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15 janvier 2011 6 15 /01 /janvier /2011 14:05

In physics, energy (from Greek ???????? - energeia, "activity, operation", from ??????? - energos, "active, working" ) is a quantity that is often understood as the ability a physical system has to produce changes on another physical system  (Dell XPS M1210 Batteryhttp://www.hdd-shop.co.uk .

The changes are produced when the energy is transferred from a system to another. A system can transfer energy by means of three ways, namely: physical or thermodynamical work, heat transfer, or mass transfer  (Dell Studio XPS 1340 Battery)     .

This quantity can be assigned to any physical system. The assigned energy, according to Classical Physics, depends on its physical state relative to the frame of reference used to study it       (Dell Studio XPS 1640 Battery)      .

On the other hand, in Relativistic Physics, when using an inertial reference frame, invariant mass energy is independent of such kind of reference frames. The invariant mass of a system is the same in all the inertial reference frames, it means that its energetic equivalent (invariant mass energy) would be the same in all the inertial reference frames, too  (Dell Vostro 1710 Battery)   .

All the forms of energy that a system has can belong to one of two great components: the internal energy and the external energy (not to be confused with the energy of the surroundings which is outside the system). All kinds of internal and external energies can, additionally, be classified as kinetic energy or potential energy  (Dell KM958 battery)         .

Kinetic energy considers the mass and the motion of a system. If the system is studied as a whole, it is called external kinetic energy. The thermal energy is the internal kinetic energy and it considers the motion of every constitutive particle of the system (molecules, atoms, electrons, etc.)        (Sony VGP-BPS13 battery)       .

The gravitational potential energy is an external potential energy and so is theelectrostatic potential energy. The elastic energy is an internal potential energy. The forms of energy are often named after a related force, as in the previous examples.

Some forms of energy are associated to the particle-like behaviour of the system  (Sony VGP-BPS13/B battery)      .

But, there might be cases like that of sound energy in which the energy overall effect is related to the wave-like behaviour of the system. In the specific case of sound, there is a transmission of oscillations in the pressure through the system  (Sony VGP-BPS13/S battery)     .

The energy associated to the sound wave converts back and forth between the elastic potential energy of the extra compression (in case of longitudinal waves) or lateral displacement strain (in case of transverse waves) of the matter and the kinetic energy of the oscillations of the medium of which the system is made up     (Sony VGP-BPS13A/B battery)    .

German physicist Hermann von Helmholtz established that all forms of energy are equivalent — energy in one form can disappear but the same amount of energy will appear in another form. A restatement of this idea is that energy is subject to a conservation law over time    (Sony VGP-BPS13B/B battery)     .

Any form of energy can be transformed into another form. When energy is in a form other than thermal energy, it may be transformed with good or even perfect efficiency, to any other type of energy. With thermal energy, however, there are often limits to the efficiency of the conversion to other forms of energy, due to the second law of thermodynamics (Sony VGP-BPL9 battery) .

As an example, when oil reacts with oxygen, potential energy is released, since new chemical bonds are formed in the products which are more stable than those in the oil and oxygen. The released energy resulting from this process may be converted directly to electricity (as in a fuel cell) with good efficiency      (Sony VGP-BPS13B/B battery)       .

Alternately it may be converted into thermal energy if the oil is simply burned. In the latter case, however, some of the thermal energy can no longer be used to perform work at that temperature, and is said to be "degraded." As such, it exists in a form unavailable for further transformation    Sony VGP-BPL15 battery .

The remainder of the thermal energy may be used to produce any other type of energy, such as electricity.

In all such energy transformation processes, the total energy remains the same. Energy may not be created nor destroyed. This principle, the conservation of energy, was first postulated in the early 19th century, and applies to any isolated system  Dell Inspiron E1505 battery .

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.

Although the total energy of a system does not change with time, its value may depend on the frame of reference  Dell Latitude E6400 battery .

