Energy

Energy (from Ancient Greek ἐνέργεια (enérgeia) 'activity') is the quantitative property that is
transferred to a body or to a physical system, recognizable in the performance of work and in the
form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that
energy can be converted in form, but not created or destroyed. The unit of measurement for energy
in the International System of Units (SI) is the joule (J).

Forms of energy include the kinetic energy of a Energy

moving object, the potential energy stored by an
object (for instance due to its position in a field),
the elastic energy stored in a solid object,
chemical energy associated with chemical
reactions, the radiant energy carried by
electromagnetic radiation, the internal energy
contained within a thermodynamic system, and
rest energy associated with an object's rest mass.
These are not mutually exclusive.

All living organisms constantly take in and release

energy. The Earth's climate and ecosystems
processes are driven primarily by radiant energy A plasma globe using electrical energy to
from the sun.[6] The energy industry provides the create plasma, light, heat, movement, and a
energy required for human civilization to function, faint sound

which it obtains from energy resources such as

Common symbols E
fossil fuels, nuclear fuel, and renewable energy.
SI unit joule[1] (J)

Other units kWh, BTU, calorie, eV,

erg, foot-pound[2]

In SI base units J = kg⋅m2⋅s−2[3]

Extensive? yes[4]

Conserved? yes

Dimension M L2 T−2[5]
Forms

In a typical lightning strike, 500 megajoules

of electric potential energy is converted
into the same amount of energy in other
forms, mostly light energy, sound energy,
and thermal energy.

Thermal energy is energy of microscopic

constituents of matter, which may include
both kinetic and potential energy.

The total energy of a system can be subdivided and classified into potential energy, kinetic energy,
or combinations of the two in various ways. Kinetic energy is determined by the movement of an
object – or the composite motion of the object's components – while potential energy reflects the
potential of an object to have motion, generally being based upon the object's position within a field
or what is stored within the field itself.[7]

While these two categories are sufficient to describe all forms of energy, it is often convenient to
refer to particular combinations of potential and kinetic energy as its own form. For example, the
sum of translational and rotational kinetic and potential energy within a system is referred to as
mechanical energy, whereas nuclear energy refers to the combined potentials within an atomic
nucleus from either the nuclear force or the weak force, among other examples.[8]
Some forms of energy (that an object or system can have as a measurable property)[9][10]

Type of energy Description

Chemical potential energy due to chemical bonds

Chromodynamic potential energy that binds quarks to form hadrons

potential energy due to the deformation of a material (or its container) exhibiting a restorative force
Elastic
as it returns to its original shape

Electric potential energy due to or stored in electric fields

Gravitational potential energy due to or stored in gravitational fields

Ionization potential energy that binds an electron to its atom or molecule

Magnetic potential energy due to or stored in magnetic fields

Mechanical the sum of macroscopic translational and rotational kinetic and potential energies

Mechanical
kinetic and potential energy in an elastic material due to a propagating oscillation of matter
wave

Nuclear potential energy that binds nucleons to form the atomic nucleus (and nuclear reactions)

potential energy stored in the fields of waves propagated by electromagnetic radiation, including
Radiant
light

Rest potential energy due to an object's rest mass

Rotational kinetic energy due to the rotation of an object

kinetic and potential energy in a material due to a sound propagated wave (a particular type of
Sound wave
mechanical wave)

kinetic energy of the microscopic motion of particles, a kind of disordered equivalent of mechanical
Thermal
energy

History

Thomas Young, the first person

to use the term "energy" in the
modern sense
The word energy derives from the Ancient Greek: ἐνέργεια, romanized: energeia, lit. 'activity,
operation',[11] which possibly appears for the first time in the work of Aristotle in the 4th century BC.
In contrast to the modern definition, energeia was a qualitative philosophical concept, broad enough
to include ideas such as happiness and pleasure.[12]

In the late 17th century, Gottfried Leibniz proposed the idea of the Latin: vis viva, or living force,
which defined as the product of the mass of an object and its velocity squared; he believed that total
vis viva was conserved. To account for slowing due to friction, Leibniz theorized that thermal energy
consisted of the motions of the constituent parts of matter, although it would be more than a
century until this was generally accepted. The modern analog of this property, kinetic energy, differs
from vis viva only by a factor of two.[13] Writing in the early 18th century, Émilie du Châtelet
proposed the concept of conservation of energy in the marginalia of her French language
translation of Newton's Principia Mathematica, which represented the first formulation of a
conserved measurable quantity that was distinct from momentum, and which would later be called
"energy".[14]

In 1807, Thomas Young was possibly the first to use the term "energy" instead of vis viva, in its
modern sense.[15] Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern
sense,[16] and in 1853, William Rankine coined the term "potential energy".[17] The law of
conservation of energy was also first postulated in the early 19th century, and applies to any
isolated system.[18] It was argued for some years whether heat was a physical substance, dubbed
the caloric, or merely a physical quantity, such as momentum. In 1845 James Prescott Joule
discovered the link between mechanical work and the generation of heat.[19]

These developments led to the theory of conservation of energy, formalized largely by William
Thomson (Lord Kelvin) as the field of thermodynamics.[20] Thermodynamics aided the rapid
development of explanations of chemical processes by Rudolf Clausius, Josiah Willard Gibbs,
Walther Nernst, and others.[21] It also led to a mathematical formulation of the concept of entropy by
Clausius[22] and to the introduction of laws of radiant energy by Jožef Stefan.[23] 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.[24] Thus, since 1918, theorists have understood that the law of
conservation of energy is the direct mathematical consequence of the translational symmetry of the
quantity conjugate to energy, namely time.[25]

Albert Einstein's 1905 theory of special relativity showed that rest mass corresponds to an
equivalent amount of rest energy. This means that rest mass can be converted to or from equivalent
amounts of (non-material) forms of energy, for example, kinetic energy, potential energy, and
electromagnetic radiant energy. When this happens, rest mass is not conserved, unlike the total
mass or total energy. All forms of energy contribute to the total mass and total energy. Thus,
conservation of energy (total, including material or rest energy) and conservation of mass (total, not
just rest) are one (equivalent) law. In the 18th century, these had appeared as two seemingly-distinct
laws.[26][27]

The first evidence of quantization in atoms was the observation of spectral lines in light from the
sun in the early 1800s by Joseph von Fraunhofer and William Hyde Wollaston. The notion of
quantized energy levels was proposed in 1913 by Danish physicist Niels Bohr in the Bohr theory of
the atom. The modern quantum mechanical theory giving an explanation of these energy levels in
terms of the Schrödinger equation was advanced by Erwin Schrödinger and Werner Heisenberg in
1926.[28] Noether's theorem shows that the symmetry of this equation is equivalent to a
conservation of probability.[29] At the quantum level, mass-energy interactions are all subject to this
principle.[30] During wave function collapse, the conservation of energy does not hold at the local
level, although statistically the principle holds on average for sufficiently large numbers of
collapses.[31] Conservation of energy does apply during wave function collapse in H. Everett's many-
worlds interpretation of quantum mechanics.[32]

Units of measure

Joule's apparatus for measuring the

mechanical equivalent of heat. A
descending weight attached to a string
causes a paddle immersed in water to
rotate.

