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Energy

2007 Schools Wikipedia Selection. Related subjects: General Physics

   In general, the word energy refers to a concept that can be paraphrased
   as "the potential for causing changes", and therefore one can say that
   energy is the cause of any change. The word is used in several
   different contexts. The use of the word in mainstream science has a
   precise, well-defined meaning, which is not the case, most often, with
   many other usages.

   The most common definition of energy is work that a certain force
   (gravitational, electromagnetic, etc) can do. Due to a variety of
   forces, energy has many different forms (gravitational, electric, heat,
   etc.) that can be grouped into two major categories: kinetic energy and
   potential energy. According to this definition, energy has the same
   units as work; a force applied through a distance. The SI unit of
   energy, the joule, equals one newton applied through one meter, for
   example. Energy has no direction in space, and is therefore considered
   a scalar quantity.

   Energy is a conserved quantity, meaning that it cannot be created or
   destroyed, but only converted from one form into another. Thus, the
   total energy of the universe always remains constant.
   Lightning is a highly visible form of energy transfer.
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   Lightning is a highly visible form of energy transfer.

Etymology

   The etymology of the term is from Greek ενέργεια, εν- means "in" and
   έργον means "work"; the -ια suffix forms an abstract noun. The compound
   εν-εργεια in Epic Greek meant "divine action" or "magical operation";
   it was later used by Aristotle in a meaning of "activity, operation" or
   "vigour", and by Diodorus Siculus for "force of an engine."

Historical perspective

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

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

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

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


   Energy

     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.


   Energy

   — The Feynman Lectures on Physics, Vol. 1.

Energy in Natural Sciences

   The concepts of energy and its transformations are useful in explaining
   natural phenomena. The law of conservation of energy is equally useful.
   The direction of transformations explained with the help of energy is
   often influenced by entropy considerations also.

   The exact context of various natural phenomena and transformations
   varies from one natural science to another. Some examples are:

Physics

   The transformation that constitutes the context of energy in physics,
   is the change in position or movement of an object which is brought
   about through the action of a force. Thus in the context of physics,
   energy is said to be the ability to do work. Work is said to be done,
   in physics, when an object (howsoever small in size and mass) is moved
   across a distance, howsoever short, by the action of a force.

   Mathematically, work is equal to the force multiplied by a distance
   (more accurately, force integrated over a certain path).

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

   The equation above says that the work (W) is equal to the integral of
   the dot product of the force ( \mathbf{F} ) on a body and the
   infinitesimal of the body's translation ( \mathbf{s} ).

   Depending on the kind of force F involved, work of this force results
   in a change of the corresponding kind of energy (gravitational,
   electrostatic, kinetic, etc).
   An instrument used by physicists to measure energy
   Enlarge
   An instrument used by physicists to measure energy

   Units of energy are thus exactly the same as units of work ( joules in
   the SI). Because work is frame dependent (i.e., can only be defined
   relative to certain initial state or reference state of the system),
   energy also becomes frame dependent. For example, although a speeding
   bullet has kinetic energy in the reference frame of a non-moving
   observer, it has zero kinetic energy in its proper (co-moving)
   reference frame -- because it takes zero work to accelerate a bullet
   from zero speed to zero speed. Of course, the selection of a reference
   state (or reference frame) is completely arbitrary - and usually is
   dictated to maximally simplify the problem to be dealt with. However,
   when the total energy of a system cannot be decreased by simple choice
   of reference frame, then the (minimal) energy remaining in the system
   is associated with an invariant mass of the system. In this special
   frame, called the center-of-momentum frame or centre-of-mass frame,
   total energy of the system E and both its invariant mass and
   relativistic mass m are related by Einstein's famous equation E = mc².

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

   According to Einstein's theory of special relativity, mass and energy
   are equivalent. For example, there are processes, such as electron-
   positron annihilation, in which mass is converted completely into
   energy, and energy also participates in gravitational interactions. The
   relationship between the two is:

          \!E = {\Delta m c^2}

   where

          Δm is the amount of rest mass released into the surroundings as
          active energy (heat, light, kinetic energy),
          c is the speed of light in a vacuum.

Chemistry

   Atoms and molecules, the central concepts of chemistry, are made up of
   electrons and protons, and therefore coulombic forces are at work
   during the rearrangement of atoms (during formation or decomposition of
   molecules). The energy associated with this movement of charge is what
   we call "chemical energy".

