In
physics,
energy (from
the
Greek 
energeia, "activity, operation", from 
energos, "active, working") is a
scalar physical quantity that describes the
amount of
work that can be performed
by a
force, an attribute of objects and
systems that is subject to a
conservation law. Different forms of energy
include
kinetic,
potential,
thermal,
gravitational,
sound,
light,
elastic, and
electromagnetic energy. The forms
of energy are often named after a related force.
Any form of energy can be
transformed into another form, but the
total energy always remains the same. 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.
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.
History
The word
energy derives from
Greek ἐνέργεια (
energeia),
which appears for the first time in the work
Nicomachean Ethics of
Aristotle in the 4th century BC. In 1021 AD, the
Arabian physicist,
Alhazen, in the
Book of Optics, held
light rays to be streams of minute
energy particles, stating that "the smallest parts of
light" retain "only properties that can be treated by geometry and
verified by
experiment" and that "they
lack all sensible qualities except energy." In 1121,
AlKhazini, in
The Book of the Balance of
Wisdom, proposed that the
gravitational potential
energy of a body varies depending on its distance from the
centre of the Earth.
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.
GustaveGaspard 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.
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 Clausius 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 Nobel
Laureate, said this about the concept of energy:
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).
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.
The
concept of energy is widespread in all
sciences.
 In biology, energy is an
attribute of all biological systems from the biosphere to the
smallest living organism. Within an
organism it is responsible for growth and development of a
biological cell or an organelle of a biological organism. Energy is thus often said to be stored by
cells in the structures of molecules
of substances such as carbohydrates
(including sugars) and lipids, which release
energy when reacted with oxygen. In human
terms, the human equivalent (He)
(Human energy conversion) The human equivalent energy 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. 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 He. 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. 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
 In geology,
continental drift, mountain range, volcanoes,
and earthquakes are phenomena that can be
explained in terms of energy
transformations in the Earth's interior. 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 atmosphere of the
planet Earth.
 In cosmology
and astronomy the phenomena of stars,
nova, supernova,
quasars and gamma
ray bursts are the universe's highestoutput 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.
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 longdestroyed stars created these atoms.
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 many weather phenomena,
save those generated by volcanic events. An example of a
solarmediated 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. Sunlight is also 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.
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.
 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 publicservice 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).
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
energymomentum 4vector). In other words, energy is invariant with
respect to rotations of
space, but not
invariant with respect to rotations of
spacetime (=
boosts).
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:
 \Delta{}E = W
(1)
if there are no other energytransfer processes involved. Here
E 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:
 \Delta{}E = 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. 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 workdone or heatadded,
in the classic senses).
 \Delta{}E = 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 (E_p) to kinetic
energy (E_k) 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:
 E_{pi} + E_{ki} = E_{pF} + E_{kF}
The equation can then be simplified further since E_p = 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 E_p + E_k =
E_{total}.
Energy and the laws of motion
In
classical mechanics, energy
is a conceptually and mathematically useful property since it is a
conserved quantity.
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 innonrelativistic quantum
mechanics.
The Lagrangian
Another energyrelated 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. 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 nonconservative 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:
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, and
that heat is included as a form of energy transfer. A commonlyused
corollary of the first law is that for a "system" subject only to
pressure forces and heat transfer (e.g. a
cylinderfull of gas), the differential change in energy of the
system (with a
gain in energy signified by a positive
quantity) is given by:
 \mathrm{d}E = T\mathrm{d}S  P\mathrm{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 d
S 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 requires work to be done on it and so the
volume change, d
V, is negative when work is done on the
system). Although this equation is the standard textbook 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.
Energy is sometimes expressed as:
 \mathrm{d}E=\delta Q+\delta W\,,
which is unsatisfactory 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.
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.
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 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.
2. On the other hand, in the key equation m^2 c^4 = E^2  p^2 c^2,
the contribution mc^2 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 0.5
p^2/m at speeds much smaller than
c, as can be proved by
writing E = mc^2 √(1 + p^2 m^{2}c^{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 energyversusmomentum 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 nonrelativistic 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 is force times distance.
 W = \int_C \mathbf{F} \cdot \mathrm{d} \mathbf{s}
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 centerofmass reference frame, the bat does no work on the
ball. But, in the reference frame of the person swinging the bat,
considerable work is done on the ball.
Quantum mechanics
In quantum mechanics energy is defined in terms of the
energy operatoras 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 timedependence of slow changing (nonrelativistic)
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
waves in a vacuum, the resulting energy states are related to the
frequency by the
Planck equation E = h\nu
(where h is the
Planck's constant
and \nu the frequency). In the case of electromagnetic wave these
energy states are called quanta of
light or
photons.
Relativity
When calculating kinetic energy (=
work to accelerate a
mass from zero
speed to some
finite speed) relativistically  using
Lorentz transformations instead of
Newtonian mechanics, Einstein
discovered an unexpected byproduct 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:
 E = m c^2 ,
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.
