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Encyclopedia > Energy
Lightning is the electric breakdown of air by strong electric fields. Heat and light from a lightning produces a plasm motion of air molecules.
Lightning is the electric breakdown of air by strong electric fields. Heat and light from a lightning produces a plasm motion of air molecules.

In physics and other sciences, energy (from the Greek ενεργός, energos, "active, working")[1] is a scalar physical quantity that is a property of objects and systems which is conserved by nature. Energy is often defined as the ability to do work. It has been suggested that Energy (Disambiguation) be merged into this article or section. ... Image File history File linksMetadata Download high resolution version (2048x3072, 3589 KB) This is a rotated version of Lightning over Oradea Romania. ... Image File history File linksMetadata Download high resolution version (2048x3072, 3589 KB) This is a rotated version of Lightning over Oradea Romania. ... Not to be confused with lighting. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... See scalar for an account of the broader concept also used in mathematics and computer science. ... A physical quantity is either a quantity within physics that can be measured (e. ... In thermodynamics, work is the quantity of energy transferred from one system to another without an accompanying transfer of entropy. ...


Several different forms of energy, including kinetic, potential, thermal, gravitational,sound energy, Light energy, elastic, electromagnetic, chemical, nuclear, and mass have been defined to explain all known natural phenomena. The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Potential energy can be thought of as energy stored within a physical system. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... Energy of two or more masses (or other forms of energy-momentum) gravitationally interacting with each other. ... The elastic energy is the energy which causes or is released by the elastic distortion of a solid or a fluid. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... This article concerns the energy stored in the nuclei of atoms; for the use of nuclear fission as a power source, see Nuclear power. ... The rest energy of a particle is its energy when it is not moving relative to a given inertial reference frame. ...


Energy is converted from one form to another. This principle, the conservation of energy, was first postulated in the early 19th century, and applies to any isolated system. According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.[2] Energy Transformation in Energy Systems Language In physics and engineering, poop transformation or energy conversion, is any process of transforming one form of energy to another. ... This article is about the law of conservation of energy in physics. ... In thermodynamics, an isolated system, as contrasted with a closed system, is a physical system that does not interact with its surroundings. ... Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ...


Although the total energy of a system does not change with time, its value may depend on the frame of reference. For example, a seated passenger in a moving airplane has zero kinetic energy relative to the airplane, but nonzero kinetic energy relative to the earth. This article or section is in need of attention from an expert on the subject. ...

Contents

History

Thomas Young - the first to use the term "energy" in the modern sense.
Thomas Young - the first to use the term "energy" in the modern sense.

The concept of energy emerged out of the idea of vis viva, which Leibniz defined as the product of the mass of an object and its velocity squared; he believed that total vis viva was conserved. To account for slowing due to friction, Leibniz claimed that heat consisted of the random motion of the constituent parts of matter — a view shared by Isaac Newton, although it would be more than a century until this was generally accepted. In 1807, Thomas Young was the first to use the term "energy", instead of vis viva, in its modern sense.[3] Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, and in 1853, William Rankine coined the term "potential energy." It was argued for some years whether energy was a substance (the caloric) or merely a physical quantity, such as momentum. The word energy seems to appear for the first time in the works of Aristotle. ... A timeline of events related to thermodynamics, statistical mechanics, and random processes. ... Since antiquity, human beings have sought to understand the workings of nature: why unsupported objects drop to the ground, why different materials have different properties, the character of the universe such as the form of the Earth and the behavior of celestial objects such as the Sun and the Moon... Image File history File links Download high resolution version (921x1152, 226 KB) This image is in the public domain because its copyright has expired in the United States and those countries with a copyright term of life of the author plus 100 years or less. ... Image File history File links Download high resolution version (921x1152, 226 KB) This image is in the public domain because its copyright has expired in the United States and those countries with a copyright term of life of the author plus 100 years or less. ... Thomas Young, English scientist Thomas Young (June 13, 1773-May 10, 1829) was an English polymath, contributing to the scientific understanding of vision, light, solid mechanics, energy, physiology, and Egyptology. ... Vis Viva is the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done. ... Leibniz redirects here. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Thomas Young, English scientist Thomas Young (June 13, 1773-May 10, 1829) was an English polymath, contributing to the scientific understanding of vision, light, solid mechanics, energy, physiology, and Egyptology. ... Vis Viva is the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done. ... Gaspard-Gustave de Coriolis or Gustave Coriolis (May 21, 1792–September 19, 1843), mathematician, mechanical engineer and scientist born in Paris, France. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... William John Macquorn Rankine (July 2, 1820 - December 24, 1872) was a Scottish engineer and physicist. ... Potential energy can be thought of as energy stored within a physical system. ... Caloric redirects here. ... This article is about momentum in physics. ...


He[citation needed] 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 Clausius, and to the introduction of laws of radiant energy by Jožef Stefan. Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician. ... Josiah Willard Gibbs (February 11, 1839 New Haven – April 28, 1903 New Haven) was one of the very first American theoretical physicists and chemists. ... Walther Hermann Nernst (June 25, 1864 – November 18, 1941) was a German physicist who is known for his theories behind the calculation of chemical affinity as embodied in the third law of thermodynamics, for which he won the 1920 Nobel Prize in chemistry. ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... Light (a form of radiant energy) observed in a forest Radiant energy is the energy of electromagnetic waves, or sometimes of other forms of radiation. ... Joseph Stefan (Slovene Jožef Stefan) (March 24, 1835 – January 7, 1893) was a Slovene physicist, mathematician and poet. ...


During a 1961 lecture[4] 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 California Institute of Technology (commonly referred to as Caltech)[1] is a private, coeducational research university located in Pasadena, California, in the United States. ... This article is about the physicist. ... The Nobel Prizes (pronounced no-BELL or no-bell) are awarded annually to people who have done outstanding research, invented groundbreaking techniques or equipment, or made outstanding contributions to society. ...

There is a fact, or if you wish, a law, governing natural phenomena that are known to date. There is no known exception to this law — it is exact so far we know. The law is called conservation of energy; it states that there is a certain quantity, which we call energy that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; 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 can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same.

The Feynman Lectures on Physics[4] This article is about the law of conservation of energy in physics. ...

Since 1918 it has been known that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time. That is, energy is conserved because the laws of physics do not distinguish between different moments of time (see Noether's theorem). This article is about the law of conservation of energy in physics. ... In geometry, a translation slides an object by a vector a: Ta(p) = p + a. ... In physics, especially in quantum mechanics, conjugate variables are pairs of variables that share an uncertainty relation. ... This article is about the concept of time. ... Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ...


Energy in various contexts since the beginning of the universe

The concept of energy and its transformations is useful in explaining and predicting most natural phenomena. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often described by entropy (equal energy spread among all available degrees of freedom) considerations, since in practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces. For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. ...


The concept of energy is used often in all fields of science.

In chemistry, the energy differences between substances determine whether, and to what extent, they can be converted into other substances or react with other substances.
In biology, chemical bonds are broken and made during metabolic processes, and the associated changes in available energy are studied in the subfield of bioenergetics. Energy is often stored by cells in the form of substances such as carbohydrate molecules (including sugars) and lipids, which release energy when reacted with oxygen.
In geology and meteorology, continental drift, mountain ranges, volcanos, and earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior. [5] While meteorological phenomena like wind, rain, hail, snow, lightning, tornadoes and hurricanes, are all a result of energy transformations brought about by solar energy on the planet Earth.
In cosmology and astronomy the phenomena of stars, nova, supernova, quasars and gamma ray bursts are the universe's highest-output energy transformations of matter. All stellar phenomena (including solar activity) are driven by various kinds of energy transformations. Energy in such transformations is either from gravitational collapse of matter (usually molecular hydrogen) into various classes of astronomical objects (stars, black holes, etc.), or from nuclear fusion (of lighter elements, primarily hydrogen).