   A chemical reaction invariably absorbs or releases heat or light.
   According to chemical thermodynamics a chemical transformation is
   possible only if so-called free energy decreases. The concept of free
   energy is a synthesis of energy and entropy. Free energy is a useful
   concept in chemistry, because energy considerations alone are not
   sufficient to decide the possibility of a chemical reaction. According
   to the second law of thermodynamics, the entropy of the universe must
   increase in all processes (including chemical processes), and energy is
   transformed from one form to another (including from heat to any other
   form) so long as the second law is not violated. For example, a gas may
   expand and thus allow some of its heat to do work, but this is only
   possible because the net entropy of the universe increases due to the
   gas expansion, more than it decreases due to the disappearance of heat.

   The concept of energy levels finds application in various kinds of
   spectroscopy, in which elucidation of atomic and molecular structure is
   based on the phenomenon of the presence of certain "lines" in
   absorption or emission spectra.
   Emission spectrum of Iron
   Emission spectrum of Iron

   These lines (so called because they appear as linear features in
   dispersion spectra (see example above), such as might be produced by a
   prism or diffraction grating) are postulated to be due to a certain
   specific amount of energy involved in the transition of atoms or
   molecules, from one state to another. Because a charactistic magnitude
   of energy is associated with a characteristic frequency (and
   wavelength) of light (or other electromagnetic radiation), such lines
   in spectra are direct clues to energetic changes which are permitted to
   happen only at certain energies, and not others.

   The speed of a chemical reaction (at given temperature T) is related to
   a yet another concept, activation energy. The activation energy E, of a
   chemical reaction, can be visualized as the height of a barrier of
   energy separating two minima of the energy of the chemically reacting
   system (the energy of reactants and the energy of products). Thus,
   according to statistical mechanics the rate of chemical reactions is
   proportional to the Boltzmann's population factor e ^− E / kT, that is
   the population of molecules having energy greater than or equal to E at
   thr temperature T. This exponential dependence of a reaction rate on
   temperature is known as the Arrhenius equation.

Biology

   Growth, development and metabolism are some of the central phenomena in
   the study of biology. They cannot be explained without invoking the
   energy concept. Indeed sustenance of life itself is critically
   dependent on energy transformations; living organisms survive because
   of exchange of energy within and without. In a living organism chemical
   bonds are constantly broken and made to make the exchange and
   transformation of energy possible. These chemical bonds are most often
   bonds in carbohydrates, including sugars.
   Flowchart of cellular respiration

   Other chemical bonds include bonds in chemical compounds that are
   important for the cell metabolism, for example, those in a molecule of
   ATP or fats and oils. These molecules, along with oxygen, are common
   stores of concentrated energy for the biological processes. One can
   therefore assert that transformation of energy from a more to a less
   concentrated form is the driving force of all biological processes or
   chemical processes that are responsible for the life of a biological
   organism. Molecular biology and biochemistry are in fact scientific
   studies concerning the making and breaking of chemical bonds in the
   molecules found in biological organisms.

   As with other natural phenomena, the exchange of metabolic energy in
   biological organisms also increases the entropy of the universe. Nearly
   all energy transformations studied in biology are due to the chemical
   synthesis and decompositions ultimately brought about by the energy
   absorbed from photons in sunlight through insolation and
   photosynthesis. The total energy captured by photosynthesis in green
   plants from the solar radiation is about 2 x 10^23 joules of energy per
   year . This is about 4% of the total sunlight energy which reaches
   Earth.

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

Meteorology

   Meteorological phenomena like wind, rain, hail, snow, lightning,
   tornados and hurricanes, are all a result of energy transformations
   brought about by solar energy on the planet Earth. It has been
   estimated that the average total solar incoming radiation (or
   insolation) is about 1350 watts per square meter incident to the summit
   of the atmosphere, at the equator at midday, a figure known as the
   solar constant. Although this amount varies a little each year, as a
   result of solar flares, prominences and the sunspot cycle. Some 34% of
   this is immediately reflected by the planetary albedo, as a result of
   clouds, snowfields, and even reflected light from water, rock or
   vegetation. As more energy is received in the tropics than is
   re-radiated, while more energy is radiated at the poles than is
   received, climatic homeostasis is only maintained by a transfer of
   energy from the tropics to the poles. This transfer of energy is what
   drives the winds and the ocean currents. Like biological processes, all
   meteorological processes involve transformation of energy from a
   concentrated form such as sunlight into a less concentrated form, such
   as far infrared radiation (i.e., heat radiation at the much smaller
   characteristic temperatures that occur on Earth, and thus is diffused
   into many photons). However, energy may be temporarily locally stored
   during this process, and the sudden release of such stored sources is
   responsible for the dramatic processes mentioned above. For example,
   the kinetic energy of a snow-avalanche or hurricane is due to the
   sudden release of energy previously captured from solar radiations.
   A volcano is the release of stored energy from below the surface of
   Earth originating in radioactive decay and gravitational sorting in the
   Earth's core and mantle of energies left over from its formation
   Enlarge
   A volcano is the release of stored energy from below the surface of
   Earth originating in radioactive decay and gravitational sorting in the
   Earth's core and mantle of energies left over from its formation