In general relativity, the
stressenergy tensor serves as the
source term for the gravitational field, in rough analogy to the
way mass serves as the source term in the nonrelativistic
Newtonian approximation.
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.
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.
Units
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. In addition to the joule, other
units of energy include the
kilowatt
hour (kWh) and the
British
thermal unit (Btu). These are both larger units of energy. One
kWh is equivalent to exactly 3.6 million joules, and one Btu is
equivalent to about 1055 joules.
Forms of 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. It has been attempted
to categorize
all forms of energy as either kinetic or
potential: this is not incorrect, but neither is it clear that it
is a real simplification, as Feynman points out:
Examples of the interconversion of energy
Mechanical energy
Mechanical energy manifest in many forms,but can be broadly
classified into elastic potential energy and kinetic energy.
However the term potential energy is a very general term, because
it exists in all force fields, such as gravitation, electrostatic
and magnetic fields. Potential energy refers to the energy any
object gets due to its position in a force field.
Potential energy, symbols
E_{p},
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,
 :E_{\rm p} = \int \mathbf{F}\cdot{\rm d}\mathbf{s}
with the dot representing the
scalar
product of the two
vector.
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.
Elastic potential energy
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,
 :F = kx
where
k is the
force
constant of the particular spring (or system). In this case,
the calculated work becomes
 :E_{\rm p,e} = {1\over 2}kx^2
only when
k is constant. 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.
Kinetic energy
Kinetic energy, symbols
E_{k},
T or
K, is the work required to accelerate an object to a given
speed. Indeed, calculating this work one easily obtains the
following:
 :E_{\rm k} = \int \mathbf{F} \cdot d \mathbf{x} = \int
\mathbf{v} \cdot d \mathbf{p}= {1\over 2}mv^2
At speeds approaching the
speed of
light,
c, this work must be calculated using
Lorentz transformations, which
results in the following:
 : E_{\rm k} = m c^2\left(\frac{1}{\sqrt{1  (v/c)^2}} 
1\right)
This equation reduces to the one above it, at small (compared to
c) speed. A mathematical byproduct 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:
 : E_{\rm rest} = mc^2
This energy is thus called
rest mass
energy.
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.
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).
Sound energy
Sound is a form of mechanical vibration, which propagates through
any mechanical medium.
Gravitational 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
 :E_{\rm p,g} = mgh
A more general expression for the potential energy due to
Newtonian gravitation between two
bodies of masses
m_{1} and
m_{2},
useful in
astronomy, is
 :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} m
^{3}kg
^{−1}s
^{−2}.
In this case, the reference point is the infinite separation of the
two bodies.
Thermal energy
Examples of the interconversion of 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
manyatomic 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.
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
C_{v} 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).
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
pound of water by 1
°F (later fixed as 1055.06 J).
Electric energy
Examples of the interconversion of energy
Electrostatic energy
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 pointlike charges
Q_{1} and
Q_{2} at a distance
r this work, and hence electric potential energy is equal
to:
 :E_{\rm p,e} = {1\over {4\pi\epsilon_0}}{{Q_1Q_2}\over{r}}
where ε
_{0} is the
electric
constant of a vacuum, 10
^{7}/4π
c_{0}²
or 8.854188…×10
^{−12} F/m. 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 purely 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 recombine
making the plates neutral). In this case the work and thus the
electric potential energy becomes
 :E_{\rm p,e} = {{Q^2}\over{2C}}
Electricity energy
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:
 :E = UQ = UIt = Pt = {{U^2}{t}\over{R}} = {I^2}Rt
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.
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
realignment of the vector of the magnetic dipole moment, and is
equal:
 :E_{\rm p,m} = m\cdot B
while the energy stored in a
inductor (of
inductance L) when current
I is passing via it is
 :E_{\rm p,m} = {1\over 2}LI^2.
This second expression forms the basis for
superconducting magnetic
energy storage.
Electromagnetic Energy
Examples of the interconversion of energy
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:
 : u_e=\frac{\epsilon_0}{2} E^2
and
 : u_m=\frac{1}{2\mu_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
 :\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
 :E = h\nu
where
h is the
Planck
constant, 6.6260693(11)×10
^{−34} Js, 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.
Chemical energy
Examples of the interconversion of energy
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 rearrangement of mutual
positions of electric charges, electrons and protons, in the
process of aggregation. So, basically it is electrostatic potential
energy of electric charges. 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 the surroundings (usually again in form of
heat or
light). For example,
 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 kilojoules per
mole.
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:
 :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:
 :ΔG = ΔH − TΔS
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:
 1 tonne of coal equivalent (TCE) = 29.3076 GJ =
8,141 kilowatt hour
 1 tonne of oil
equivalent (TOE) = 41.868 GJ = 11,630 kilowatt hour
On the same basis, a tankfull of
gasoline
(45 litres, 12 gallons) is equivalent to about
1.6 GJ of chemical energy. Another chemicallybased 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.
Simple examples of storage of chemical energy are batteries and
food. When food is digested and metabolized (often with oxygen),
chemical energy is released, which can in turn be transformed into
heat, or by muscles into kinetic energy.