Energy transformations in the universe over time are characterized by various kinds of potential energy which has been available since the Big Bang, later being "released" (transformed to more active types of energy such as kinetic or radiant energy), when a triggering mechanism is available. For other uses, see Chemistry (disambiguation). ... Water and steam are two different forms of the same chemical substance A chemical substance is a material with a definite chemical composition. ... For the song by Girls Aloud see Biology (song) Biology studies the variety of life (clockwise from top-left) E. coli, tree fern, gazelle, Goliath beetle Biology (from Greek: Βιολογία - βίος, bio, life; and λόγος, logos, speech lit. ... A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. ... Structure of the coenzyme adenosine triphosphate, a central intermediate in energy metabolism. ... Bioenergetics, loosely defined, is the study of energy investment and flow through living systems. ... Drawing of the structure of cork as it appeared under the microscope to Robert Hooke from Micrographia which is the origin of the word cell being used to describe the smallest unit of a living organism Cells in culture, stained for keratin (red) and DNA (green) The cell is the... Lactose is a disaccharide found in milk. ... Some common lipids. ... This article is about the chemical element and its most stable form, or dioxygen. ... Earth science (also known as geoscience, the geosciences or the Earth Sciences), is an all-embracing term for the sciences related to the planet Earth. ... Plates in the crust of the earth, according to the plate tectonics theory Continental drift refers to the movement of the Earths continents relative to each other. ... For other uses, see Mountain (disambiguation). ... Cleveland Volcano in the Aleutian Islands of Alaska photographed from the International Space Station For other uses, see Volcano (disambiguation). ... This article is about the natural seismic phenomenon. ... Energy Transformation in Energy Systems Language In physics and engineering, poop transformation or energy conversion, is any process of transforming one form of energy to another. ... For other uses, see Wind (disambiguation). ... This article is about precipitation. ... This article is about the precipitation. ... For other uses, see Snow (disambiguation). ... Not to be confused with lighting. ... This article is about the weather phenomenon. ... This article is about weather phenomena. ... Ultraviolet image of the Sun. ... This article is about the physics subject. ... This article is about the astronomical object. ... Artists conception of a white dwarf star accreting hydrogen from a larger companion A nova (pl. ... For other uses, see Supernova (disambiguation). ... This article is about the astronomical object. ... The image above shows the optical afterglow of gamma ray burst GRB-990123 taken on January 23, 1999. ... Energy Transformation in Energy Systems Language In physics and engineering, poop transformation or energy conversion, is any process of transforming one form of energy to another. ... For other uses, see Big Bang (disambiguation). ...


Familiar examples of such processes include nuclear decay, in which energy is released which was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process which ultimately uses the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs. In a slower process, heat from nuclear decay of these atoms in the core of the Earth releases heat, which in turn may lift mountains, via orogenesis. This slow lifting represents a kind of gravitational potential energy storage of the heat energy, which may be released to active kinetic energy in landslides, after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a store which has been produced ultimately from the same radioactive heat sources. Thus, according to present understanding, familiar events such as landslides and earthquakes release energy which has been stored as potential energy in the Earth's gravitational field or elastic strain (mechanical potential energy) in rocks; but prior to this, represents energy that has been stored in heavy atoms since the collapse of long-destroyed stars created these atoms. This article is about the chemical element. ... General Name, Symbol, Number thorium, Th, 90 Chemical series Actinides Group, Period, Block n/a, 7, f Appearance silvery white Standard atomic weight 232. ... Nucleosynthesis is the process of creating new atomic nuclei from preexisting nucleons (protons and neutrons). ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, in 1945 lifted nuclear fallout some 18 km (60,000 feet) above the epicenter. ... Orogeny is the process of mountain building. ...


In another similar chain of transformations beginning at the dawn of the universe, nuclear fusion of hydrogen in the Sun releases another store of potential energy which was created at the time of the Big Bang. At that time, according to theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements. This meant that hydrogen represents a store of potential energy which can be released by fusion. Such a fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into sunlight. Such sunlight from our Sun may again be stored as gravitational potential energy after it strikes the Earth, as (for example) water evaporates from oceans and is deposited upon mountains (where, after being released at a hydroelectric dam, it can be used to drive turbine/generators to produce electricity). Sunlight also drives all weather phenomenon, including such events as those triggered in a hurricane, when large unstable areas of warm ocean, heated over months, give up some of their thermal energy suddenly to power a few days of violent air movement. Sunlight is also is captured by plants as chemical potential energy, when carbon dioxide and water are converted into a combustible combination of carbohydrates, lipids, and oxygen. Release of this energy as heat and light may be triggered suddenly by a spark, in a forest fire; or it may be available more slowly for animal or human metabolism, when these molecules are ingested, and catabolism is triggered by enzyme action. Through all of these transformation chains, potential energy stored at the time of the Big Bang is later released by intermediate events, sometimes being stored in a number of ways over time between releases, as more active energy. In all these events, one kind of energy is converted to other types of energy, including heat. The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing sustainable fusion power. ... For other uses, see Big Bang (disambiguation). ... The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing sustainable fusion power. ... Anabolism is the aspect of metabolism that contributes to growth. ... Ribbon diagram of the enzyme TIM, surrounded by the space-filling model of the protein. ...


Regarding applications of the concept of energy

Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.[6] In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ...

  • The total energy of a system can be subdivided and classified in various ways. For example, it is sometimes convenient to distinguish potential energy (which is a function of coordinates only) from kinetic energy (which is a function of coordinate time derivatives only). It may also be convenient to distinguish gravitational energy, electric 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).[7]

In classical physics energy is considered a scalar quantity, the canonical conjugate to time. In special relativity energy is also a scalar (although not a Lorentz scalar but a time component of the energy-momentum 4-vector).[8] In other words, energy is invariant with respect to rotations of space, but not invariant with respect to rotations of space-time (= boosts). For other uses, see System (disambiguation). ... Potential energy can be thought of as energy stored within a physical system. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... For other uses, see Derivative (disambiguation). ... Classical physics is physics based on principles developed before the rise of quantum theory, usually including the special theory of relativity and general theory of relativity. ... A pair of variables mathematically defined in such a way that they become Fourier transform duals of one-another, or more generally are related through Pontryagin duality. ... This article is about the concept of time. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... In physics a Lorentz scalar is a scalar which is invariant under a Lorentz transformation. ... It has been suggested that this article or section be merged with Momentum#Momentum_in_relativistic_mechanics. ... In relativity, a four-vector is a vector in a four-dimensional real vector space, called Minkowski space, whose components transform like the space and time coordinates (t, x, y, z) under spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). ... This article is about the idea of space. ... In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ... The Lorentz transformation (LT), named after its discoverer, the Dutch physicist and mathematician Hendrik Antoon Lorentz (1853-1928), forms the basis for the special theory of relativity, which has been introduced to remove contradictions between the theories of electromagnetism and classical mechanics. ...


Energy transfer

Because energy is strictly conserved and is also locally conserved (wherever it can be defined), it is important to remember that by definition of energy the transfer of energy between the "system" and adjacent regions is work. A familiar example is mechanical work. In simple cases this is written as: In physics, mechanical work is the amount of energy transferred by a force. ...

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 two categories:

ΔE = W + Q             (2)

where Q  represents the heat flow into the system.


There are other ways in which an open system can gain or lose energy. If mass is counted as energy (as in many relativistic problems) then E must contain a term for mass lost or gained. In chemical systems, energy can be added to 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 addition of either work or heat). Winding a clock would be adding energy to a mechanical system. These terms may be added to the above equation, or they can generally be subsumed into a quantity called "energy addition term E" which refers to any type of energy carried over the surface of a 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 work-done or heat-added, in the classic senses).

ΔE = W + Q + E             (3)

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


Energy is also transferred from potential energy (Ep) to kinetic energy (Ek) and then back to potential energy constantly. This is referred to as conservation of energy. In this closed system, energy can not be created or destroyed, so the initial energy and the final energy will be equal to each other. This can be demonstrated by the following:

Epi + Eki = EpF + EkF'''

The equation can then be simplified further since Ep = mgh (mass times acceleration due to gravity times the height) and E_k = frac{1}{2} mv^2 (half times mass times velocity squared). Then the total amount of energy can be found by adding Ep + Ek = Etotal.


Energy and the laws of motion

Classical mechanics
vec{F} = frac{mathrm{d}}{mathrm{d}t}(m vec{v})
Newton's Second Law
History of ...
Fundamental concepts
Space · Time · Mass · Force
Energy · Momentum
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In classical mechanics, energy is a conceptually and mathematically useful property since it is a conserved quantity. Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... The Greeks, and Aristotle in particular, were the first to propose that there are abstract principles governing nature. ... This article is about the idea of space. ... This article is about the concept of time. ... For other uses, see Mass (disambiguation). ... For other uses, see Force (disambiguation). ... This article is about momentum in physics. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... Lagrangian mechanics is a re-formulation of classical mechanics that combines conservation of momentum with conservation of energy. ... Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton. ... Applied mechanics, also known as theoretical and applied mechanics, is a branch of the physical sciences and the practical application of mechanics. ... Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ... Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... See also list of optical topics. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Galileo redirects here. ... Kepler redirects here. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Pierre-Simon, marquis de Laplace (March 23, 1749 - March 5, 1827) was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy. ... For other persons named William Hamilton, see William Hamilton (disambiguation). ... Jean le Rond dAlembert, pastel by Maurice Quentin de La Tour Jean le Rond dAlembert (November 16, 1717 – October 29, 1783) was a French mathematician, mechanician, physicist and philosopher. ... Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... Joseph-Louis, comte de Lagrange (January 25, 1736 Turin, Kingdom of Sardinia - April 10, 1813 Paris) was an Italian-French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century. ... Euler redirects here. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... This article is about the law of conservation of energy in physics. ...