For example, a seated passenger in a moving airplane has zero kinetic energy relative to the airplane, but non-zero kinetic energy (and higher total energy) relative to the Earth.

Energy is a scalar physical quantity       HP Pavilion dv6000 Battery .

In the International System of Units (SI), energy is measured in joules, but in some fields other units such as kilowatt-hours and kilocalories are also used.


The word energy derives from Greek ???????? (energeia), which possibly appears for the first time in the work of Aristotle in the 4th century BC      SONY VAIO VGN-FZ Battery .

The concept of energy emerged out of the idea of vis viva (living force), 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 theorized that thermal energy consisted of the random motion of the constituent parts of matter  SONY VAIO VGN-FZ18 Battery ,

a view shared by Isaac Newton, although it would be more than a century until this was generally accepted. In 1807, Thomas Young was possibly the first to use the term "energy" instead of vis viva, in its modern sense. Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, and in 1853, William Rankine coined the term "potential energy" SONY VAIO VGN-FZ180E Battery .

It was argued for some years whether energy was a substance (thecaloric) or merely a physical quantity, such as momentum.

William Thomson (Lord Kelvin) amalgamated all of these laws into the laws of thermodynamics  SONY VAIO VGN-FZ220E Battery ,

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   SONY VAIO VGN-FZ340E Battery .

During a 1961 lecture[7] 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:

There is a fact, or if you wish, a law, governing all natural phenomena that are known to date  SONY VAIO VGN-FZ430E Battery .

There is no known exception to this law—it is exact so far as we know. The law is called theconservation of energy. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes  SONY VAIO VGN-FZ460E Battery .

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 SONY VAIO VGN-FZ480E Battery .

The Feynman Lectures on 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        SONY VAIO VGN-FZ4000 Battery .

That is, energy is conserved because the laws of physics do not distinguish between different moments of time (see Noether's theorem).

Energy in various contexts

The concept of energy and its transformations is useful in explaining and predicting most natural phenomena  SONY VAIO VGN-FZ31E Battery .

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, as in practice all energy transformations are permitted on a small scale       SONY VAIO VGN-FZ31B Battery ,

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.

The concept of energy is widespread in all sciences      SONY VAIO VGN-FZ31J Battery .

  • In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is invariably accompanied by an increase or decrease of energy of the substances involved  SONY VAIO VGN-FZ31M Battery .
  • Some energy is transferred between the surroundings and the reactants of the reaction in the form of heat or light; thus the products of a reaction may have more or less energy than the reactants. A reaction is said to be exergonic if the final state is lower on the energy scale than the initial state SONY VAIO VGN-FZ31Z Battery ;
  • in the case of endergonic reactions the situation is the reverse. Chemical reactions are invariably not possible unless the reactants surmount an energy barrier known as the activation energy. The speed of a chemical reaction (at given temperature T) is related to the activation energy E  SONY VAIO VGN-FZ38M Battery ,
  • by the Boltzmann's population factor e E / kT - that is the probability of molecule to have energy greater than or equal to E at the given temperature T. This exponential dependence of a reaction rate on temperature is known as the Arrhenius equation.The activation energy necessary for a chemical reaction can be in the form of thermal energy  SONY VGP-BPS8 Battery .
  • In biology, energy is an attribute of all biological systems from the biosphere to the smallest living organism. Within an organism it is responsible for growth and development of a biological cell or anorganelle of a biological organism  SONY VGP-BPS13 Battery .
  • Energy is thus often said to be stored by cells in the structures of molecules of substances such as carbohydrates (including sugars), lipids, and proteins, which release energy when reacted with oxygen in respiration      SONY VGP-BPS13/S Battery .
  • In human terms, the human equivalent (H-e) (Human energy conversion) indicates, for a given amount of energy expenditure, the relative quantity of energy needed for human metabolism, assuming an average human energy expenditure of 12,500kJ per day and a basal metabolic rate of 80 watts      SONY VGP-BPS13A/B Battery .
  • For example, if our bodies run (on average) at 80 watts, then a light bulb running at 100 watts is running at 1.25 human equivalents (100 ÷ 80) i.e. 1.25 H-e. For a difficult task of only a few seconds' duration, a person can put out thousands of watts, many times the 746 watts in one official horsepower. For tasks lasting a few minutes, a fit human can generate perhaps 1,000 watts        SONY VGP-BPS13B/B Battery .
  • For an activity that must be sustained for an hour, output drops to around 300; for an activity kept up all day, 150 watts is about the maximum. The human equivalent assists understanding of energy flows in physical and biological systems by expressing energy units in human terms: it provides a “feel” for the use of a given amount of energy SONY VGP-BPS13A/S Battery .
  • In geology, continental drift, mountain ranges, volcanoes, and earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior., while meteorologicalphenomena      SONY VGP-BPS13AS Batterylike wind, rain, hail, snow, lightning, tornadoes and hurricanes, are all a result of energy transformations brought about by solar energy on the atmosphere of the planet Earth       Dell Inspiron 1320n Battery .
  • 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      Dell Inspiron 1464 Battery .
  • 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)  Dell Inspiron 1564 Battery .