In dimensional analysis, the base units of energy are given by: Work = Force × Distance = M L2 T−2,
with the fundamental dimensions of Mass M, Length L, and time T.[5] In the International System of
Units (SI), the unit of energy is the joule. It is a derived unit that is equal to the energy expended, or
work done, in applying a force of one newton through a distance of one metre.[1] However energy
can also be expressed in many other units not part of the SI, such as ergs, calories, British thermal
units, and kilocalories, which require a conversion factor when expressed in SI units.[2]
The SI unit of power, defined as energy per unit of time, is the watt, which is one joule in one second.
Thus, one Joule of energy consumed in one second is one Watt,[3] 3600 joules of energy consumed
in one hour is one watt-hour, and 3.6 million Joules consumed in one hour is one kilowatt-hour
(kWh). In defining the difference between "energy" and "power", the key understanding is that power
always contains a time unit whether second, hour, day, year, or other time measure. Although the
base units of energy includes time, energy-specific units do not specify a time unit. SI units are set
up to make conversion of Watts to Joules simple such that 1 kilowatt-hour (kWh) implies 3.6 million
Joules of energy being consumed in one hour. One kWh is a measure of Power while 3.6 million
Joules is the amount of energy expressed in that kWh. The CGS energy unit is the erg and the
imperial and US customary unit is the foot pound.[33] Other energy units such as the electronvolt,
food calorie or thermodynamic kcal (based on the temperature change of water in a heating
process), and BTU are used in specific areas of science and commerce.[34]

Scientific use

Classical mechanics

In classical mechanics, energy is a conceptually and mathematically useful property, as it is a

conserved quantity. Several formulations of mechanics have been developed using energy as a core
concept.

Work, a function of energy, is force times distance.[35]

This says that the work ( ) is equal to the line integral of the force F along a path C; for details see
the mechanical work article. Work and thus energy is frame dependent. For example, consider a ball
being hit by a bat. In the center-of-mass reference frame, the bat does no work on the ball. But, in
the reference frame of the person swinging the bat, considerable work is done on the ball.[36]

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.[37] These classical equations have direct analogs in nonrelativistic
quantum mechanics.[38]

Another energy-related concept is called the Lagrangian, after Joseph-Louis Lagrange. This
formalism is as fundamental as the Hamiltonian, and both can be used to derive the equations of
motion or be derived from them. It was invented in the context of classical mechanics, but is
generally useful in modern physics. The Lagrangian is defined as the kinetic energy minus the
potential energy. Usually, the Lagrange formalism is mathematically more convenient than the
Hamiltonian for non-conservative systems (such as systems with friction).[39]

Noether's theorem (1918) states that any differentiable symmetry of the action of a physical system
has a corresponding conservation law. Noether's theorem has become a fundamental tool of
modern theoretical physics and the calculus of variations. A generalisation of the seminal
formulations on constants of motion in Lagrangian and Hamiltonian mechanics (1788 and 1833,
respectively), it does not apply to systems that cannot be modeled with a Lagrangian;[40] for
example, dissipative systems with continuous symmetries need not have a corresponding
conservation law.

Chemistry

In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic,

molecular, or aggregate structure. Since a chemical transformation is accompanied by a change in
one or more of these kinds of structure, it is usually accompanied by a decrease, and sometimes an
increase, of the total energy of the substances involved. Some energy may be transferred between
the surroundings and the reactants in the form of heat or light; thus the products of a reaction have
sometimes more but usually less energy than the reactants. A reaction is said to be exothermic or
exergonic if the final state is lower on the energy scale than the initial state; in the less common
case of endothermic reactions the situation is the reverse.[41]

Chemical reactions are usually not possible unless the reactants surmount an energy barrier known
as the activation energy. The speed of a chemical reaction (at a given temperature T) is related to
the activation energy E by the Boltzmann population factor e−E/kT; that is, the probability of a
molecule to have energy greater than or equal to E at a given temperature T. This exponential
dependence of a reaction rate on temperature is known as the Arrhenius equation. The activation
energy necessary for a chemical reaction can be provided in the form of thermal energy.[42]
Biology

Basic overview of energy and human life

In biology, energy is an attribute of all biological systems, from the biosphere to the smallest living
organism. It enables the growth, development, and functioning of a biological cell or organelle in an
organism. All living creatures rely on an external source of energy to be able to grow and reproduce
– radiant energy from the Sun in the case of green plants and chemical energy (in some form) in the
case of animals. Energy provided through cellular respiration is stored in nutrients such as
carbohydrates (including sugars), lipids, and proteins by cells.[43]

Sunlight's radiant energy is captured by plants as chemical potential energy in photosynthesis, when
carbon dioxide and water (two low-energy compounds) are converted into carbohydrates, lipids,
proteins, and oxygen.[44] Release of the energy stored during photosynthesis as heat or light may be
triggered suddenly by a spark in a forest fire, or it may be made available more slowly for animal or
human metabolism when organic molecules are ingested and catabolism is triggered by enzyme
action.[45]

Humans

The basal metabolism rate measures the food energy expenditure per unit time by endothermic
animals at rest.[46] In other words it is the energy required by body organs to perform normally. For
humans, metabolic equivalent of task (MET) compares the energy expenditure per unit mass while
performing a physical activity, relative to a baseline. By convention, this baseline is 3.5 mL of oxygen
consumed per kg per minute, which is the energy consumed by a typical individual when sitting
quietly.[47]

In human terms, the human equivalent (H-e) (Human energy conversion) indicates, for a given
amount of energy expenditure, the relative quantity of energy needed for human metabolism, using
as a standard an average human energy expenditure of 6,900 kJ 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 H-e. For a difficult task of only a few
seconds' duration, a person can put out thousands of watts, many times the 746 watts in one
official horsepower. For tasks lasting a few minutes, a fit human can generate perhaps 1,000 watts.
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.[48] 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.[49]

The daily 1,600–3,000 calories (7–13 MJ) recommended for a human adult are taken as food
molecules,[50] mostly carbohydrates and fats. Only a tiny fraction of the original chemical energy is
used for work:[note 1]

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: 3 kJ
daily food intake of a normal adult: 6–8 MJ

It would appear that living organisms are remarkably inefficient (in the physical sense) in their use
of the energy they receive (chemical or radiant energy); most machines manage higher efficiencies.

In growing organisms the energy that is converted to heat serves a vital purpose, as it allows the
organism's 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").[note 2]
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. As an example, 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,[51] i.e. reconverted into carbon dioxide
and heat.

Cell metabolism

Multicellular organisms such as humans have cell forms that are classified as Eukaryote. These
cells include an organelle called the mitochondria that generates chemical energy for the rest of the
hosting cell. Ninety percent of the oxygen intake by humans is utilized by the mitochondria,
especially for nutrient processing.[52] The molecule adenosine triphosphate (ATP) is the primary
energy transporter in living cells, providing an energy source for cellular processes. It is continually
being broken down and synthesized as a component of cellular respiration.[53]
Two examples of nutrients consumed by animals are glucose (C6H12O6) and stearin (C57H110O6).
These food molecules are oxidized to carbon dioxide and water in the mitochondria:[54]

and some of the energy is used to convert ADP into ATP:[55][52]

ADP + HPO42− → ATP + H2O

The rest of the chemical energy of the nutrients are converted into heat: the ATP is used as a sort of
"energy currency", and some of the chemical energy it contains is used for other metabolism when
ATP reacts with OH groups and eventually splits into ADP and phosphate (at each stage of a
metabolic pathway, some chemical energy is converted into heat).