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.[9] In physics and mathematics, Hamiltons equations is the set of differential equations that arise in Hamiltonian mechanics, but also in many other related and sometimes apparently not related areas of science. ... For other persons named William Hamilton, see William Hamilton (disambiguation). ...


The Lagrangian

Another energy-related concept is called the Lagrangian, after Joseph Louis Lagrange. This is even more fundamental than the Hamiltonian, and can be used to derive the equations of motion. In non-relativistic physics, the Lagrangian is the kinetic energy minus potential energy. A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a function of the dynamical variables and concisely describes the equations of motion of the system. ... Joseph-Louis, comte de Lagrange (January 25, 1736 Turin, Kingdom of Sardinia - April 10, 1813 Paris) was an Italian-French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century. ...


Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (like systems with friction).


Energy and thermodynamics

Internal energy

Internal energy – the sum of all microscopic forms of energy of a system. It is related to the molecular structure and the degree of molecular activity and may be viewed as the sum of kinetic and potential energies of the molecules; it comprises the following types of energy:[10] In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of...

Type Composition of Internal Energy (U)
Sensible energy the portion of the internal energy of a system associated with kinetic energies (molecular translation, rotation, and vibration; electron translation and spin; and nuclear spin) of the molecules.
Latent energy the internal energy associated with the phase of a system.
Chemical energy the internal energy associated with the different kinds of aggregation of atoms in matter.
Nuclear energy the tremendous amount of energy associated with the strong bonds within the nucleus of the atom itself.
Energy interactions those types of energies not stored in the system (e.g. heat transfer, mass transfer, and work), but which are recognized at the system boundary as they cross it, which represent gains or losses by a system during a process.
Thermal energy the sum of sensible and latent forms of internal energy.

In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... Sensible heat is heat energy that is transported by a body that has a temperature higher than its surroundings via conduction, convection, or both. ... In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... In thermochemistry, latent heat is the amount of energy in the form of heat released or absorbed by a substance during a change of phase (i. ... In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... Properties For alternative meanings see atom (disambiguation). ... This article is about matter in physics and chemistry. ... This article concerns the energy stored in the nuclei of atoms; for the use of nuclear fission as a power source, see Nuclear power. ... This article concerns the energy stored in the nuclei of atoms; for the use of nuclear fission as a power source, see Nuclear power. ... A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... In thermal physics, heat transfer is the passage of thermal energy from a hot to a colder body. ... Mass transfer is the phrase commonly used in engineering for physical processes that involve molecular and convective transport of atoms and molecules within physical systems. ... In thermodynamics, work is the quantity of energy transferred from one system to another without an accompanying transfer of entropy. ... Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ...

The laws of thermodynamics

According to the second law of thermodynamics, work can be totally converted into heat, but not vice versa.This is a mathematical consequence of statistical mechanics. The first law of thermodynamics simply asserts that energy is conserved,[11] and that heat is included as a form of energy transfer. A commonly-used corollary of the first law is that for a "system" subject only to pressure forces and heat transfer (e.g. a cylinder-full of gas), the differential change in energy of the system (with a gain in energy signified by a positive quantity) is given by: The second law of thermodynamics is an expression of the universal law of increasing entropy. ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... In thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the conservation of energy. ... This article is about pressure in the physical sciences. ...

mathrm{d}E = Tmathrm{d}S - Pmathrm{d}V,,

where the first term on the right is the heat transfer into the system, defined in terms of temperature T and entropy S (in which entropy increases and the change dS is positive when the system is heated); and the last term on the right hand side is identified as "work" done on the system, where pressure is P and volume V (the negative sign results since compression of the system is needed to do work on it, so that the volume change dV is negative when work is done on the system). Although this equation is the standard text-book example of energy conservation in classical thermodynamics, it is highly specific, ignoring all chemical, electric, nuclear, and gravitational forces, effects such as advection of any form of energy other than heat, and because it contains a term that 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. For other uses, see Temperature (disambiguation). ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... Advection is the transport of a conserved scalar quantity that is transported in a vector field. ...


Energy is sometimes expressed as:

mathrm{d}E=delta Q+delta W,,

which is unsatisfactory[7] because there cannot exist any thermodynamic state functions W or Q that are meaningful on the right hand side of this equation, except perhaps in trivial cases.


Equipartition of energy

The energy of a mechanical harmonic oscillator (a mass on a spring) is alternatively kinetic and potential. At two points 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 is called equipartition principle - total energy of a system with many degrees of freedom is equally split among all available degrees of freedom. An undamped spring-mass system is a simple harmonic oscillator. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... In physics, a potential may refer to the scalar potential or to the vector potential. ... Cycle or Cycles may be: Look up cycle in Wiktionary, the free dictionary. ... In classical statistical mechanics, the equipartition theorem is a general formula that allows average energies of many physical systems to be calculated as a function of temperature. ...


This principle is vitally important to understanding the behavior of a quantity closely related to energy, called entropy. Entropy is a measure of evenness of a distribution of energy between parts of a system. When an isolated system is given more degrees of freedom (= is given new available energy states which are the same as existing states), then total energy spreads over all available degrees equally without distinction between "new" and "old" degrees. This mathematical result is called the second law of thermodynamics. For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... In mathematical analysis, distributions (also known as generalized functions) are objects which generalize functions and probability distributions. ... An energy level is a quantified stable energy, which a physical system can have; the term is most commonly used in reference to the electron configuration of electrons, in atoms or molecules. ... The second law of thermodynamics is an expression of the universal law of increasing entropy. ...


Oscillators, phonons, and photons

In an ensemble (connected collection) of unsynchronized oscillators, the average energy is spread equally between kinetic and potential types.


In a solid, thermal energy (often referred to loosely as heat content) 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 thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ...


In an ideal gas, the interaction potential between particles is essentially the delta function which stores no energy: thus, all of the thermal energy is kinetic.


Because an electric 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 electric 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.
  1. 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. Light (a form of radiant energy) observed in a forest Radiant energy is the energy of electromagnetic waves, or sometimes of other forms of radiation. ...


Work and virtual work

Work is roughly force times distance. But more precisely, it is For other uses, see Mechanic (disambiguation). ... In physics, mechanical work is the amount of energy transferred by a force. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ...

 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. For other uses, see Force (disambiguation). ... In physics, mechanical work is the amount of energy transferred by a force. ...


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


Quantum mechanics

In quantum mechanics energy is defined in terms of the energy operator as a time derivative of the wave function. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. It thus can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of slow changing (non-relativistic) wave function of quantum systems. The solution of this equation for bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic wave in vacuum, the resulting energy states are related to the frequency by the Planck equation E = hν (where h is the Planck's constant and ν the frequency). In the case of electromagnetic wave these energy states are called quanta of light or photons. The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space (or, in the case of ensembles, as a trace class operator with trace 1). ... A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ... This box:      For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ... In physics quanta is the plural of quantum. ... This article is about Planck, the German physicist. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... For other uses, see Light (disambiguation). ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ...


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 unexpected by-product of 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 to the mass of body: In physics, mechanical work is the amount of energy transferred by a force. ... For other uses, see Mass (disambiguation). ... This article does not cite any references or sources. ... The Lorentz transformation (LT), named after its discoverer, the Dutch physicist and mathematician Hendrik Antoon Lorentz (1853-1928), forms the basis for the special theory of relativity, which has been introduced to remove contradictions between the theories of electromagnetism and classical mechanics. ... It has been suggested that this article or section be merged with Classical mechanics. ... Energy E = mc^2 of mass m. ...

E = mc2,

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 is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process - the inverse process is called pair creation - in which the rest mass of particles is created from energy of two (or more) annihilating photons. A line showing the speed of light on a scale model of Earth and the Moon, taking about 1â…“ seconds to traverse that distance. ... For other uses, see Electron (disambiguation). ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... The invariant mass or intrinsic mass or proper mass or just mass is a measurement or calculation of the mass of an object that is the same for all frames of reference. ... Pair production is a nuclear physics process which occurs where a high-energy photon, generally interacting with an atomic nucleus, produces a particle and an antiparticle. ...


In general relativity, the stress-energy tensor serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation.[8]


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


Measurement

There is no absolute measure of energy, because energy is defined as the work that one system does (or can do) on another. Thus, only of the transition of a system from one state into another can be defined and thus measured.