Energy transformations in the universe over time are characterized by various kinds of potential energy that 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     Dell Inspiron 1764 Battery .

Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae     Dell Studio 1450 Battery ,

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, radioactive decay of these atoms in the core of the Earth releases heat       Dell Studio 1457 Battery .

This thermal energy drives plate tectonics and may lift mountains, via orogenesis. This slow lifting represents a kind of gravitational potential energy storage of the thermal energy, which may be later released to active kinetic energy in landslides, after a triggering event    Dell Latitude D610 Battery .

Earthquakes also release stored elastic potential energy in rocks, a store that has been produced ultimately from the same radioactive heat sources        Toshiba NB100 Battery .

Thus, according to present understanding, familiar events such as landslides and earthquakes release energy that has been stored as potential energy in the Earth's gravitational field or elastic strain (mechanical potential energy) in rocks. Prior to this, they represent release of energy that has been stored in heavy atoms since the collapse of long-destroyed supernova stars created these atomsToshiba Satellite M65 battery .

In another similar chain of transformations beginning at the dawn of the universe, nuclear fusion of hydrogen in the Sun also releases another store of potential energy which was created at the time of the Big Bang. At that time, according to theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements  Toshiba Satellite M60 battery .

This meant that hydrogen represents a store of potential energy that can be released by fusion. Such a fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into sunlight       Dell Latitude D830 Battery .

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 turbines or generators to produce electricity)         Dell Latitude D620 Battery .

Sunlight also drives many weather phenomena, save those generated by volcanic events. An example of a solar-mediated weather event is a hurricane, which occurs 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    Dell Inspiron Mini 10 Battery .

Sunlight is also captured by plants as chemical potential energy in photosynthesis, when carbon dioxide and water (two low-energy compounds) are converted into the high-energy compounds carbohydrates, lipids, and proteins. Plants also release oxygen during photosynthesis     Sony VGN-FW11S Battery ,

which is utilized by living organisms as an electron acceptor, to release the energy of carbohydrates, lipids, and proteins. Release of the energy stored during photosynthesis as heat or light may be triggered suddenly by a spark, in a forest fire, or it may be made available more slowly for animal or human metabolism  Sony VGN-FW11M Battery ,

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  Sony VGN-FW139E/H battery .

In all these events, one kind of energy is converted to other types of energy, including heat.

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 by itself. It can only be transformed     Dell Latitude E5400 Battery .

Most kinds of energy (with gravitational energy being a notable exception) 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     Dell Latitude E4200 Battery .

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.Conservation of energy is the mathematical consequence of translational symmetry of time (that is, the indistinguishability of time intervals taken at different time) - see Noether's theorem  Dell Inspiron 300M Battery .

