Chap25.ppt#256,1,Biochemical Energetics
9. ^ http://www.geographypages.co.uk/insolation.htm
10. ^ The biological communities surrounding hydrothermal vents oxidize sulfur, obtaining their energy via chemosynthesis rather than photosynthesis. The oxygen used to do this is photosynthetically derived, but the sulfur in the thermodynamically unstable, non-oxidized state exists due to geothermal energy.
11. ^ Annual energy captured by photosynthesis in green plantsPDF (2.12 MiB)
12. ^ Science 20 June 2003:Vol. 300. no. 5627, pp. 1914 - 1918 Throwing Light on Dark Energy, Robert P. Kirshner. Accessed December 2006
13. ^
14. ^ http://www.lhup.edu/~dsimanek/glossary.htm
15. ^ http://ptolemy.eecs.berkeley.edu/eecs20/week9/timeinvariance.html
Other books
• Alekseev, G. N. (1986). Energy and Entropy. Moscow: Mir Publishers.
• Walding, Richard,  Rapkins, Greg,  Rossiter, Glenn (1999-11-01). New Century Senior Physics. Melbourne, Australia: Oxford University Press. ISBN 0-19-551084-4.

• Conservation of Energy - a chapter from an online textbook
• Work, Power, Kinetic EnergyPDF (399 KiB) on Project PHYSNET
• Freeview video 'Endless Energy' scientists discuss renewable energy. A programme by the Vega Science Trust and the BBC/OU
• What does energy really mean? From Physics World
• Compact description of various energy sources. Energy sources and ecology.
• World Energy Education Foundation
• Glossary of Energy Terms
• International Energy Agency IEA - OECD
• Energy & Environmental Security
• Energy for kids
• Energy riddle and transformations

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