Methods

The methods for the measurement of energy often deploy methods for the measurement of still more fundamental concepts of science, namely mass, distance, radiation, temperature, time, electric charge and electric current. Measurement is the estimation of the magnitude of some attribute of an object, such as its length or weight, relative to a unit of measurement. ... For other uses, see Mass (disambiguation). ... Distance is a numerical description of how far apart objects are at any given moment in time. ... For other uses, see Radiation (disambiguation). ... For other uses, see Temperature (disambiguation). ... This article is about the concept of time. ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... This box:      Electric current is the flow (movement) of electric charge. ...

A Calorimeter - An instrument used by physicists to measure energy
A Calorimeter - An instrument used by physicists to measure energy

Conventionally the technique most often employed is calorimetry, a thermodynamic technique that relies on the measurement of temperature using a thermometer or of intensity of radiation using a bolometer. Wikipedia does not have an article with this exact name. ... Wikipedia does not have an article with this exact name. ... A calorimeter is a device used for calorimetry, the science of measuring the heat of chemical reactions or physical changes as well as heat capacity. ... The world’s first ice-calorimeter, used in the winter of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in various chemical changes; calculations which were based on Joseph Black’s prior discovery of latent heat. ... Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes. ... A clinical mercury thermometer A thermometer is a device that measures temperature or temperature gradient, using a variety of different principles. ... Rendition of an imaging bolometer from Los Alamos National Laboratory A bolometer is a device for measuring incident electromagnetic radiation. ...

Units

Main article: Units of energy

Throughout the history of science, energy has been expressed in several different units such as ergs and calories. At present, the accepted unit of measurement for energy is the SI unit of energy, the joule. Because energy is defined via work, the SI unit for energy is the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. ... An erg is the unit of energy and mechanical work in the centimetre-gram-second (CGS) system of units, symbol erg. Its name is derived from the Greek word meaning work. The erg is a small unit, equal to a force of one dyne exerted for a distance of one... Etymology: French calorie, from Latin calor (heat), from calere (to be warm). ... Look up si, Si, SI in Wiktionary, the free dictionary. ... The joule (IPA: or ) (symbol: J) is the SI unit of energy. ...


Forms of energy

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

Classical mechanics distinguishes between potential energy, which is a function of the position of an object, and kinetic energy, which is a function of its movement. Both position and movement are relative to a frame of reference, which must be specified: this is often (and originally) an arbitrary fixed point on the surface of the Earth, the terrestrial frame of reference. Some introductory authors[citation needed] attempt to separate all forms of energy in either kinetic or potential: this is not incorrect, but neither is it clear that it is a real simplification, as Feynman points out: Download high resolution version (1600x1163, 240 KB) Wikipedia does not have an article with this exact name. ... Download high resolution version (1600x1163, 240 KB) Wikipedia does not have an article with this exact name. ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... Potential energy can be thought of as energy stored within a physical system. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... Potential energy can be thought of as energy stored within a physical system. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... This article or section is in need of attention from an expert on the subject. ... This article or section is in need of attention from an expert on the subject. ...

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.

Examples of the interconversion of energy
Mechanical energy is converted
into by
Mechanical energy Lever
Thermal energy Brakes
Electric energy Dynamo
Electromagnetic radiation Synchrotron
Chemical energy Matches
Nuclear energy Particle accelerator

In physics, mechanical energy describes the potential energy and kinetic energy present in the components of a mechanical system. ... For the Portuguese town and parish, see Lever, Portugal. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... This article is about the vehicle component. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... Dynamo, or Dinamo, may refer to: Dynamo, an electrical generator Dynamo (sports society) of the Soviet Union Operation Dynamo, the 1940 mass evacuation at Dunkirk Dynamo, the rock band based in Belfast Dynamo theory, a theory relating to magnetic fields of celestial bodies Dynamo Open Air, annual heavy metal music... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... Synchrotrons are now mostly used for producing monochromatic high intensity X-ray beams; here, the synchrotron is the circular track, off which the beamlines branch. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... For other uses, see Match (disambiguation). ... This article concerns the energy stored in the nuclei of atoms; for the use of nuclear fission as a power source, see Nuclear power. ... Atom Smasher redirects here. ...

Potential energy

Main article: Potential energy

Potential energy, symbols Ep, V or Φ, is defined as the work done against a given force (= work of given force with minus sign) in changing the position of an object with respect to a reference position (often taken to be infinite separation). If F is the force and s is the displacement, Potential energy can be thought of as energy stored within a physical system. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ...

E_{rm p} = -int mathbf{F}cdot{rm d}mathbf{s}

with the dot representing the scalar product of the two vectors. In mathematics, the dot product (also known as the scalar product and the inner product) is a function (·) : V × V → F, where V is a vector space and F its underlying field. ... This article is about vectors that have a particular relation to the spatial coordinates. ...


The name "potential" energy originally signified the idea that the energy could readily be transferred as work—at least in an idealized system (reversible process, see below). This is not completely true for any real system, but is often a reasonable first approximation in classical mechanics.


The general equation above can be simplified in a number of common cases, notably when dealing with gravity or with elastic forces. Gravity is a force of attraction that acts between bodies that have mass. ...


Gravitational potential energy

The gravitational force near the Earth's surface varies very little with the height, h, and is equal to the mass, m, multiplied by the gravitational acceleration, g = 9.81 m/s². In these cases, the gravitational potential energy is given by Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ... This article covers the physics of gravitation. ... For other uses, see Mass (disambiguation). ... In physics, gravitational acceleration is the acceleration of an object caused by the force of gravity from another object. ...

Ep,g = mgh

A more general expression for the potential energy due to Newtonian gravitation between two bodies of masses m1 and m2, useful in astronomy, is Isaac Newtons theory of universal gravitation (part of classical mechanics) states the following: Every single point mass attracts every other point mass by a force pointing along the line combining the two. ... For other uses, see Astronomy (disambiguation). ...

E_{rm p,g} = -G{{m_1m_2}over{r}},

where r is the separation between the two bodies and G is the gravitational constant, 6.6742(10)×10−11 m³kg−1s−2.[12] In this case, the reference point is the infinite separation of the two bodies. The gravitational constant G is a key element in Newtons law of universal gravitation. ...


Elastic potential energy

As a ball falls freely under the influence of gravity, it accelerates downward, its initial potential energy converting into kinetic energy. On impact with a hard surface the ball deforms, converting the kinetic energy into elastic potential energy. As the ball springs back, the energy converts back firstly to kinetic energy and then as the ball re-gains height into potential energy. Energy losses due to inelastic deformation and air resistance cause each successive bounce to be lower than the last.
As a ball falls freely under the influence of gravity, it accelerates downward, its initial potential energy converting into kinetic energy. On impact with a hard surface the ball deforms, converting the kinetic energy into elastic potential energy. As the ball springs back, the energy converts back firstly to kinetic energy and then as the ball re-gains height into potential energy. Energy losses due to inelastic deformation and air resistance cause each successive bounce to be lower than the last.

Elastic potential energy is defined as a work needed to compress (or expand) a spring. The force, F, in a spring or any other system which obeys Hooke's law is proportional to the extension or compression, x, Image File history File links Metadata Size of this preview: 800 × 515 pixelsFull resolution (1800 × 1159 pixel, file size: 293 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Metadata Size of this preview: 800 × 515 pixelsFull resolution (1800 × 1159 pixel, file size: 293 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Gravity is a force of attraction that acts between bodies that have mass. ... Potential energy can be thought of as energy stored within a physical system. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... The elastic potential energy stored in an elastic string or spring of natural length l and modulus of elasticity λ under an extension of x is given by: This equation is often used in calculations of positions of mechanical equilibrium. ... Elasticity is a branch of physics which studies the properties of elastic materials. ... In engineering mechanics, deformation is a change in shape due to an applied force. ... For a solid object moving through a fluid or gas, drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of the external fluid flow. ... The elastic potential energy stored in an elastic string or spring of natural length l and modulus of elasticity λ under an extension of x is given by: This equation is often used in calculations of positions of mechanical equilibrium. ... Springs A spring is a flexible elastic object used to store mechanical energy. ... Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...

F = − kx

where k is the force constant of the particular spring (or system). In this case, the calculated work becomes Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...

E_{rm p,e} = {1over 2}kx^2.

Hooke's law is a good approximation for behaviour of chemical bonds under normal conditions, i.e. when they are not being broken or formed. A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. ...


Kinetic energy

Main article: Kinetic energy

Kinetic energy, symbols Ek, T or K, is the work required to accelerate an object to a given speed. Indeed, calculating this work one easily obtains the following: The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ...

E_{rm k} = int mathbf{F} cdot d mathbf{x} = int mathbf{v} cdot d mathbf{p}= {1over 2}mv^2

At speeds approaching the speed of light, c, this work must be calculated using Lorentz transformations, which results in the following: A line showing the speed of light on a scale model of Earth and the Moon, taking about 1â…“ seconds to traverse that distance. ... The Lorentz transformation (LT), named after its discoverer, the Dutch physicist and mathematician Hendrik Antoon Lorentz (1853-1928), forms the basis for the special theory of relativity, which has been introduced to remove contradictions between the theories of electromagnetism and classical mechanics. ...