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

This law is a fundamental principle of physics   Dell Vostro A840 Battery .

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   Dell Studio 1737 battery .

This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval  Dell Inspiron E1505 battery .

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.

In quantum mechanics energy is expressed using the Hamiltonian operator  Dell RM791 battery .

On any time scales, the uncertainty in the energy is bywhich 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)    Dell XPS M1530 battery .

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 knownfundamental forces (more accurately known as fundamental interactions)    Dell XPS M2010 battery .

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  Acer Aspire One battery .

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 constantToshiba Satellite P10 Battery .

  • 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) fromkinetic energy (which is a function of coordinate time derivatives only)       SONY VGN-FZ210CE Battery .
  • 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  Dell Precision M70 Battery .
  • 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  Toshiba Satellite L305 Battery .
  • For example, while energy is always conserved (in the sense that the total energy does not change despite energy transformations), energy can be converted into a form, e.g., thermal energy, that cannot be utilized to perform work  Toshiba Satellite T4900 Battery .
  • When one talks about "conserving energy by driving less," one talks about conserving fossil fuels and preventing useful energy from being lost as heat. This usage of "conserve" differs from that of the law of conservation of energy       Toshiba PA3399U-2BRS battery .

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 theenergy-momentum 4-vector). In other words, energy is invariant with respect to rotations of space, but not invariant with respect to rotations of space-time (= boosts)  Toshiba Satellite A200 Battery.

Energy transfer

Because energy is strictly conserved and is also locally conserved (wherever it can be defined), it is important to remember that by the definition of energy the transfer of energy between the "system" and adjacent regions is work  Toshiba Satellite 1200 Battery .

A familiar example is mechanical work. In simple cases this is written as the following equation:

if there are no other energy-transfer processes involved. Here E is the amount of energy transferred, and W represents the work done on the system     Toshiba Satellite M300 Battery .

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

where Q represents the heat flow into the system.

There are other ways in which an open system can gain or lose energy      Sony Vaio PCG-5G2L Battery .

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)    Sony Vaio PCG-5G3L Battery .

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       Sony Vaio PCG-5J1L Battery .

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)     Sony Vaio PCG-5K2L Battery .

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  Sony Vaio PCG-5J2L Battery .

This is referred to as conservation of energy. In this closed system, energy cannot be created or destroyed; therefore, the initial energy and the final energy will be equal to each other. This can be demonstrated by the following  Sony Vaio PCG-5K1L Battery :

The equation can then be simplified further since Ep = mgh (mass times acceleration due to gravity times the height) and   (half mass times velocity squared). Then the total amount of energy can be found by adding Ep + Ek = Etotal Sony Vaio PCG-5L1L Battery .

Energy and the laws of motion

In classical mechanics, energy is a conceptually and mathematically useful property, as it is a conserved quantity. Several formulations of mechanics have been developed using energy as a core concept  Sony Vaio PCG-6S2L Battery .

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  Sony Vaio PCG-6S3L Battery .

These classical equations have remarkably direct analogs in nonrelativistic quantum mechanics.

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     Sony Vaio PCG-6V1L Battery .

It was invented in the context of classical mechanics, but is generally useful in modern physics. The Lagrangian is defined as the kinetic energy minus the potential energy.

Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (such as systems with friction)          Sony Vaio PCG-6W1L Battery .

Energy and thermodynamics

Internal energy

Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to create the system. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometric aspects, as well as the motion of the particles, in form of kinetic energy       Sony Vaio PCG-6W2L Battery .

Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value, which is impossible to determine with thermodynamics alone.

[edit]The laws of thermodynamics

According to the second law of thermodynamics, work can be totally converted into heat, but not vice versa  Sony Vaio PCG-6W3L Battery .