Earth sciences

In geology, continental drift, mountain ranges, volcanoes, and earthquakes are phenomena that can
be explained in terms of energy transformations in the Earth's interior,[56] while meteorological
phenomena like wind, rain, hail, snow, lightning, tornadoes, and hurricanes are all a result of energy
transformations in our atmosphere brought about by solar energy.

Sunlight is the main input to Earth's energy budget which accounts for its temperature and climate
stability, after accounting for interaction with the atmosphere.[57] Sunlight may be stored as
gravitational potential energy after it strikes the Earth, as (for example when) water evaporates from
oceans and is deposited upon mountains (where, after being released at a hydroelectric dam, it can
be used to drive turbines or generators to produce electricity).[58] Sunlight also drives most weather
phenomena, save a few exceptions, like those generated by volcanic events for example.[59] An
example of a solar-mediated weather event is a hurricane, which occurs when large unstable areas
of warm ocean, heated over months, suddenly give up some of their thermal energy to power a few
days of violent air movement.[60]

In a slower process, radioactive decay of atoms in the core of the Earth releases heat, which
supplies more than half of the planet's internal heat budget.[61] In the present day, this radiogenic
heat production was primarily driven by the decay of Uranium-235, Potassium-40, and Thorium-232
some time in the past.[62] This thermal energy drives plate tectonics and may lift mountains, via
orogenesis. This slow lifting represents a kind of gravitational potential energy storage of the
thermal energy, which may later be transformed into active kinetic energy during landslides, after a
triggering event. Earthquakes also release stored elastic potential energy in rocks, a store that has
been produced ultimately from the same radioactive heat sources. Thus, according to present
understanding, familiar events such as landslides and earthquakes release energy that has been
stored as potential energy in the Earth's gravitational field or elastic strain (mechanical potential
energy) in rocks.[63] Prior to this, they represent release of energy that has been stored in heavy
atoms since the collapse of long-destroyed supernova stars (which created these atoms).[64]

Early in a planet's history, the accretion process provides impact energy that can partially or
completely melt the body. This allows a planet to become differentiated by chemical element.
Chemical phase changes of minerals during formation provide additional internal heating. Over time
the internal heat is brought to the surface then radiated away into space, cooling the body. Accreted
radiogenic heat sources settle toward the core, providing thermal energy to the planet on a geologic
time scale.[65] Ongoing sedimentation provides a persistent internal energy source for gas giant
planets like Jupiter and Saturn.[66]

Cosmology

In cosmology and astronomy the phenomena of stars, nova, supernova, quasars, and gamma-ray
bursts are the universe's highest-output energy transformations of matter. All stellar phenomena
(including solar activity) are driven by various kinds of energy transformations. Energy in such
transformations is either from gravitational collapse of matter (usually molecular hydrogen) into
various classes of astronomical objects (stars, black holes, etc.), or from nuclear fusion (of lighter
elements, primarily hydrogen).[67]

The nuclear fusion of hydrogen in the Sun also releases another store of potential energy which was
created at the time of the Big Bang. At that time, according to theory, space expanded and the
universe cooled too rapidly for hydrogen to completely fuse into heavier elements. This meant that
hydrogen represents a store of potential energy that can be released by fusion. Such a fusion
process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds
when they produce stars, and some of the fusion energy is then transformed into sunlight.[68]

The accretion of matter onto a compact object is a very efficient means of generating energy from
gravitational potential. This behavior is responsible for some of the universe's brightest persistent
energy sources.[69] The Penrose process is a theoretical method by which energy could be extracted
from a rotating black hole.[70] Hawking radiation is the emission of black-body radiation from a
black hole, which results in a steady loss of mass and rotational energy. As the object evaporates,
the temperature of this radiation is predicted to increase, speeding up the process.[71]
Quantum mechanics

In quantum mechanics, energy is defined in terms of the energy operator (Hamiltonian) as a time
derivative of the wave function. The Schrödinger equation equates the energy operator to the full
energy of a particle or a system. Its results can be considered as a definition of measurement of
energy in quantum mechanics. The Schrödinger equation describes the space- and time-
dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution
of this equation for a bound system is discrete (a set of permitted states, each characterized by an
energy level) which results in the concept of quanta.[72]

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 relation:
, where is the Planck constant and the frequency. In the case of an electromagnetic
wave these energy states are called quanta of light or photons. For matter waves, the de Broglie
relation yields , where is the momentum.[73]

Relativity

When calculating kinetic energy (work to accelerate a massive body from zero speed to some finite
speed) relativistically – using Lorentz transformations instead of Newtonian mechanics – Einstein
discovered an unexpected by-product of these calculations to be an energy term which does not
vanish at zero speed. He called it rest energy: energy which every massive body must possess even
when being at rest. The amount of energy is directly proportional to the mass of the body:[74]

where

m0 is the rest mass of the body,

c is the speed of light in vacuum,

is the rest energy.

For example, consider electron–positron annihilation, in which the rest energy of these two
individual particles (equivalent to their rest mass) is converted to the radiant energy of the photons
produced in the process. In this system the matter and antimatter (electrons and positrons) are
destroyed and changed to non-matter (the photons). However, the total mass and total energy do
not change during this interaction. The photons each have no rest mass but nonetheless have
radiant energy which exhibits the same inertia as did the two original particles. This is a reversible
process – the inverse process is called pair creation – in which the rest mass of the particles is
created from a sufficiently energetic photon near a nucleus.[75]

In general relativity, the stress–energy tensor serves as the source term for the gravitational field, in
rough analogy to the way mass serves as the source term in the non-relativistic Newtonian
approximation.[76]

Energy and mass are manifestations of one and the same underlying physical property of a system.
This property is responsible for the inertia and strength of gravitational interaction of the system
("mass manifestations"),[77] and is also responsible for the potential ability of the system to perform
work or heating ("energy manifestations"), subject to the limitations of other physical laws.

In classical physics, energy is a scalar quantity, the canonical conjugate to time. In special relativity
energy is also a scalar (although not a Lorentz scalar but a time component of the energy–
momentum 4-vector).[76] In other words, energy is invariant with respect to rotations of space, but
not invariant with respect to rotations of spacetime (= boosts).

Transformation

Some forms of transfer of energy ("energy in transit") from one object or system to another

Type of transfer process Description

Heat equal amount of thermal energy in transit spontaneously towards a lower-temperature object

Work equal amount of energy in transit due to a displacement in the direction of an applied force

Transfer of material equal amount of energy carried by matter that is moving from one system to another

A turbo generator transforms the energy of

pressurized steam into electrical energy.