Nuclear energy
Examples of the interconversion of energy
Nuclear potential
energy, along with
electric potential energy,
provides the energy released from
nuclear fission and
nuclear fusion processes. The result of both
these processes are nuclei in which the moreoptimal size of the
nucleus allows the
nuclear force
(which is opposed by the
electromagnetic force) to bind nuclear
particles more tightly together than before the reaction.
The
Weak nuclear force (different
from the strong force) provides the potential energy for certain
kinds of radioactive decay, such as
beta
decay.
The energy released in nuclear processes is so large that the
relativistic change in mass (after the energy has been removed) can
be as much as several parts per thousand.
Nuclear particles (
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.
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
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.
Energy gives rise to weight and is equivalent to
matter and vice versa. The formula
E =
mc², derived by
Albert Einstein (1905) quantifies the
relationship between mass and rest energy within the concept of
special relativity. In different theoretical frameworks, similar
formulas were derived by
J. J. Thomson
(1881),
Henri Poincaré (1900),
Friedrich Hasenöhrl (1904)
and others (see
Massenergy
equivalence#History for further information). Since c^2 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 (~9x10^{16}
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.
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 heatlike increase in disorder in quantum states, in the
universe (such as an expansion of matter, or a randomization in a
crystal).
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 produce work through a
heat engine, or be transformed to other usable
forms of energy (through the use of generators attached to heat
engines), grows less and less.
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 by itself. It can only be transformed.
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. 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.
According to
energy conservation
law the total inflow of energy into a system must equal the total
outflow of energy from the system, plus the change in the energy
contained within the system.
This law is a fundamental principle of physics. It follows from the
translational symmetry of
time, a property of most phenomena below the
cosmic scale that makes them independent of their locations on the
time coordinate. Put differently, yesterday, today, and tomorrow
are physically indistinguishable.
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. 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.
On any time scales, the uncertainty in the energy is by
 \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
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.
Energy and life
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 (C
_{6}H
_{12}O
_{6})
and
stearin
(C
_{57}H
_{110}O
_{6}) are convenient
examples. The food molecules are oxidised to
carbon dioxide and
water in the
mitochondria
 :C_{6}H_{12}O_{6} + 6O_{2} →
6CO_{2} + 6H_{2}O
 :C_{57}H_{110}O_{6} + 81.5O_{2}
→ 57CO_{2} + 55H_{2}O
and some of the energy is used to convert
ADP into
ATP
 :ADP + HPO_{4}^{2−} → ATP + H_{2}O
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:
 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 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"). 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, i.e. reconverted into carbon
dioxide and heat.
Energy and Information Society
Modern society continues to rely largely on fossil fuels to
preserve economic growth and today's standard of living. However,
for the first time, physical limits of the Earth are met in our
encounter with finite resources ofoil and natural gas and its
impact of greenhouse gas emissions onto the global climate.
Neverbefore has accurate accounting of our energy dependency been
more pertinent to developing public policies for a sustainable
development of our society, both in the industrial world and the
emerging economies. At present, much emphasis is put on the
introduction of a worldwide capandtrade system, to limit global
emissions in greenhouse gases by balancing regional differences on
a financial basis. In the near future, society may be permeated at
all levels with information systems for direct feedback on energy
usage, as fossil fuels continue to be used privately and for
manufacturing and transportation services. Information in today's
society, focused on knowledge, news and entertainment, is expected
to extend to energy usage in realtime. A collective medium for
energy information may arise, serving to balance our individual and
global energy dependence on fossil fuels. Yet, this development is
not without restrictions, notably privacy issues. Recently, the
Dutch Senate rejected a proposed law for mandatory national
introduction of smart metering, in part, on the basis of privacy
concerns .
See also
Notes and references
 Aristotle, "Nicomachean Ethics", 1098b33, at
Perseus
 Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", p.
621, in

http://www.uic.edu/aa/college/gallery400/notions/human%20energy.htm
Retrieved on May2909
 Bicycle calculator  speed, weight, wattage etc. [1].
 Earth's Energy Budget
 Berkeley Physics Course Volume 1. Charles Kittel, Walter D
Knight and Malvin A Ruderman
 The Hamiltonian MIT OpenCourseWare website
18.013A Chapter 16.3 Accessed February 2007
 Ristinen, Robert A., and Kraushaar, Jack J. Energy and the
Environment. New York: John Wiley & Sons, Inc., 2006.
 E. Noether's Discovery of the Deep Connection
Between Symmetries and Conservation Laws
 The Laws of Thermodynamics including careful
definitions of energy, free energy, et cetera.
 Time Invariance
 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.
 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.
 Ito, Akihito; Oikawa, Takehisa (2004). " Global Mapping of Terrestrial Primary Productivity and
LightUse Efficiency with a ProcessBased Model." in Shiyomi,
M. et al. (Eds.) Global Environmental Change in the Ocean and
on Land. pp. 343–58.
 Minutes Eerste Kamer Debat " (part a)", " (part b)"
Further reading
External links