 E_{rm k} = m c^2left(frac{1}{sqrt{1 - (v/c)^2}} - 1right)

This equation reduces to the one above it, at small (compared to c) speed. A mathematical by-product of this work (which is immediately seen in the last equation) is that even at rest a mass has the amount of energy equal to:

Erest = mc2

This energy is thus called rest mass energy. Energy E = mc^2 of mass m. ...


Thermal energy

Examples of the interconversion of energy
Thermal energy is converted
into by
Mechanical energy Steam turbine
Thermal energy Heat exchanger
Electric energy Thermocouple
Electromagnetic radiation Hot objects
Chemical energy Blast furnace
Nuclear energy Supernova
Main article: Thermal energy

Thermal energy (of some media - gas, plasma, solid, etc) is the energy associated with the microscopical random motion of particles constituting the media. For example, in case of monoatomic gas it is just a kinetic energy of motion of atoms of gas as measured in the reference frame of the center of mass of gas. In case of many-atomic gas rotational and vibrational energy is involved. In the case of liquids and solids there is also potential energy (of interaction of atoms) involved, and so on. In physics, mechanical energy describes the potential energy and kinetic energy present in the components of a mechanical system. ... A rotor of a modern steam turbine, used in a power plant A steam turbine is a mechanical device that extracts thermal energy from pressurized steam, and converts it into useful mechanical work. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... A heat exchanger is a device built for efficient heat transfer from one fluid to another, whether the fluids are separated by a solid wall so that they never mix, or the fluids are directly contacted. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... In electronics, thermocouples are a widely used type of temperature sensor and can also be used as a means to convert thermal potential difference into electric potential difference. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... Blast furnace in Sestao, Spain. ... This article concerns the energy stored in the nuclei of atoms; for the use of nuclear fission as a power source, see Nuclear power. ... For other uses, see Supernova (disambiguation). ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ...


A heat is defined as a transfer (flow) of thermal energy across certain boundary (for example, from a hot body to cold via the area of their contact. A practical definition for small transfers of heat is

Delta q = int C_{rm v}{rm d}T

where Cv is the heat capacity of the system. This definition will fail if the system undergoes a phase transition—e.g. if ice is melting to water—as in these cases the system can absorb heat without increasing its temperature. In more complex systems, it is preferable to use the concept of internal energy rather than that of thermal energy (see Chemical energy below). To meet Wikipedias quality standards, this article or section may require cleanup. ... This diagram shows the nomenclature for the different phase transitions. ... In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of...


Despite the theoretical problems, the above definition is useful in the experimental measurement of energy changes. In a wide variety of situations, it is possible to use the energy released by a system to raise the temperature of another object, e.g. a bath of water. It is also possible to measure the amount of electric energy required to raise the temperature of the object by the same amount. The calorie was originally defined as the amount of energy required to raise the temperature of one gram of water by 1 °C (approximately 4.1855 J, although the definition later changed), and the British thermal unit was defined as the energy required to heat one gallon (UK) of water by 1 °F (later fixed as 1055.06 J). Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... Etymology: French calorie, from Latin calor (heat), from calere (to be warm). ... The British thermal unit (BTU or Btu) is a unit of energy used in the Power, Steam Generation and Heating and Air Conditioning industry globally. ... The gallon (abbreviation: gal) is a unit of volume. ... Fahrenheit is a temperature scale named after the German physicist Gabriel Fahrenheit (1686–1736), who proposed it in 1724. ...


Electric energy

Main articles: Electromagnetism and Electricity
Examples of the interconversion of energy
Electric energy is converted
into by
Mechanical energy Electric motor
Thermal energy Resistor
Electric energy Transformer
Electromagnetic radiation Light-emitting diode
Chemical energy Electrolysis
Nuclear energy Synchrotron

The electric potential energy of given configuration of charges is defined as the work which must be done against the Coulomb force to rearrange charges from infinite separation to this configuration (or the work done by the Coulomb force separating the charges from this configuration to infinity). For two point-like charges Q1 and Q2 at a distance r this work, and hence electric potential energy is equal to: Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... Electricity (from New Latin Ä“lectricus, amberlike) is a general term for a variety of phenomena resulting from the presence and flow of electric charge. ... In physics, mechanical energy describes the potential energy and kinetic energy present in the components of a mechanical system. ... For other kinds of motors, see motor. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... Resistor symbols (American) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... For other uses, see Transformer (disambiguation). ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... LED redirects here. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... In chemistry and manufacturing, electrolysis is a method of separating chemically bonded elements and compounds by passing an electric current through them. ... This article concerns the energy stored in the nuclei of atoms; for the use of nuclear fission as a power source, see Nuclear power. ... Synchrotrons are now mostly used for producing monochromatic high intensity X-ray beams; here, the synchrotron is the circular track, off which the beamlines branch. ... The electric potential energy is the potential energy associated with the conservative Coulomb forces between charged particles contained within a system, where the reference potential energy is usually chosen to be zero for particles at infinite separation. ... In thermodynamics, work is the quantity of energy transferred from one system to another without an accompanying transfer of entropy. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrical force that one stationary, electrically charged substance of small volume (ideally, a point source) exerts on another. ...

E_{rm p,e} = {1over {4piepsilon_0}}{{Q_1Q_2}over{r}}

where ε0 is the electric constant of a vacuum, 107/4πc0² or 8.854188…×10−12 F/m.[12] If the charge is accumulated in a capacitor (of capacitance C), the reference configuration is usually selected not to be infinite separation of charges, but vice versa - charges at an extremely close proximity to each other (so there is zero net charge on each plate of a capacitor). The justification for this choice is pure practical - it is easier to measure both voltage difference and magnitude of charges on a capacitor plates not versus infinite separation of charges but rather versus discharged capacitor where charges return to close proximity to each other (electrons and ions rtecombined back making plates neutral). In this case the work and thus the electric potential energy becomes The electric constant () is the permittivity of vacuum, a physical constant, defined by: where: - magnetic constant - speed of light In SI units, the value is exactly expressed by: = 2. ... See Capacitor (component) for a discussion of specific types. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ...

E_{rm p,e} = {{Q^2}over{2C}}

If an electric current passes through a resistor, electric energy is converted to heat; if the current passes through an electric appliance, some of the electric energy will be converted into other forms of energy (although some will always be lost as heat). The amount of electric energy due to an electric current can be expressed in a number of different ways: This box:      Electric current is the flow (movement) of electric charge. ... Resistor symbols (American) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ...

E = UQ = UIt = Pt = U2t / R

where U is the electric potential difference (in volts), Q is the charge (in coulombs), I is the current (in amperes), t is the time for which the current flows (in seconds), P is the power (in watts) and R is the electric resistance (in ohms). The last of these expressions is important in the practical measurement of energy, as potential difference, resistance and time can all be measured with considerable accuracy. In the physical sciences, potential difference is the difference in potential between two points in a conservative vector field. ... Josephson junction array chip developed by NIST as a standard volt. ... The coulomb (symbol: C) is the SI unit of electric charge. ... For other uses, see Ampere (disambiguation). ... In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time. ... For other uses, see Watt (disambiguation). ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... A multimeter can be used to measure resistance in ohms. ...


Magnetic energy

There is no fundamental difference between magnetic energy and electric energy: the two phenomena are related by Maxwell's equations. The potential energy of a magnet of magnetic moment m in a magnetic field B is defined as the work of magnetic force (actually of magnetic torque) on re-alignment of the vector of the magnetic dipole moment, and is equal: For thermodynamic relations, see Maxwell relations. ... For other uses, see Magnet (disambiguation). ... A bar magnet. ... For the indie-pop band, see The Magnetic Fields. ... In physics, mechanical work is the amount of energy transferred by a force. ... For other senses of this word, see torque (disambiguation). ...

E_{rm p,m} = -mcdot B

while the energy stored in a inductor (of inductance L) when current I is passing via it is An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. ...

E_{rm p,m} = {1over 2}LI^2.

This second expression forms the basis for superconducting magnetic energy storage. the flow of direct current in a superconducting coil which has been cryogenically cooled to a temperature below its superconducting critical temperature. ...