Energy may be transformed between different forms at various efficiencies. Devices that usefully
transform between these forms are called transducers. Examples of transducers include a battery
(from chemical energy to electric energy), a dam (from gravitational potential energy to the kinetic
energy of water spinning the blades of a turbine, and ultimately to electric energy through an electric
generator), and a heat engine (from heat to work).[78][79]

Examples of energy transformation include generating electric energy from heat energy via a steam
turbine,[79] or lifting an object against gravity using electrical energy driving a crane motor. Lifting
against gravity performs mechanical work on the object and stores gravitational potential energy in
the object. If the object falls to the ground, gravity does mechanical work on the object which
transforms the potential energy in the gravitational field to the kinetic energy released as heat on
impact with the ground.[80] The Sun transforms nuclear potential energy to other forms of energy; its
total mass does not decrease due to that itself (since it still contains the same total energy even in
different forms) but its mass does decrease when the energy escapes out to its surroundings,
largely as radiant energy.[81]

There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a
heat engine, as described by Carnot's theorem and the second law of thermodynamics.[82] However,
some energy transformations can be quite efficient.[83] The direction of transformations in energy
(what kind of energy is transformed to what other kind) is often determined by entropy (equal
energy spread among all available degrees of freedom) considerations. In practice all energy
transformations are permitted on a sufficiently small scale, but certain larger transformations are
highly improbable because it is statistically unlikely that energy or matter will randomly move into
more concentrated forms or smaller spaces.[84]

Energy transformations in the universe over time are characterized by various kinds of potential
energy, that has been available since the Big Bang, being "released" (transformed to more active
types of energy such as kinetic or radiant energy) when a triggering mechanism is available.[85]
Familiar examples of such processes include nucleosynthesis, a process ultimately using the
gravitational potential energy released from the gravitational collapse of supernovae to "store"
energy in the creation of heavy isotopes (such as uranium and thorium), and nuclear decay, a
process in which energy is released that was originally stored in these heavy elements, before they
were incorporated into the Solar System and the Earth.[86] This energy is triggered and released in
nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical
explosion, chemical potential energy is transformed to kinetic and thermal energy in a very short
time.[87]

Yet another example of energy transformation is that of a simple gravity pendulum. At its highest
points the kinetic energy is zero and the gravitational potential energy is at its maximum. At its
lowest point the kinetic energy is at its maximum and is equal to the decrease in potential energy. If
one (unrealistically) assumes that there is no friction or other losses, the conversion of energy
between these processes would be perfect, and the pendulum would continue swinging forever.
Energy is transferred from potential energy ( ) to kinetic energy ( ) and then back to potential
energy constantly. This is referred to as conservation of energy.

In this isolated system, energy cannot be created or destroyed; therefore, the initial energy and the
final energy will be equal to each other. This can be demonstrated by the following:

(4)

The equation can then be simplified further since (mass times acceleration due to
gravity times the height) and (half mass times velocity squared). Then the total
amount of energy can be found by adding .[88]

Conservation of energy and mass in transformation

Within a gravitational field, both mass and energy give rise to a measureable weight when trapped in
a system with zero momentum. The formula E = mc2, derived by Albert Einstein (1905) quantifies
this mass–energy equivalence between relativistic mass and 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 Mass–energy
equivalence#History for further information).[89]

Part of the rest energy (equivalent to rest mass) of matter may be converted to other forms of
energy (still exhibiting mass), but neither energy nor mass can be destroyed; rather, both remain
constant during any process. However, since is extremely large relative to ordinary human scales,
the conversion of an everyday amount of rest mass from rest energy to other forms of energy (such
as kinetic energy, thermal energy, or the radiant energy carried by light and other radiation) can
liberate tremendous amounts of energy, as can be seen in nuclear reactors and nuclear weapons.[90]
For example, 1 kg of rest mass equals 9 × 1016 joules, equivalent to 21.5 megatonnes of TNT.[91]

Conversely, the mass equivalent of an everyday amount energy is minuscule, which is why a loss of
energy from most systems is difficult to measure on a weighing scale, unless the energy loss is very
large. Examples of large-scale transformations between the rest energy of matter and other forms
of energy are found in nuclear physics and particle physics. The complete conversion of matter,
such as atoms, to non-matter, such as photons, occurs during interaction with antimatter.[92]
Reversible and non-reversible transformations

Thermodynamics divides energy transformation into two kinds: reversible processes and
irreversible processes. An irreversible process is one in which 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.[93]

At the atomic scale, thermal energy is present in the form of motion and vibrations of individual
atoms and molecules. When heat is generated, radiation excites lower energy states of these atoms
and their surrounding fields. This heating process acts as a reservoir for part of the applied energy,
from which it cannot be converted with 100% efficiency into other forms of energy.[94] According to
the second law of thermodynamics, this heat can only be completely recovered as usable energy at
the price of an increase in some other kind of heat-like disorder in quantum states.

As the universe evolves with time, more and more of its energy becomes trapped in irreversible
states (i.e., as heat or as other kinds of increases in disorder). This has led to the hypothesis of the
inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe
does not change, but the fraction of energy which is available to do work through a heat engine, or
be transformed to other usable forms of energy (through the use of generators attached to heat
engines), continues to decrease.[95]

Conservation of energy

The fact that energy can be neither created nor destroyed is called the law of conservation of
energy. In the form of the first law of thermodynamics, this states that a closed system's energy is
constant unless energy is transferred in or out as work or heat, and that no energy is lost in transfer.
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. 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.[96]

While heat can always be fully converted into work in a reversible isothermal expansion of an ideal
gas, for cyclic processes of practical interest in heat engines the second law of thermodynamics
states that the system doing work always loses some energy as waste heat. This creates a limit to
the amount of heat energy that can do work in a cyclic process, a limit called the available energy.
Mechanical and other forms of energy can be transformed in the other direction into thermal energy
without such limitations.[97] The total energy of a system can be calculated by adding up all forms of
energy in the system.

Richard Feynman said during a 1961 lecture:[98]

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

— The Feynman Lectures on Physics

Most kinds of energy (with gravitational energy being a notable exception)[99] are 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.[97][98]

This law is a fundamental principle of physics. As shown rigorously by Noether's theorem, the
conservation of energy is a mathematical consequence of translational symmetry of time,[100] 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 (though this is
practically significant only for very short time intervals). 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.

Each of the basic forces of nature is associated with a different type of potential energy, and all
types of potential energy (like all other types of energy) appear as system mass, whenever present.
For example, a compressed spring will be slightly more massive than before it was compressed.
Likewise, whenever energy is transferred between systems by any mechanism, an associated mass
is transferred with it.[101]

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

which is similar in form to the Heisenberg Uncertainty Principle,[102] but not really mathematically
equivalent thereto, since E and t are not dynamically conjugate variables, neither in classical nor in
quantum mechanics.[103]

In particle physics, this inequality permits a qualitative understanding of virtual particles, which
carry momentum.[103] The exchange of virtual particles with real particles is responsible for the
creation of all known fundamental forces (more accurately known as fundamental
interactions).[104]: 101 Virtual photons are also responsible for the electrostatic interaction between
electric charges (which results in Coulomb's law),[104]: 336 for spontaneous radiative decay of excited
atomic and nuclear states, for the Casimir force,[105] for the Van der Waals force,[106] and some
other observable phenomena.[107]

Energy transfer

Closed systems

Energy transfer can be considered for the special case of systems which are closed to transfers of
matter. The portion of the energy which is transferred by conservative forces over a distance is
measured as the work the source system does on the receiving system. The portion of the energy
which does not do work during the transfer is called heat.[note 3] Energy can be transferred between
systems in a variety of ways. Examples include the transmission of electromagnetic energy via
photons, physical collisions which transfer kinetic energy,[note 4] tidal interactions,[108] and the
conductive transfer of thermal energy.[109]

Energy is strictly conserved and is also locally conserved wherever it can be defined. In
thermodynamics, for closed systems, the process of energy transfer is described by the first
law:[note 5][109]

(1)

where is the amount of energy transferred, represents the work done on or by the system, and
represents the heat flow into or out of the system. As a simplification, the heat term, , can
sometimes be ignored, especially for fast processes involving gases, which are poor conductors of
heat, or when the thermal efficiency of the transfer is high. For such adiabatic processes,

(2)

This simplified equation is the one used to define the joule, for example.