This is a mathematical consequence of statistical mechanics. The first law of thermodynamics simply asserts that energy is conserved, and that heat is included as a form of energy transfer        Sony Vaio PCG-7111L Battery .

A commonly used corollary of the first law is that for a "system" subject only topressure 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 as the following equation      Sony Vaio PCG-7112L Battery :

,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         Sony Vaio PCG-7113L Battery ,

where pressure is P and volume V (the negative sign results since compression of the system requires work to be done on it and so the volume change, dV, is negative when work is done on the system). Although this equation is the standard textbook example of energy conservation in classical thermodynamics       Sony Vaio PCG-7133L Battery ,

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   Sony Vaio PCG-7Z2L Battery .

Energy is sometimes expressed as the following equation:which is unsatisfactorybecause 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  Sony Vaio PCG-8Y1L Battery .

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  Sony Vaio PCG-8Y2L Battery .

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   Sony Vaio PCG-8Z1L Battery .

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 (i.e., given new available energy states that are the same as existing states)  Sony Vaio PCG-8Z2L Battery ,

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        Sony VAIO PCG-5G2L Battery .

Oscillators, phonons, and photons

In an ensemble (connected collection) of unsynchronized oscillators, the average energy is spread equally between kinetic and potential types        Sony VAIO PCG-5G3L Battery .

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  Sony VAIO PCG-5J1L Battery .

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   Sony VAIO PCG-5K2L Battery ,

its energy must be, on average, equally kinetic and potential. It is entirely arbitrary whether the magnetic energy is considered kinetic and whether the electric energy is 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      Sony VAIO PCG-5J2L Battery .

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  Sony VAIO PCG-5K1L Battery .

2. On the other hand, in the key equation m2c4 = E2 ? p2c2, the contribution mc2 is called the rest energy, and all other contributions to the energy are called kinetic energy       Sony VAIO PCG-5L1L Battery .

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      Sony VAIO PCG-6S2L Battery .

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          Sony VAIO PCG-6S3L Battery .

For non-relativistic particles these two notions of potential versus kinetic energy are numerically equal, so the ambiguity is harmless, but not so for relativistic particles.

Work and virtual work

Work, a form of energy, is force times distance       Sony VAIO PCG-6V1L Battery .

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

Work and thus energy is frame dependent. For example, consider a ball being hit by a bat. In the center-of-mass reference frame, the bat does no work on the ball. But, in the reference frame of the person swinging the bat, considerable work is done on the ball  Sony VAIO PCG-6W1L Battery .

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. In results can be considered as a definition of measurement of energy in quantum mechanics     Sony VAIO PCG-6W2L Battery .

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        Sony VAIO PCG-6W3L Battery .

In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by the Planckequation E = h? (where h is the Planck's constant and ? the frequency). In the case of electromagnetic wave these energy states are called quanta of light or photons        Sony VAIO PCG-7111L Battery .


When calculating kinetic energy (work to accelerate a mass from zero speed to some finite speed) relativistically - using Lorentz transformations instead of Newtonian mechanics, Einstein discovered an unexpected by-product of these calculations to be an energy term which does not vanish at zero speed       Sony VAIO PCG-7112L Battery .

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:

E = mc2,


m is the mass,      Sony VAIO PCG-7113L Battery

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 Sony VAIO PCG-7133L Battery ,

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  Sony VAIO PCG-7Z1L Battery .

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. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons)    Sony VAIO PCG-7Z2L Battery .

However, the total system mass and energy do not change during this interaction.

In general relativity, the stress-energy tensor serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation       Sony VAIO PCG-8Y1L Battery .

It is not uncommon to hear that energy is "equivalent" to mass. It would be more accurate to state that every energy has an inertia and gravity equivalent, and because mass is a form of energy, then mass too has inertia and gravity associated with it  Sony VAIO PCG-8Y2L Battery Sony VAIO PCG-8Z1L Battery Sony VAIO PCG-8Z2L Battery.

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