Electromagnetic fields

Examples of the interconversion of energy
Electromagnetic radiation is converted
into by
Mechanical energy Solar sail
Thermal energy Solar collector
Electric energy Solar cell
Electromagnetic radiation Non-linear optics
Chemical energy Photosynthesis
Nuclear energy Mössbauer spectroscopy

Calculating work needed to create an electric or magnetic field in unit volume (say, in a capacitor or an inductor) results in the electric and magnetic fields energy densities: In physics, mechanical energy describes the potential energy and kinetic energy present in the components of a mechanical system. ... A artists depiction of a Cosmos 1 type spaceship in orbit Solar sails (also called light sails or photon sails, especially when they use light sources other than the Sun) are a proposed form of spacecraft propulsion using large membrane mirrors. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... A laundromat in California with solar collectors on the roof. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... A solar cell, made from a monocrystalline silicon wafer A solar cell or photovoltaic cell is a device that converts light energy into electrical energy. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... Nonlinear optics is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization P responds nonlinearly to the electric field E of the light. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... Photosynthesis splits water to liberate O2 and fixes CO2 into sugar The leaf is the primary site of photosynthesis in plants. ... This article concerns the energy stored in the nuclei of atoms; for the use of nuclear fission as a power source, see Nuclear power. ... Mößbauer spectroscopy is a spectroscopic technique based on the Mössbauer effect. ... In physics, mechanical work is the amount of energy transferred by a force. ... Energy density is the amount of energy stored in a given system or region of space per unit volume, or per unit mass, depending on the context. ...

 u_e=frac{epsilon_0}{2} E^2

and

 u_m=frac{1}{2mu_0} B^2 ,

in SI units.


Electromagnetic radiation, such as microwaves, visible light or gamma rays, represents a flow of electromagnetic energy. Applying the above expressions to magnetic and electric components of electromagnetic field both the volumetric density and the flow of energy in e/m field can be calculated. The resulting Poynting vector, which is expressed as This article is about the type of Electromagnetic radiation. ... The optical spectrum (light or visible spectrum) is the portion of the electromagnetic spectrum that is visible to the human eye. ... This article is about electromagnetic radiation. ... The Poynting vector describes the energy flux (J·m−2·s−1) of an electromagnetic field. ...

mathbf{S} = frac{1}{mu} mathbf{E} times mathbf{B},

in SI units, gives the density of the flow of energy and its direction.


The energy of electromagnetic radiation is quantized (has discrete energy levels). The spacing between these levels is equal to An energy level is a quantified stable energy, which a physical system can have; the term is most commonly used in reference to the electron configuration of electrons, in atoms or molecules. ...

E = hν

where h is the Planck constant, 6.6260693(11)×10−34 Js,[12] and ν is the frequency of the radiation. This quantity of electromagnetic energy is usually called a photon. The photons which make up visible light have energies of 270–520 yJ, equivalent to 160–310 kJ/mol, the strength of weaker chemical bonds. A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... For other uses, see Frequency (disambiguation). ... A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. ...


Chemical energy

Examples of the interconversion of energy
Chemical energy is converted
into by
Mechanical energy Muscle
Thermal energy Fire
Electric energy Fuel cell
Electromagnetic radiation Glowworms
Chemical energy Chemical reaction

Chemical energy is the energy due to associations of atoms in molecules and various other kinds of aggregates of matter. It may be defined as a work done by electric forces during re-arrangement of electric charges, electrons and protons, in the process of aggregation. If the chemical energy of a system decreases during a chemical reaction, the difference is transferred to the surroundings in some form (often heat or light); on the other hand if the chemical energy of a system increases as a result of a chemical reaction - the difference then is supplied by from the surroundings (usually again in form of heat or light). For example, Willard Gibbs - founder of chemical thermodynamics In thermodynamics, chemical thermodynamics is the mathematical study of the interrelation of heat and work with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics. ... In physics, mechanical energy describes the potential energy and kinetic energy present in the components of a mechanical system. ... For other uses of Muscles, see Muscles (disambiguation). ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... For other uses, see Fire (disambiguation). ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... A fuel cell is an electrochemical device similar to a battery, but differing from the latter in that it is designed for continuous replenishment of the reactants consumed; i. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... Photo of a glowworm on a stick. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... For other uses, see Chemical reaction (disambiguation). ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... This article is about matter in physics and chemistry. ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... For other uses, see Light (disambiguation). ... For other uses, see Chemical reaction (disambiguation). ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... For other uses, see Light (disambiguation). ...

when two hydrogen atoms react to form a dihydrogen molecule, the chemical energy decreases by 724 zJ (the bond energy of the H–H bond);
when the electron is completely removed from a hydrogen atom, forming a hydrogen ion (in the gas phase), the chemical energy increases by 2.18 aJ (the ionization energy of hydrogen).

It is common to quote the changes in chemical energy for one mole of the substance in question: typical values for the change in molar chemical energy during a chemical reaction range from tens to hundreds of kJ/mol. This article is about the chemistry of hydrogen. ... In chemistry, bond energy (E) is a measure of bond strength in a chemical bond. ... The ionization energy (IE) of an atom or of a molecule is the energy required to strip it of an electron. ... The mole (symbol: mol) is the SI base unit that measures an amount of substance. ...


The chemical energy as defined above is also referred to by chemists as the internal energy, U: technically, this is measured by keeping the volume of the system constant. However, most practical chemistry is performed at constant pressure and, if the volume changes during the reaction (e.g. a gas is given off), a correction must be applied to take account of the work done by or on the atmosphere to obtain the enthalpy, H: A chemist is a scientist who specializes in chemistry. ... In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... For other uses, see Volume (disambiguation). ... t In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ...

ΔH = ΔU + pΔV

A second correction, for the change in entropy, S, must also be performed to determine whether a chemical reaction will take place or not, giving the Gibbs free energy, G: For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... In thermodynamics, the Gibbs free energy is a thermodynamic potential which measures the useful work obtainable from a closed thermodynamic system at a constant temperature and pressure. ...

ΔG = ΔHTΔS

These corrections are sometimes negligible, but often not (especially in reactions involving gases).


Since the industrial revolution, the burning of coal, oil, natural gas or products derived from them has been a socially significant transformation of chemical energy into other forms of energy. the energy "consumption" (one should really speak of "energy transformation") of a society or country is often quoted in reference to the average energy released by the combustion of these fossil fuels: A Watt steam engine, the steam engine that propelled the Industrial Revolution in Britain and the world. ... This article is about the chemical reaction combustion. ... Coal Example chemical structure of coal Coal is a fossil fuel formed in ecosystems where plant remains were saved by water and mud from oxidization and biodegradation. ... Synthetic motor oil being poured. ... For other uses, see Natural gas (disambiguation). ... This article is about the chemical reaction combustion. ... Fossil fuels or mineral fuels are fossil source fuels, that is, hydrocarbons found within the top layer of the earth’s crust. ...

1 tonne of coal equivalent (TCE) = 29 GJ
tonne of oil equivalent (TOE) = 41.87 GJ

On the same basis, a tank-full of gasoline (45 litres, 12 gallons) is equivalent to about 1.6 GJ of chemical energy. Another chemically-based unit of measurement for energy is the "tonne of TNT", taken as 4.184 GJ. Hence, burning a tonne of oil releases about ten times as much energy as the explosion of one tonne of TNT: fortunately, the energy is usually released in a slower, more controlled manner. The ton of oil equivalent (TOE) is a unit for measuring energy. ... Petrol redirects here. ... R-phrases S-phrases Related Compounds Related compounds picric acid hexanitrobenzene Except where noted otherwise, data are given for materials in their standard state (at 25 Â°C, 100 kPa) Infobox disclaimer and references Trinitrotoluene (TNT) is a chemical compound with the formula C6H2(NO2)3CH3. ...


Simple examples of chemical energy are batteries and food. When you eat the food is digested and turned into chemical energy which can be transformed to kinetic energy.


Nuclear energy

Examples of the interconversion of energy
Nuclear binding energy is converted
into by
Mechanical energy Alpha radiation
Thermal energy Sun
Electric energy Beta radiation
Electromagnetic radiation Gamma radiation
Chemical energy Radioactive decay
Nuclear energy Nuclear isomerism

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. Binding energy is the energy required to disassemble a whole into separate parts. ... In physics, mechanical energy describes the potential energy and kinetic energy present in the components of a mechanical system. ... An alpha particle is deflected by a magnetic field Alpha particles or alpha rays are a form of particle radiation which are highly ionizing and have low penetration. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... Sol redirects here. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... Beta particles are high-energy electrons emitted by certain types of radioactive nuclei such as potassium-40. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... This article is about electromagnetic radiation. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. ... This article concerns the energy stored in the nuclei of atoms; for the use of nuclear fission as a power source, see Nuclear power. ... A nuclear isomer is a metastable state of an atomic nucleus caused by the excitation of one or more of its protons or neutrons or both. ... This article concerns the energy stored in the nuclei of atoms; for the use of nuclear fission as a power source, see Nuclear power. ... The electric potential energy is the potential energy associated with the conservative Coulomb forces between charged particles contained within a system, where the reference potential energy is usually chosen to be zero for particles at infinite separation. ... For the generation of electrical power by fission, see Nuclear power plant. ... The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing sustainable fusion power. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... In nuclear physics, beta decay (sometimes called neutron decay) is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. ...