Open systems

Beyond the constraints of closed systems, open systems can gain or lose energy in association with
matter transfer (this process is illustrated by injection of an air-fuel mixture into a car engine, a
system which gains in energy thereby, without addition of either work or heat). Denoting this energy
by , one may write:[110]

(3)

Thermodynamics

Internal energy

Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to
create the system. It is related to the potential energy, e.g., molecular structure, crystal structure,
and other geometric aspects, as well as the motion of the particles, in form of kinetic energy.
Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value,
which is impossible to determine with thermodynamics alone.[111]

First law of thermodynamics

The first law of thermodynamics asserts that the total energy of a system and its surroundings (but
not necessarily thermodynamic free energy) is always conserved[112] and that heat flow is a form of
energy transfer. For homogeneous systems, with a well-defined temperature and pressure, a
commonly used corollary of the first law is that, for a system subject only to pressure forces and
heat transfer (e.g., a cylinder-full of gas) without chemical changes, the differential change in the
internal energy of the system (with a gain in energy signified by a positive quantity) is given as:[113]

where the first term on the right is the heat transferred into the system, expressed in terms of
temperature T and entropy S (in which entropy increases and its change dS is positive when heat is
added to the system), 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, dV, is negative when work is done
on the system).

This equation is highly specific, ignoring all chemical, electrical, nuclear, and gravitational forces,
effects such as advection of any form of energy other than heat and PV-work. The general
formulation of the first law (i.e., conservation of energy) is valid even in situations in which the
system is not homogeneous. For these cases the change in internal energy of a closed system is
expressed in a general form by:[109]

where is the heat supplied to the system and is the work applied to the system.

Equipartition of energy

The energy of a mechanical harmonic oscillator (a mass on a spring) is alternately kinetic and
potential energy. At two points in the oscillation cycle it is entirely kinetic, and at two points it is
entirely potential.[88] Over a whole cycle, or over many cycles, average energy is equally split
between kinetic and potential. This is an example of the equipartition principle: the total energy of a
system with many degrees of freedom is equally split among all available degrees of freedom, on
average.[114]

This principle is vitally important to understanding the behavior of a quantity closely related to
energy, called entropy. Entropy is a measure of evenness of a distribution of energy between parts
of a system. When an isolated system is given more degrees of freedom (i.e., given new available
energy states that are the same as existing states), then total energy spreads over all available
degrees equally without distinction between "new" and "old" degrees. This mathematical result is
part of the second law of thermodynamics. The second law of thermodynamics is simple only for
systems which are near or in a physical equilibrium state. For non-equilibrium systems, the laws
governing the systems' behavior are still debatable. One of the guiding principles for these systems
is the principle of maximum entropy production.[115][116] It states that nonequilibrium systems
behave in such a way as to maximize their entropy production.[117]

See also

Combustion Energy democracy

Energy portal
Efficient energy use Energy crisis Physics portal
 Energy recovery Power station Renewable energy
portal
Energy recycling Sustainable energy

Index of energy articles Transfer energy

Index of wave articles Waste-to-energy

List of low-energy building Waste-to-energy plant

techniques
Zero-energy building
Orders of magnitude (energy)

Notes

1. 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 (in case of a sprinter) and the force (in
case of a weightlifter).

2. 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.

3. Although heat is "wasted" energy for a specific energy transfer (see: waste heat), it can often
be harnessed to do useful work in subsequent interactions. However, the maximum energy that
can be "recycled" from such recovery processes is limited by the second law of
thermodynamics.

4. The mechanism for most macroscopic physical collisions is actually electromagnetic, but it is
very common to simplify the interaction by ignoring the mechanism of collision and just
calculate the beginning and end result.

5. There are several sign conventions for this equation. Here, the signs in this equation follow the
IUPAC convention.

References

1. Soman, K. (2010). International System Of Units: A Handbook On S.I. Unit For Scientists And
Engineers (https://books.google.com/books?id=d-euEMU2cX8C&pg=PA15) . PHI Learning
Pvt. Ltd. p. 15. ISBN 9788120336537.
 2. Dougherty, Heather N.; Schissler, Andrew P., eds. (2020). SME Mining Reference Handbook (htt
ps://books.google.com/books?id=sVTHDwAAQBAJ&pg=PA2) (2nd ed.). Society for Mining,
Metallurgy & Exploration. pp. 2–3. ISBN 9780873354356.

3. Mechtly, E. A. (1964). The International System of Units: Physical Constants and Conversion
Factors (https://books.google.com/books?id=xFUCAAAAIAAJ&pg=PA3) . NASA SP.
Vol. 7012. Scientific and Technical Information Division, National Aeronautics and Space
Administration. p. 3.

4. Chandra, Sanjeev (2016). Energy, Entropy and Engines: An Introduction to Thermodynamics (htt
ps://books.google.com/books?id=AKfQCwAAQBAJ&pg=PA34) . John Wiley & Sons. p. 34.
ISBN 9781119013181.

5. Fuller, Ą. J. Baden (2014). Hammon, P. (ed.). Engineering Field Theory (https://books.google.co

m/books?id=IJKjBQAAQBAJ&pg=PA7) . The Commonwealth and international library. Applied
electricity and electronics division. Elsevier. ISBN 9781483187006.

6. "Earth's energy flow" (https://energyeducation.ca/encyclopedia/Earth%27s_energy_flow) .

Energy Education. Retrieved 2024-08-28.

7. Bobrowsky, Matt (2021). "SCIENCE 101: Q: What Is Energy?" (https://www.jstor.org/stable/271

33353) . Science and Children. 59 (1): 61–65. doi:10.1080/19434812.2021.12291716 (http
s://doi.org/10.1080%2F19434812.2021.12291716) . ISSN 0036-8148 (https://search.worldca
t.org/issn/0036-8148) . JSTOR 27133353 (https://www.jstor.org/stable/27133353) .
S2CID 266084433 (https://api.semanticscholar.org/CorpusID:266084433) . Retrieved
February 5, 2024.

8. "Nuclear Energy | Definition, Formula & Examples | nuclear-power.com" (https://www.nuclear-po

wer.com/nuclear-power/nuclear-energy/) . Nuclear Power. Archived (https://web.archive.org/
web/20220706153815/https://www.nuclear-power.com/nuclear-power/nuclear-energy/)
from the original on 2022-07-06. Retrieved 2022-07-06.

9. Rosen, Marc A.; Dincer, Ibrahim (2007). Exergy: Energy, Environment and Sustainable
Development (https://books.google.com/books?id=ruR7U3IjrR0C&pg=PA3) . Elsevier. p. 3.
ISBN 9780080531359.

10. Goel, Anup (2021). Systems in Mechanical Engineering: Fundamentals and Applications (http
s://books.google.com/books?id=XjcfEAAAQBAJ&pg=SA1-PA20) . Technical Publications.
ISBN 9789333221832.
11. Harper, Douglas. "Energy" (http://www.etymonline.com/index.php?term=energy) . Online
Etymology Dictionary. Archived (https://web.archive.org/web/20071011122441/http://etymonl
ine.com/index.php?term=energy) from the original on October 11, 2007. Retrieved May 1,
2007.

12. Chen, Chung-Hwan (September 1956). "Different meanings of the term Energeia in the
philosophy of Aristotle". Philosophy and Phenomenological Research. 17 (1): 56–65.
doi:10.2307/2104687 (https://doi.org/10.2307%2F2104687) . JSTOR 2104687 (https://www.j
stor.org/stable/2104687) .