Geology

   Continental drift, mountain ranges, volcanos, and earthquakes are
   phenomena that are a result of energy transformations in the Earth's
   crust. Recent studies suggest that the Earth transforms about 6.18 x
   10^-12 J/s (joules per second) per kilogram. Given the Earth's mass of
   about 5.97 x 10^24 kilograms, this means that the rate of energy
   transformations inside the Earth is about 37 x 10^12 J/s (37
   terawatts).

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

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

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

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

Astronomy and cosmology

   The phenomona of stars, nova, supernova, quasars and gamma ray bursts
   are the universe's highest-output energy transformations of matter. All
   stellar phenomena (including of course solar activity) are driven by
   various kinds of energy transformations. Energy in such transformations
   is either from gravitational collapse of matter (usually molecular
   hydrogen) into various classes of astronomical objects (stars, black
   holes, etc.), or from nuclear fusion (of lighter elements, primarily
   hydrogen).
   Dark energy is believed to make up 70% of the universe
   Enlarge
   Dark energy is believed to make up 70% of the universe

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

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

Methods of Measurement

   The methods for the measurement of energy often deploy methods for the
   measurement of still more fundamental concepts of science, viz. mass,
   distance, radiation, temperature, time, electric charge and electric
   current. Conventionally the technique most often employed are
   calorimetry, in thermodynamics that relies on the measurement of
   temperature: a thermometer or a bolometer for measurement of intensity
   of a radiation.

Different forms of energy and their inter-relations

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

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

Kinetic

   Kinetic energy is energy due to motion of a body or particles within
   it.

   Thermal energy, often referred to as heat is a kind of kinetic energy
   because it is partly because of the motion of atoms or molecules within
   a solid, liquid or gas. The case of an ideal gas is perhaps one that
   has been analyzed mathematically in maximum detail. The kinetic
   energy,ε of the particles that comprise an ideal gas is expressed by
   the equipartition theorem to be equal to \!{\frac{1}{2} k T} , so the
   energy per particle is proportional to temperature. For a monatomic gas
   having N particles each with three degrees of freedom, the internal
   energy is:

                \overline{E_{kT}}= {3\over{2}} NkT

   where k is the Boltzmann constant and T is absolute temperature.
   Whereas all internal energy is kinetic in an ideal gas at low
   temperatures, at higher temperatures in gases, and in liquids and
   solids, there is more energy in vibrations within the molecules. Thus,
   whenever there is energy due to vibrations, half of it is stored as
   kinetic energy and the other half in electromagnetic potential energy
   between particles.

   Similarly, radiation energy, also commonly known as light energy, is
   often portrayed as being carried by moving photons and electrical
   energy is portrayed as being transferred from one place to another
   through movement of electrons. However, close examination reveals that
   this is not really true. Radiation energy cannot be neatly categorized
   as classical kinetic energy, since photons have no invariant mass and
   thus the energy required to accelerate them to their velocity (and thus
   which is associated with their motion) cannot be calculated using other
   kinetic equations.

   The electrical energy of an electric current is not due to the motion
   of electrons from one end of the conducting wire to another - simply
   because speed of electrons on both ends of wire is the same (thus their
   kinetic energy is the same and can not be the sourse of energy
   delivered to a load in between). An electric current is in fact induced
   motion of charges at one end of a wire, by introduction of an electric
   field at the other. The electric field and the wave of current it
   drives are established over a conductor with a speed v almost equal to
   the speed of light (v=c/sqrt(με)≈c/1.83=1.6x10^8 m/sec in household
   copper or aluminium wires with polyvinil chloride insulation), but
   conduction electrons move at a tiny fraction of that speed (~0.1 mm/sec
   at current I ~ 1 A). The energy of an electric current is carried in
   the electric field and magnetic field of the current - as given by the
   Poynting vector. If a wire is made of a good conductor, then
   practically all electric energy flows outside the wire (because
   electric field and thus Poynting vector flux inside conductive wire are
   negligible), and it enters low conductive load (where Poynting vector
   tilts inward). This electric energy flux can be transformed in the load
   into heat, light, kinetic energy or other forms of energy.