Nuclear particles (nucleons) like protons and neutrons are not destroyed (law of conservation of baryon number) in fission and fusion processes. A few lighter particles may be created or destroyed (example: beta minus and beta plus decay, or electron capture decay), but these minor processes are not important to the immediate energy release in fission and fusion. Rather, fission and fusion release energy when collections of baryons become more tightly bound, and it is the energy associated with a fraction of the mass of the nucleons (but not the whole particles) which appears as the heat and electromagnetic radiation generated by nuclear reactions. This heat and radiation retains the "missing" mass, but the mass is missing only because it escapes in the form of heat and light, which retain the mass and conduct it out of 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, but during this process, the number of total protons and neutrons in the sun does not change. In this system, the light itself retains the inertial equivalent of this mass, and indeed the mass itself (as a system), which represents 4 million tons per second of electromagnetic radiation, moving into space. Each of the helium nuclei which are formed in the process are less massive than the four protons from they were formed, but (to a good approximation), no particles or atoms are destroyed in the process of turning the sun's nuclear potential energy into light. In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... In particle physics, the baryon number is an approximate conserved quantum number. ... Sol redirects here. ... Ultraviolet image of the Sun. ... Sol redirects here. ...


Surface energy

If there is any kind of tension in a surface, such as a stretched sheet of rubber or material interfaces, it is possible to define surface energy. In particular, any meeting of dissimilar materials that don't mix will result in some kind of surface tension, if there is freedom for the surfaces to move then, as seen in capillary surfaces for example, the minimum energy will as usual be sought. This box:      Surface tension is a property of the surface of a liquid that causes it to behave as an elastic sheet. ... In fluid mechanics and mathematics, a capillary surface is a surface that represents the interface between two different fluids. ...


A minimal surface, for example, represents the smallest possible energy that a surface can have if its energy is proportional to the area of the surface. For this reason, (open) soap films of small size are minimal surfaces (small size reduces gravity effects, and openness prevents pressure from building up. Note that a bubble is a minimum energy surface but not a minimal surface by definition). Verrill Minimal Surface In mathematics, a minimal surface is a surface with a mean curvature of zero. ... Verrill Minimal Surface In mathematics, a minimal surface is a surface with a mean curvature of zero. ...


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 electric 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 electric 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. In physics and engineering, energy conversion is any process of converting energy from one form to another. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... This article is about structures for water impoundment. ... Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... A Siemens steam turbine with the case opened. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... Generator redirects here. ... This article is concerned solely with chemical explosives. ... In thermodynamics and chemistry, chemical potential, symbolized by μ, is a term introduced in 1876 by the American mathematical physicist Willard Gibbs, which he defined as follows: Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given proportions may be considered a... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... In thermal physics, thermal energy is the energy portion of a system that increases with its temperature. ... For other uses, see Pendulum (disambiguation). ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Potential energy can be thought of as energy stored within a physical system. ... For other uses, see Friction (disambiguation). ... For other uses, see Pendulum (disambiguation). ...


Energy can be converted into matter and vice versa. The mass-energy equivalence formula E = mc², derived independently by Albert Einstein and Henri Poincaré,[citation needed] quantifies the relationship between mass and rest energy. Since c2 is extremely large relative to ordinary human scales, the conversion of ordinary amount of mass (say, 1 kg) to other forms of energy can liberate tremendous amounts of energy (~9x1016 Joules), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a 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. This article is about matter in physics and chemistry. ... 15ft sculpture of Einsteins 1905 E = mc² formula at the 2006 Walk of Ideas, Germany In physics, mass-energy equivalence is the concept that all mass has an energy equivalence, and all energy has a mass equivalence. ... “Einstein” redirects here. ... Jules Henri Poincaré (April 29, 1854 – July 17, 1912) (IPA: [1]) was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ... This box:      Nuclear physics is the branch of physics concerned with the nucleus of the atom. ...


In nature, transformations of energy can be fundamentally classed into two kinds: those that are thermodynamically reversible, and those that are thermodynamically irreversible. A reversible process in thermodynamics is one in which no energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, however, quantum states of lower energy, present as possible exitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomization in a crystal). In thermodynamics, a reversible process (or reversible cycle if the process is cyclic) is a process that can be reversed by means of infinitesimal changes in some property of the system. ... Irreversibility is that property of an event which makes reverting back to the state before the occurrence of the event impossible. ... In thermodynamics, a reversible process (or reversible cycle if the process is cyclic) is a process that can be reversed by means of infinitesimal changes in some property of the system. ...


As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work, or be transformed to other usable forms of energy, grows less and less. The heat death is a possible final state of the universe, in which it has reached maximum entropy. ... The heat death is a possible final state of the universe, in which it has reached maximum entropy. ...


Law of conservation of energy

Energy is subject to the law of conservation of energy. According to this law, energy can neither be created (produced) nor destroyed itself. It can only be transformed. This article is about the law of conservation of energy in physics. ...


Most kinds of energy (with gravitational energy being a notable exception)[1] are also subject to strict local conservation laws, as well. In this case, energy can only be exchanged between adjacent regions of space, and all observers agree as to the volumetric density of energy in any given space. There is also a global law of conservation of energy, stating that the total energy of the universe cannot change; this is a corollary of the local law, but not vice versa.[4][7] Conservation of energy is the mathematical consequence of translational symmetry of time (that is, the indistinguishability of time intervals taken at different time)[13] - see Noether's theorem. This article is about the law of conservation of energy in physics. ... In geometry, a translation slides an object by a vector a: Ta(p) = p + a. ... This article is about the concept of time. ... Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ...


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. For the physical concepts, see conservation of energy and energy efficiency. ...


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. In geometry, a translation slides an object by a vector a: Ta(p) = p + a. ... This article is about the concept of time. ...


Thus is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured. A pair of variables mathematically defined in such a way that they become Fourier transform duals of one-another, or more generally are related through Pontryagin duality. ...


In quantum mechanics energy is expressed using the Hamiltonian operator. On any time scales, the uncertainty in the energy is by For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... In mathematics, an operator is a function that performs some sort of operation on a number, variable, or function. ...

Delta E Delta t ge frac { hbar } {2 }

which is similar in form to the Heisenberg uncertainty principle (but not really mathematically equivalent thereto, since H and t are not dynamically conjugate variables, neither in classical nor in quantum mechanics). In quantum physics, the Heisenberg uncertainty principle, sometimes called the Heisenberg indeterminacy principle, expresses a limitation on accuracy of (nearly) simultaneous measurement of observables such as the position and the momentum of a particle. ...


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 (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. Thousands of particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... This article is about momentum in physics. ... A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... This article or section does not cite its references or sources. ... An energy level is a quantified stable energy, which a physical system can have; the term is most commonly used in reference to the electron configuration of electrons, in atoms or molecules. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... Spontaneous fission (SF) is a form of radioactive decay characteristic of very heavy isotopes, and is theoretically possible for any atomic nucleus whose mass is greater than or equal to 100 amu (elements near ruthenium). ... In 1948 Dutch physicist Hendrik B. G. Casimir of Philips Research Labs predicted that two uncharged parallel metal plates will be subject to a force pressing them together. ... In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ...


Energy and life

Main article: Bioenergetics

Any living organism relies on an external source of energy—radiation from the Sun in the case of green plants; chemical energy in some form in the 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 food molecules, the latter mostly carbohydrates and fats, of which glucose (C6H12O6) and stearin (C57H110O6) are convenient examples. The food molecules are oxidised to carbon dioxide and water in the mitochondria Bioenergetics, loosely defined, is the study of energy investment and flow through living systems. ... A calorie refers to a unit of energy. ... Glucose (Glc), a monosaccharide (or simple sugar), is an important carbohydrate in biology. ... Stearine is a glyceryl ester of stearic acid, derived from animal fats created as a byproduct of processing beef. ... Carbon dioxide (chemical formula: ) is a chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom. ... This article is about the properties of water. ... Electron micrograph of a mitochondrion showing its mitochondrial matrix and membranes In cell biology, a mitochondrion (plural mitochondria) is a membrane-enclosed organelle that is found in most eukaryotic cells. ...

C6H12O6 + 6O2 → 6CO2 + 6H2O
C57H110O6 + 81.5O2 → 57CO2 + 55H2O

and some of the energy is used to convert ADP into ATP Adenosine diphosphate, abbreviated ADP, is a nucleotide. ... Adenosine 5-triphosphate (ATP) is a multifunctional nucleotide that is most important as a molecular currency of intracellular energy transfer. ...