13. McDonough, Jeffrey K. (2021). "Leibniz's Philosophy of Physics" (https://plato.stanford.edu/ar

chives/fall2021/entries/leibniz-physics/) . In Zalta, Edward N. (ed.). The Stanford
Encyclopedia of Philosophy (Fall 2021 ed.). Metaphysics Research Lab, Stanford University.
Retrieved 2025-07-25.

14. "December 1706: Birth of Émilie du Châtelet" (https://www.aps.org/apsnews/2008/12/emilie-d

u-chatelet) . APS News. This month in physics history. American Physical Society. December
1, 2008. Retrieved 2025-07-26.

15. Smith, Crosbie (1998). The Science of Energy – a Cultural History of Energy Physics in
Victorian Britain. The University of Chicago Press. ISBN 978-0-226-76420-7.

16. "Gustave-Gaspard Coriolis" (https://www.oxfordreference.com/display/10.1093/oi/authority.20

110803095639380) . Oxford Reference. Retrieved 2025-07-26.

17. Young, John (April 13, 2015). "Heat, work and subtle fluids: a commentary on Joule (1850) 'On
the mechanical equivalent of heat' " (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC436009
3) . Philosophical Transactions A. 373 (2039). 20140348. Bibcode:2015RSPTA.37340348Y (ht
tps://ui.adsabs.harvard.edu/abs/2015RSPTA.37340348Y) . doi:10.1098/rsta.2014.0348 (http
s://doi.org/10.1098%2Frsta.2014.0348) . PMC 4360093 (https://www.ncbi.nlm.nih.gov/pmc/
articles/PMC4360093) . PMID 25750152 (https://pubmed.ncbi.nlm.nih.gov/25750152) .

18. Sarton, G.; et al. (September 1929). "The Discovery of the Law of Conservation of Energy". Isis.
13 (1): 18–44. doi:10.1086/346430 (https://doi.org/10.1086%2F346430) . JSTOR 224595 (htt
ps://www.jstor.org/stable/224595) .

19. Williams, Richard (June 1, 2015). "June 1849: James Prescott Joule and the Mechanical
Equivalent of Heat" (https://www.aps.org/apsnews/2015/06/joule-mechanical-equivalent-hea
t) . APS News. This month in physics history. American Physical Society. Retrieved
2025-07-26.
20. McEvoy, Paul (2002). Classical Theory (https://books.google.com/books?id=dj0wFIxn-PoC&pg
=PA151) . Theory of interacting systems. Vol. 2. Microanalytix. p. 151. ISBN 9781930832022.

21. Fegley, Bruce; Osborne, Rose (2013). Practical Chemical Thermodynamics for Geoscientists (ht
tps://books.google.com/books?id=Z8VNZNLNsTcC&pg=PA1) . Academic Press. p. 1.
ISBN 9780122511004.

22. Grossinger, Richard (2012). Embryos, Galaxies, and Sentient Beings: How the Universe Makes
Life (https://books.google.com/books?id=NThvbCJiqFUC&pg=PA22) . North Atlantic Books.
p. 22. ISBN 9781583946985.

23. "Josef Stefan" (https://catholicscientists.org/scientists-of-the-past/josef-stefan/) . Catholic

scientists of the past. Society of Catholic Scientists. Retrieved 2025-07-26.

24. Lofts, G.; O'Keeffe, D.; et al. (2004). "11 – Mechanical Interactions". Jacaranda Physics 1
(2 ed.). Milton, Queensland, Australia: John Wiley & Sons Australia Limited. p. 286. ISBN 978-0-
7016-3777-4.

25. Foot, Robert (2002). Shadowlands: Quest for Mirror Matter in the Universe (https://books.googl
e.com/books?id=3evE2K-ylVIC&pg=PA114) . Universal-Publishers. p. 114.
ISBN 9781581126457.

26. Egdall, Ira Mark (2014). Einstein Relatively Simple: Our Universe Revealed In Everyday
Language (https://books.google.com/books?id=KUG7CgAAQBAJ&pg=PA99) . World
Scientific. p. 99. ISBN 9789814525619.

27. Kolek, Erik (2024). On the general, the special and the general-special relativity theory (https://b
ooks.google.com/books?id=85wWEQAAQBAJ&pg=PA127) . Chronicles of Business
Informatics Physics (CBIP). Vol. 1 (2nd ed.). BoD – Books on Demand. pp. 126–128.
ISBN 9783759712189.

28. Ruedenberg, Klaus; Schwarz, W. H. Eugen (February 13, 2013). "Three Millennia of Atoms and
Molecules". Pioneers of Quantum Chemistry. ACS Symposium Series. Vol. 1122. American
Chemical Society. pp. 1–45. doi:10.1021/bk-2013-1122.ch001 (https://doi.org/10.1021%2Fbk-
2013-1122.ch001) . ISBN 9780841227163.

29. Phillips, Lee (2024). Einstein's Tutor: The Story of Emmy Noether and the Invention of Modern
Physics (https://books.google.com/books?id=sbDrEAAAQBAJ&pg=PT280) . PublicAffairs.
ISBN 9781541702974.

30. Lipkin, Harry J. (2014). Quantum Mechanics: New Approaches to Selected Topics (https://book
s.google.com/books?id=pUpMBAAAQBAJ&pg=PA205) . Dover books on physics. Courier
Corporation. ISBN 9780486151854.
31. Pearle, P. (August 2000). "Wavefunction Collapse and Conservation Laws". Foundations of
Physics. 30 (8): 1145–1160. arXiv:quant-ph/0004067 (https://arxiv.org/abs/quant-ph/000406
7) . Bibcode:2000FoPh...30.1145P (https://ui.adsabs.harvard.edu/abs/2000FoPh...30.1145
P) . doi:10.1023/A:1003677103804 (https://doi.org/10.1023%2FA%3A1003677103804) .

32. Carroll, S. M.; Lodman, J. (2021). "Energy Non-conservation in Quantum Mechanics".

Foundations of Physics. 51 (83) 83. arXiv:2101.11052 (https://arxiv.org/abs/2101.11052) .
Bibcode:2021FoPh...51...83C (https://ui.adsabs.harvard.edu/abs/2021FoPh...51...83C) .
doi:10.1007/s10701-021-00490-5 (https://doi.org/10.1007%2Fs10701-021-00490-5) .

33. Patience, Gregory S. (2013). Experimental Methods and Instrumentation for Chemical
Engineers (https://books.google.com/books?id=nY-MQXBmZBAC&pg=PA9) . Newnes. p. 9.
ISBN 9780444538055.

34. Orecchini, Fabio; Naso, Vincenzo (2011). Energy Systems in the Era of Energy Vectors: A Key to
Define, Analyze and Design Energy Systems Beyond Fossil Fuels (https://books.google.com/bo
oks?id=vGiBKQ40c7QC&pg=PA7) . Springer Science & Business Media. pp. 6–8.
ISBN 9780857292445.

35. Greiner, Walter (2006). Classical Mechanics: Point Particles and Relativity (https://books.googl
e.com/books?id=CynrBwAAQBAJ&pg=PA109) . Classical Theoretical Physics. Springer
Science & Business Media. p. 109. ISBN 9780387218519.

36. Obodovskiy, Ilya (2019). Radiation: Fundamentals, Applications, Risks, and Safety (https://book
s.google.com/books?id=xmOMDwAAQBAJ&pg=PA74) . Elsevier. ISBN 9780444639868.