Potential

   Potential energy is the energy due to the position of an object
   relative to other objects. It is analogous to the concept of wealth
   that indicates the capacity of an individual or an organization to
   influence people in the society. This form of energy can be positive or
   negative because it can be either work done on an object by a force, or
   work done by the object against a force. Negative energy is a thus a
   mathematical construct in reference to another system. Each of the
   fundamental interactions of nature can be linked to a kind of potential
   energy:

Gravitational potential energy

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

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

   where

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

   In case of small displacement h << r near the Earth's surface where
   GM/r = g, the above formula results in the widely used E = mgh
   approximation for gravitational potential energy.

Electric potential energy

   Electric potential energy is the work of electric forces during
   rearrangement of positions of charges, and also includes the common
   chemical potential energies (energy required to break chemical bonds,
   or obtained from forming them). The energy released in lightning, from
   burning a litre of fuel oil, or from using an amount of electrical
   power from an electrical-wiring system, are all common examples of
   electromagnetic potential energy. Quantitatively, electromagnetic
   potential energy is:

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

   where

          q and Q are the electric charges on the objects in question,
          r is the distance between them,
          ε[0] is the electric constant of a vacuum.

   In use of electrical energy from an electrical wiring system, the
   electric potential energy available is represented by the electrical
   potential difference (measured in volts) between the conductors, and
   the amount of charge which is to be transferred between them. Released
   energy in joules is given by voltage multiplied by coulombs of charge
   transferred.

Magnetic potential energy

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

Thermal potential energy

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

Chemical potential energy

   Potential chemical energy is the energy which may potentially be
   liberated, when the bonds of chemical structures are rearranged. Energy
   is never stored in chemical bonds except as a negative quantity (i.e.,
   it always requires energy to break a bond), but net energy may be
   released when weak chemical bonds are broken so that stonger bonds can
   be made. The mixture of a fuel and oxygen is an example: this stores
   chemical energy as compared to the products of combustion, i.e., the
   energy is not stored in the fuel, but rather exists as a potential
   energy to be converted to heat when the fuel combines with oxygen.
   Other common examples of chemical potential are a rechargable battery,
   or a food item (where again the energy is not stored in the item
   itself, but actually in the system of item-plus-oxygen). Some chemical
   fuels or explosives (for example, nitroglycerine) do not require a
   second reactant substance to release potential energy, but even in
   these cases, the energy released does not come from the bonds of the
   molecule, but rather is released from the stronger bonds of the
   products into which it decomposes (in the case of nitroglycerine, from
   the powerful bond in the new N[2] produced when it explodes).

Elastic potential energy

   Potential elastic energy is the energy stored in the elastic nature of
   objects. Elastic energy is actually of several types: it is sometimes a
   kind of electric potential energy (as in metal springs), and in these
   cases energy is released as charged atoms which have been compressed
   are allowed to move apart. However, in other cases (such as compressed
   ideal gases or rubber bands) the potential energy is not stored as
   electrical potential, but rather is stored as a low-entropy arrangement
   of atoms which can allow rapid conversion of thermal energy into work,
   when they are rearranged into higher-entropy structures.

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

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

   where

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

Nuclear potential energy

   Nuclear potential energy, along with electric potential energy,
   provides the energy released from nuclear fission and nuclear fusion
   processes. In both cases strong nuclear forces bind nuclear particles
   more strongly and closely, after the reaction has completed. 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 can be as much as several parts per thousand.

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

Transformations of energy

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

   Energy can be converted into matter and vice versa, although both
   energy and matter continue to exhibit rest mass throughout any such
   process (thus in a closed system, conversion of matter to energy or
   energy to matter makes no difference in the system mass). The equation
   E=mc^2, mathematically derived independently by Albert Einstein and
   Henri Poincaré reflects the equivalence between mass and energy. This
   equation states that the liberated active energy (light, heat,
   radiation) that is equivalent to a unit of inactive matter is enormous.
   This can be witnessed in the tremendous energies liberated by a nuclear
   bomb. Conversely, the mass equivalent of a unit of energy is miniscule,
   which is why loss of energy from most systems is difficult to measure
   by weight, unless the energy loss is very large. Examples of energy
   transformation into matter (particles) are found in high energy nuclear
   physics. However, all energy in any form exhibits rest mass, even if it
   has not been converted into new particles.