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 for other metabolism (at each stage of a metabolic pathway, some chemical energy is converted into heat). Only a tiny fraction of the original chemical energy is used for work:[14] Structure of the coenzyme adenosine triphosphate, a central intermediate in energy metabolism. ... In biochemistry, a metabolic pathway is a series of chemical reactions occurring within a cell. ...

gain in kinetic energy of a sprinter during a 100 m race: 4 kJ
gain in gravitational potential energy of a 150 kg weight lifted through 2 metres: 3kJ
Daily food intake of a normal adult: 6–8 MJ

It would appear that living organisms are remarkably inefficient (in the physical sense) in their use of the energy they receive (chemical energy or radiation), and it is true that most real machines manage higher efficiencies. However, in growing organisms the energy that is converted to heat serves a vital purpose, as it allows the organism tissue to be highly ordered with regard to the molecules it is built from. The second law of thermodynamics states that energy (and matter) tends to become more evenly spread out across the universe: to concentrate energy (or matter) in one specific place, it is necessary to spread out a greater amount of energy (as heat) across the remainder of the universe ("the surroundings").[15] Simpler organisms can achieve higher energy efficiencies than more complex ones, but the complex organisms can occupy ecological niches that are not available to their simpler brethren. The conversion of a portion of the chemical energy to heat at each step in a metabolic pathway is the physical reason behind the pyramid of biomass observed in ecology: to take just the first step in the food chain, of the estimated 124.7 Pg/a of carbon that is fixed by photosynthesis, 64.3 Pg/a (52%) are used for the metabolism of green plants,[16] i.e. reconverted into carbon dioxide and heat. tytytrtyty This article is about energy efficiency as a ratio. ... This article is about devices that perform tasks. ... The second law of thermodynamics is an expression of the universal law of increasing entropy. ... Two lichens on a rock, in two different ecological niches In ecology, a niche; (pronounced nich, neesh or nish)[1] is a term describing the relational position of a species or population in its ecosystem[1]. The ecological niche; describes how an organism or population responds to the distribution of... For the journal, see Ecology (journal). ... Food chains, food webs and/or food networks describe the feeding relationships between species to another within an ecosystem. ... Carbon fixation is a process found in autotrophs, usually driven by photosynthesis, whereby carbon dioxide is changed into organic materials. ... Photosynthesis splits water to liberate O2 and fixes CO2 into sugar The leaf is the primary site of photosynthesis in plants. ...


See also

Energy Portal
Physics Portal

Image File history File links Portal. ... Image File history File links Portal. ... The sparks generated by striking steel against a flint provide the activation energy to initiate combustion in this Bunsen burner. ... Located in the heart of the city the American Museum of Science and Energy (AMSE) inspires young and old to explore atomic energy. ... Americans for Balanced Energy Choices (ABEC) is a U.S. special interest non-profit organization dealing primarily with U.S. energy policy. ... t In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... For the physical concepts, see conservation of energy and energy efficiency. ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... In physics, interaction energy is the contribution to the total energy that is caused by an interaction between the objects being considered. ... In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... Energy portal This is a list of energy topics which identifies articles and categories that relate to energy in general. ... Vacuum energy is an underlying background energy that exists in space even when devoid of matter (known as free space). ... This article or section does not cite any references or sources. ... In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time. ... Renewable energy effectively utilizes natural resources such as sunlight, wind, tides and geothermal heat, which are naturally replenished. ... Solar irradiance spectrum at top of atmosphere. ... The thermodynamic free energy is a measure of the amount of mechanical (or other) work that can be extracted from a system, and is helpful in engineering applications. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Because energy is defined via work, the SI unit for energy is the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. ... World power usage in terawatts (TW), 1965-2005. ...

Notes and references

  1. ^ Harper, Douglas. Energy. Online Etymology Dictionary. Retrieved on May 1, 2007.
  2. ^ Lofts, G; O'Keeffe D; et al (2004). "11 — Mechanical Interactions", Jacaranda Physics 1, 2, Milton, Queensland, Australia: John Willey & Sons Australia Ltd., 286. ISBN 0 7016 3777 3. 
  3. ^ Smith, Crosbie (1998). The Science of Energy - a Cultural History of Energy Physics in Victorian Britain. The University of Chicago Press. ISBN 0-226-76420-6. 
  4. ^ a b c Feynman, Richard (1964). The Feynman Lectures on Physics; Volume 1. U.S.A: Addison Wesley. ISBN 0-201-02115-3. 
  5. ^ Earth's Energy Budget
  6. ^ Berkeley Physics Course Volume 1. Charles Kittel, Walter D Knight and Malvin A Ruderman
  7. ^ a b c The Laws of Thermodynamics including careful definitions of energy, free energy, et cetera.
  8. ^ a b Misner, Thorne, Wheeler (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0716703440. 
  9. ^ The Hamiltonian MIT OpenCourseWare website 18.013A Chapter 16.3 Accessed February 2007
  10. ^ Cengel, Yungus, A.; Boles, Michael (2002). Thermodynamics - An Engineering Approach, 4th ed.. McGraw-Hill, 17-18. ISBN 0-07-238332-1. 
  11. ^ Kittel and Kroemer (1980). Thermal Physics. New York: W. H. Freeman. ISBN 0-7167-1088-9. 
  12. ^ a b c International Council of Science Committee on Data for Science and Technology (2007). 2006 CODATA recommended values.
  13. ^ Time Invariance
  14. ^ 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 a supermarket does more work (in the physical sense) than either of the athletes, but does it more slowly.
  15. ^ Crystals are another example of highly ordered systems that exist in nature: in this case too, the order is associated with the transfer of a large amount of heat (known as the lattice energy) to the surroundings.
  16. ^ Ito, Akihito; Oikawa, Takehisa (2004). "Global Mapping of Terrestrial Primary Productivity and Light-Use Efficiency with a Process-Based Model." in Shiyomi, M. et al. (Eds.) Global Environmental Change in the Ocean and on Land. pp. 343–58.

Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... The International Council for Science (ICSU), formerly called the International Council of Scientific Unions, was founded in 1931 as an international non-governmental organization devoted to international co-operation in the advancement of science. ... CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ... In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... For other uses, see Crystal (disambiguation). ... Diamond Crystal Lattice The lattice energy of an ionic solid is a measure of the strength of bonds in that ionic compound. ...

Further reading

  • 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. 

External links

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Wikipedia does not have an article with this exact name. ... Image File history File links Wikibooks-logo. ... Image File history File links Wikiquote-logo. ... Image File history File links Wikisource-logo. ... Image File history File links Commons-logo. ... Image File history File links WikiNews-Logo. ... Image File history File links Wikiversity-logo-Snorky. ... “PDF” redirects here. ... A kibibyte (a contraction of kilo binary byte) is a unit of information or computer storage, commonly abbreviated KiB (never kiB). 1 kibibyte = 210 bytes = 1,024 bytes The kibibyte is closely related to the kilobyte, which can be used either as a synonym for kibibyte or to refer to... This article is about the physical universe. ... This article is about Earth as a planet. ... Geological time put in a diagram called a geological clock, showing the relative lengths of the eons of the Earths history. ... Earth science (also known as geoscience, the geosciences or the Earth Sciences), is an all-embracing term for the sciences related to the planet Earth. ... Earth cutaway from core to exosphere. ... The tectonic plates of the world were mapped in the second half of the 20th century. ... Geological time scale. ... This article includes a list of works cited but its sources remain unclear because it lacks in-text citations. ... For the geological process, see Weathering or Erosion. ... Air redirects here. ... This article is about life in general. ... For other uses, see Biosphere (disambiguation). ... For the definition, see Life. ... A cluster of Escherichia coli bacteria magnified 10,000 times. ... For other uses, see Plant (disambiguation). ... For the fictional character, see Fungus the Bogeyman. ... Fauna is a collective term for animal life of any particular region or time. ... For other uses, see Animal (disambiguation). ... For the song by Girls Aloud see Biology (song) Biology studies the variety of life (clockwise from top-left) E. coli, tree fern, gazelle, Goliath beetle Biology (from Greek: Βιολογία - βίος, bio, life; and λόγος, logos, speech lit. ... The evolutionary history of life and the origin of life are fields of ongoing geological and biological research. ... For other uses, see Wilderness (disambiguation). ... For the journal, see Ecology (journal). ... A coral reef near the Hawaiian islands is an example of a complex marine ecosystem. ... For other uses, see Universe (disambiguation). ... This article is about matter in physics and chemistry. ... Layers of Atmosphere - not to scale (NOAA)[1] Outer space, sometimes simply called space, refers to the relatively empty regions of the universe outside the atmospheres of celestial bodies. ...

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