37. "Chapter 16.3 – The Hamiltonian" (https://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/

chapter16/section03.html) . MIT OpenCourseWare website 18.013A. Retrieved 2025-07-28.

38. Marchildon, Louis (2013). Quantum Mechanics: From Basic Principles to Numerical Methods
and Applications (https://books.google.com/books?id=XibsCAAAQBAJ&pg=PA38) .
Advanced Texts in Physics. Springer Science & Business Media. p. 38. ISBN 9783662047507.

39. Widnall, S. (2009). "Lecture L20 - Energy Methods: Lagrange's Equations" (https://ocw.mit.edu/
courses/16-07-dynamics-fall-2009/b39e882f1524a0f6a98553ee33ea6f35_MIT16_07F09_Lec2
0.pdf) (PDF). MIT OpenCourseWare website 16.07 Dynamics. 3.0. Retrieved 2025-07-28.

40. Berman, Jules J. (2025). Proofs and Logical Arguments Supporting the Foundational Laws of
Physics: A Handy Guide for Students and Scientists (https://books.google.com/books?id=LbM
1EQAAQBAJ&pg=PA144) . CRC Press. pp. 144–146. ISBN 9781040300732.
41. See chemical change in: Lewis, Robert A. (2016). Larrañaga, Michael D.; Lewis, Sr., Richard J.
(eds.). Hawley's Condensed Chemical Dictionary (https://books.google.com/books?id=KPrfCw
AAQBAJ&pg=PA295) (16 ed.). John Wiley & Sons. ISBN 9781119267843.

42. Kondepudi, Dilip; Prigogine, Ilya (2014). Modern Thermodynamics: From Heat Engines to
Dissipative Structures (https://books.google.com/books?id=SPU8BQAAQBAJ&pg=PA249)
(2nd ed.). John Wiley & Sons. pp. 248–250. ISBN 9781118698709.

43. Hayamizu, Kohsuke (2017). "Amino Acids and Energy Metabolism: An Overview" (https://book
s.google.com/books?id=5epGDgAAQBAJ&pg=PA339) . In Bagchi, Debasis (ed.). Sustained
Energy for Enhanced Human Functions and Activity. Academic Press. p. 339.
ISBN 9780128093320.

44. Dimmitt, Mark A. (2016). "Plant ecology of the Sonoran desert region" (https://books.google.co
m/books?id=Vef5DwAAQBAJ&pg=PA154) . In Malloy, Richard; et al. (eds.). Design with the
Desert: Conservation and Sustainable Development. CRC Press. pp. 154–155.
ISBN 9781000218848.

45. Sinn, Hans-Werner (2012). The Green Paradox: A Supply-Side Approach to Global Warming (htt
ps://books.google.com/books?id=NnwCVOso9vgC&pg=PA85) . MIT Press.
ISBN 9780262300582.

46. McNab, Brian K. (1997). "On the Utility of Uniformity in the Definition of Basal Rate of
Metabolism". Physiological Zoology. 70 (6): 718–720. doi:10.1086/515881 (https://doi.org/10.
1086%2F515881) . PMID 9361146 (https://pubmed.ncbi.nlm.nih.gov/9361146) .
S2CID 34996894 (https://api.semanticscholar.org/CorpusID:34996894) .

47. Byrne, Nuala M.; et al. (September 2005). "Metabolic equivalent: one size does not fit all".
Applied Physiology. 99 (3): 1112–1119. doi:10.1152/japplphysiol.00023.2004 (https://doi.org/
10.1152%2Fjapplphysiol.00023.2004) . PMID 15831804 (https://pubmed.ncbi.nlm.nih.gov/15
831804) .

48. "Human Energy" (https://web.archive.org/web/20100604191319/http://www.uic.edu/aa/colleg

e/gallery400/notions/human%20energy.htm) . Uic.edu. Archived from the original (http://ww
w.uic.edu/aa/college/gallery400/notions/human%20energy.htm) on 2010-06-04. Retrieved
2010-12-12.

49. Bicycle calculator – speed, weight, wattage etc. "Bike Calculator" (http://bikecalculator.co
m/) . Archived (https://web.archive.org/web/20090513091201/http://bikecalculator.com/)
from the original on 2009-05-13. Retrieved 2009-05-29..
50. "How many calories should I eat in a day?" (https://www.medicalnewstoday.com/articles/2455
88) . Medical News Today. 12 February 2018. Retrieved 2025-07-31.

51. Ito, Akihito; Oikawa, Takehisa (2004). "Global Mapping of Terrestrial Primary Productivity and
Light-Use Efficiency with a Process-Based Model" (http://www.terrapub.co.jp/e-library/kawahat
a/pdf/343.pdf) (PDF). In Shiyomi, Masae; et al. (eds.). Global Environmental Change in the
Ocean and on Land. pp. 343–58. Archived (https://web.archive.org/web/20061002083948/htt
p://www.terrapub.co.jp/e-library/kawahata/pdf/343.pdf) (PDF) from the original on 2006-10-
02. Retrieved 2006-10-02.

52. Liesa, Marc; et al. (2020). Arias, Irwin M.; et al. (eds.). The Liver: Biology and Pathobiology (http
s://books.google.com/books?id=80bLEAAAQBAJ&pg=PA87) (6th ed.). John Wiley & Sons.
pp. 86–87. ISBN 9781119436829.

53. Papachristodoulou, Despo; et al. (2014). Biochemistry and Molecular Biology (https://books.go
ogle.com/books?id=oPtzBAAAQBAJ&pg=PA5) . OUP Oxford. ISBN 9780199609499.

54. Cohen, Barbara Janson; Hull, Kerry L. (2020). Memmler's Structure & Function of the Human
Body, Enhanced Edition (12th ed.). Jones & Bartlett Learning. p. 375. ISBN 9781284591606.

55. Lehninger, Albert L. (1960). "The Enzymic and Morphological Organiation of the Mitochondria".
Pediatrics. 26 (3): 466–475. doi:10.1542/peds.26.3.466 (https://doi.org/10.1542%2Fpeds.26.
3.466) .

56. "Earth's Energy Budget" (http://okfirst.ocs.ou.edu/train/meteorology/EnergyBudget.html) .

Okfirst.ocs.ou.edu. Archived (https://web.archive.org/web/20080827194704/http://okfirst.ocs.
ou.edu/train/meteorology/EnergyBudget.html) from the original on 2008-08-27. Retrieved
2010-12-12.

57. Jackson, Richard E. (2019). Earth Science for Civil and Environmental Engineers (https://book
s.google.com/books?id=VJiHDwAAQBAJ&pg=PA123) . Cambridge University Press. pp. 123–
125. ISBN 9781108615815.

58. Demirel, Yaşar (2012). Energy: Production, Conversion, Storage, Conservation, and Coupling (ht
tps://books.google.com/books?id=TsY8gJP7b58C&pg=PA305) . Green Energy and
Technology. Springer Science & Business Media. p. 305. ISBN 9781447123712.