Law of conservation of energy

   Energy, in the context of natural sciences, is subject to the law of
   conservation of energy. According to this law it can neither be created
   (produced) nor destroyed. It can only be transformed.

   According to the first law of thermodynamics 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
   used in all branches of physics, but frequently violated for short
   enough periods of time during which energy can not be mathematically
   defined yet (see quantum electrodynamics and off shell concept).
   Noether's theorem relates the conservation of energy to the time
   invariance of physical laws.

   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. The fact that energy can not be defined
   for arbitrary short periods of time in quantum mechanics follows from
   the definition of energy operator which results mathematically in the
   mutual uncertainty of time and energy known as the uncertainty
   principle:

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

   Despite being seemingly insignificant, this principle has made profound
   impact on our understanding many phenomena in the realm of particle
   physics. It led to the introduction of the concept of virtual particles
   which carry momentum, exchange by which with real particles is
   responsible for creation of all known fundamental forces (more
   accurately known as fundamental interactions). Virtual photons (which
   are simply lowest quantum mechanical energy state of photons) are also
   responsible for spontaneous radiative decay of exited atomic and
   nuclear states, for the Casimir force, for Van der Waals bond forces
   and some other observable phenomena.

Energy in Society

   In the context of society the word energy is synonymous to energy
   resources, it most often refers to substances like fuels, petroleum
   products and electric power installations. This difference vis a vis
   energy in natural sciences can lead to some confusion, because energy
   resources (which represent usable energy) are not conserved in nature
   in the same way as energy is conserved in the context of physics.
   People often talk about energy crisis and the need to conserve energy,
   something contrary to the principle of energy conservation in natural
   sciences. Efforts, normally referred to as energy conservation, are
   actually efforts that are targeted at conserving currently available
   energy resources that can be applied to do useful work.

Economics

   Energy consumption per capita per country (2001). Red hues indicate
   increase, green hues decrease of consumption during the 1990s.
   Enlarge
   Energy consumption per capita per country (2001). Red hues indicate
   increase, green hues decrease of consumption during the 1990s.

   Production and consumption of energy resources is very important to the
   global economy. All economic activity requires energy resources,
   whether to manufacture goods, provide transportation, run computers and
   other machines, or to grow food to feed workers, or even to harvest new
   fuels. Thus the way in which a human society uses its existing energy
   resources, develops means of their production or acquisition is a
   defining characteristic of its economy. The progression from animal
   power to steam power, then the internal combustion engine and
   electricity, are key elements in the development of modern
   civilization. The cost of energy resources depends on its demand and
   production at any particular time. Scarcity of cheap fuels is a key
   concern in future energy development.

   Some attempts have been made to define " embodied energy" - the sum
   total of energy expended to deliver a good or service as it travels
   through the economy.

Environment

   Consumption of energy resources, (e.g. turning on a light) is
   apparently harmless. However, producing that energy requires resources
   and contributes to air and water pollution. Many electric power plants
   burn coal oil or natural gas in order to generate electricity for
   energy needs. While burning these fossil fuels produces a readily
   available and instantaneous supply of electricity, it also generates
   air pollutants including carbon dioxide (CO2), sulfur dioxide and
   trioxide (SOx) and nitrogen oxides (NOx). Carbon dioxide is an
   important greenhouse gas which is thought to be responsible for some
   fraction of the rapid increase in global warming seen especially
   temperature records in the 19th century, as compared with tens of
   thousands of years worth of temperature records which can be read from
   ice cores taken in artic regions.

   Burning fossil fuels for electricity generation also releases trace
   metals such as beryllium, cadmium, chromium, copper, manganese,
   mercury, nickel, and silver into the environment, which also act as
   pollutants. Certain renewable energy technologies do not pollute the
   environment in the same ways, and therefore can help contribute to a
   cleaner energy future for the world. Renewable energy technologies
   available for electricity production include biofuels, solar power,
   tidal power, wind turbines, hydroelectric power etc. However, serious
   environmental concerns have been articulated by several environmental
   activists regarding these modes of electricity generation. According to
   them, some pollution is invariably produced during the manufacture and
   retirement of the materials associated with the machinery used in these
   technologies. A central way to avoid downsides of expanding energy
   production is energy conservation.

Exploration and research

   Scientists have realized that the known energy resources may not
   suffice forever, there is thus an urgent need to explore new avenues,
   which include prospecting for newer territories rich in oil or gas or
   methods for producing energy resources using methods that have been
   explored very little.While some scientists are busy in exploring the
   possibility of cold fusion many countries are diverting significant
   economic resources towards space exploration . Space exploration of
   long duration demands compact energy resources because the huge
   consumption of energy resources by a large size spacecraft cannot be
   met by chemical portable energy resources carried on board from the
   Earth. For missions to the outer solar system, compact nuclear power
   sources (in the form of nuclear reactors or radioisotope thermoelectric
   generators) are a necessity. It has been proposed to explore
   annihilation of matter for this purpose, although no practical way of
   producing significant amounts of antimatter, or storing them is
   presently known. Yet another field of research to explore a future
   source of energy is through artificial photosynthesis, a process being
   actively researched to convert the carbon dioxide into useful fuel,
   other than biomass without the intervention of plants.

Management

   Since the cost of energy has become a significant factor in the
   performance of economy of societies, management of energy resources has
   become very crucial.Energy management involves utilizing the available
   energy resources more effectively that is with minimum incremental
   costs. Many times it is possible to save expenditure on energy without
   incorporating fresh technology by simple management techniques. Most
   often energy management is the practice of using energy more
   efficiently by eliminating energy wastage or to balance justifiable
   energy demand with appropriate energy supply. The process couples
   energy awareness with energy conservation.

Politics

   Since energy plays an essential role in industrial societies, the
   ownership and control of energy resources plays an increasing role in
   politics at the national level. Governments may seek to influence the
   sharing (distribution) of energy resources among various sections of
   the society through pricing mechanisms; or even who owns resources
   within their borders. They may also seek to influence the use of energy
   by individuals and business in an attempt to tackle environmental
   issues.

   The most recent international political controversy regarding energy
   resources is in the context of Iraq wars. Some political analysts
   maintain that the hidden reason for both 1991 and 2003 wars can be
   traced to strategic control of international energy resources. Others
   counter this analysis with the numbers related to its economics.
   According to the latter group of analysts, U.S. has spent about $336
   billion in Iraq as compared with a background current value of $25
   billion per year budget for the entire U.S. oil import dependence See
   Energy wars

Production

   Producing energy to sustain human needs is an essential social
   activity, and a great deal of effort goes into the activity. While most
   of such effort is limited towards increasing the production of
   electricity and oil, newer ways of producing usable energy resources
   from the available energy resources are being explored. One such effort
   is to explore means of producing hydrogen from water. Though hydrogen
   use is environmentally friendly, its production requires energy and
   existing technologies to make it, are not very efficient. Research is
   underway to explore enzymatic decomposition of biomass. See hydrogen
   economy.

   Other forms of conventional energy resources are also being used in new
   ways. Coal gasification and liquefaction are recent technologies that
   are becoming attractive after the realization that oil reserves, at
   present consumption rates, may be rather short lived. See alternative
   fuels.

Transportation

   While energy resources are an essential ingredient for all modes of
   transportation in society, the transportation of energy resources is
   becoming equally important. Energy resources are invariably located far
   from the place where they are consumed. Therefore their transportation
   is always in question. Some energy resources like liquid or gaseous
   fuels are transported using tankers or pipelines, while electricity
   transportation invariably requires a network of grid cables. The
   transportation of energy, whether by tanker, pipeline, or transmission
   line, poses challenges for scientists and engineers, policy makers, and
   economists to make it more riskfree and efficient.

Usage

   Ever since humanity discovered various energy resources available in
   nature, it has been busy in inventing devices, commonly known as
   machines, that make life more comfortable by using one or the other
   energy resource. Thus, although the primitive man knew the utility of
   fire to cook food, the invention of very many devices like gas burners
   and microwave ovens have increased the usage of energy for this purpose
   alone manifold. The trend is the same in any other field of social
   activity, be it construction of social infrastructure, manufacturing of
   fabrics for covering; porting; printing; decorating for example,
   textiles), air conditioning; communication of information or for moving
   people and/or goods( automobiles)

Other links

   Look up Energy in Wiktionary, the free dictionary. Look up Energy in
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   in Wikisource, the free source. Look up Energy in Commons, the free
   repository. Look up Energy in Wikispecies, directory of species.
     * Principles of energetics
     * List of energy topics
     * Orders of magnitude (energy)

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