59. Hagen, Marilia; Azevedo, Anibal (April 2023). "Influence of Volcanic Activity on Weather and
Climate Changes" (https://doi.org/10.4236%2Facs.2023.132009) . Atmospheric and Climate
Sciences. 13 (2): 138–158. Bibcode:2023AGUFM.G43A0485H (https://ui.adsabs.harvard.edu/a
bs/2023AGUFM.G43A0485H) . doi:10.4236/acs.2023.132009 (https://doi.org/10.4236%2Fac
s.2023.132009) .
60. Ahmadi, Pouria; Dincer, Ibrahim (2018). "Energy Optimization" (https://books.google.com/book
s?id=foxODwAAQBAJ&pg=RA1-PA1139) . In Dincer, Ibrahim (ed.). Comprehensive Energy
Systems. Vol. 1. Elsevier. pp. 1139–1140. ISBN 9780128149256.

61. Dye, S. T. (September 2012). "Geoneutrinos and the radioactive power of the Earth". Reviews of
Geophysics. 50 (3) 2012RG000400. arXiv:1111.6099 (https://arxiv.org/abs/1111.6099) .
Bibcode:2012RvGeo..50.3007D (https://ui.adsabs.harvard.edu/abs/2012RvGeo..50.3007D) .
doi:10.1029/2012RG000400 (https://doi.org/10.1029%2F2012RG000400) .

62. Nédélec, Anne (2025). Earth and Life: A History of Four Billion Years (https://books.google.co
m/books?id=ojZpEQAAQBAJ&pg=PA65) . Oxford University Press. pp. 64–66.
ISBN 9780198945437.

63. Kennett, Brian (2009). Seismic Wave Propagation in Stratified Media (https://books.google.co
m/books?id=Gn89socs0RcC&pg=PA59) . DOAB Directory of Open Access Books. ANU E
Press. p. 59. ISBN 9781921536731.

64. Manuel, Oliver K. (2007). Origin of Elements in the Solar System: Implications of Post-1957
Observations (https://books.google.com/books?id=h-zxBwAAQBAJ&pg=PA626) . Springer
Science & Business Media. pp. 589–634. doi:10.1007/0-306-46927-8_44 (https://doi.org/10.10
07%2F0-306-46927-8_44) . ISBN 9780306469275.

65. Condie, Kent C. (2005). Earth as an Evolving Planetary System (https://books.google.com/boo

ks?id=I_t-hUWi5I8C&pg=PA394) . Elsevier. pp. 393–394. ISBN 9780080494586.

66. Mankovich, C.; Fortney, J. J. (December 2019). "Evidence for a Dichotomy in the Interior
Structures of Jupiter and Saturn from Helium Phase Separation" (https://doi.org/10.3847%2F1
538-4357%2Fab6210) . The Astrophysical Journal. 889 (1): 51. arXiv:1912.01009 (https://arxi
v.org/abs/1912.01009) . Bibcode:2019AGUFM.P24B..02M (https://ui.adsabs.harvard.edu/ab
s/2019AGUFM.P24B..02M) . doi:10.3847/1538-4357/ab6210 (https://doi.org/10.3847%2F15
38-4357%2Fab6210) .

67. Hogan, Craig J. (December 6, 2012). "Energy flow in the universe" (https://books.google.com/b
ooks?id=HC7yCAAAQBAJ&pg=PA290) . In Crittenden, Robert G.; Turok, Neil G. (eds.).
Structure Formation in the Universe. NASA Science Series. Kluwer Academic Publishers.
pp. 283–292. ISBN 9789401005401.

68. Rolfs, Claus E.; Rodney, William S. (1988). Cauldrons in the Cosmos: Nuclear Astrophysics (http
s://books.google.com/books?id=BHKLFPUS1RcC&pg=PA153) . Theoretical Astrophysics.
University of Chicago Press. p. 153. ISBN 9780226724577. ISSN 1050-0510 (https://search.wo
rldcat.org/issn/1050-0510) .
69. Longair, Malcolm S. (1996). Our Evolving Universe (https://books.google.com/books?id=qyA4A
AAAIAAJ&pg=PA86) . CUP Archive. pp. 86−88. ISBN 9780521550918.

70. Penrose, R.; Floyd, R. M. (February 1971). "Extraction of Rotational Energy from a Black Hole".
Nature Physical Science. 229 (6): 177–179. Bibcode:1971NPhS..229..177P (https://ui.adsabs.
harvard.edu/abs/1971NPhS..229..177P) . doi:10.1038/physci229177a0 (https://doi.org/10.10
38%2Fphysci229177a0) . ISSN 0300-8746 (https://search.worldcat.org/issn/0300-8746) .

71. Kreitler, Paul V. (2006). Trends in Black Hole Research (https://books.google.com/books?id=D

GwYf8cOCq4C&pg=PA34) . Nova Publishers. ISBN 9781594544750.

72. Parker, Michael A. (2018). Physics of Optoelectronics (https://books.google.com/books?id=Re

XLBQAAQBAJ&pg=PA299) . Optical Science and Engineering. CRC Press. p. 299.
ISBN 9781420027716.

73. Alenitsyn, Alexander G.; et al. (2020). Concise Handbook of Mathematics and Physics (https://
books.google.com/books?id=51gMEAAAQBAJ&pg=PA462) . CRC Press. p. 462.
ISBN 9781000161526.

74. Rahaman, Farook (2022). The Special Theory of Relativity: A Mathematical Approach (https://b
ooks.google.com/books?id=GL9pEAAAQBAJ&pg=PA143) (2 ed.). Springer Nature. p. 143.
ISBN 9789811904974.

75. Norton, Andrew (2021). Understanding the Universe: The Physics of the Cosmos from Quasars
to Quarks (https://books.google.com/books?id=N1kkEAAAQBAJ&pg=PA119) . CRC Press.
ISBN 9781000383911.

76. Misner, Charles W.; et al. (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 978-0-7167-
0344-0.

77. Cao, Tian Yu (1998). Conceptual Developments of 20th Century Field Theories (https://books.g
oogle.com/books?id=l4PtgYXpb_oC&pg=PA60) . Cambridge University Press. pp. 60–63.
ISBN 9780521634205.

78. Blokhina, Elena; et al. (2016). "Introduction to Vibration Energy Harvesting" (https://books.goog
le.com/books?id=Zc15DQAAQBAJ&pg=PA8) . Nonlinearity in Energy Harvesting Systems:
Micro- and Nanoscale Applications. Springer. pp. 7–8. ISBN 9783319203553.

79. Stonier, Tom (2012). Information and the Internal Structure of the Universe: An Exploration into
Information Physics (https://books.google.com/books?id=5FPlBwAAQBAJ&pg=PA96) .
Springer Science & Business Media. pp. 96–98. ISBN 9781447132653.
80. Smith, K. M.; Holroyd, P. (2013). Hiller, N. (ed.). Engineering Principles for Electrical Technicians
(https://books.google.com/books?id=-D4fAwAAQBAJ&pg=PA63) . The Commonwealth and
International Library: Electrical Engineering Division. Elsevier. pp. 63–64.
ISBN 9781483140308.

81. Pinsonneault, Marc; Ryden, Barbara (2023). Stellar Structure and Evolution (https://books.googl
e.com/books?id=Fv-xEAAAQBAJ&pg=PA30) . The Ohio State astrophysics series. Vol. 2.
Cambridge University Press. p. 30. ISBN 9781108835817.

82. Fleck, Robert (2023). Entropy and the Second Law of Thermodynamics: ... or Why Things Tend
to Go Wrong and Seem to Get Worse (https://books.google.com/books?id=aDfZEAAAQBAJ&p
g=PA64) . Springer Nature. ISBN 9783031349508.

83. Wald, Robert M. (1992). Space, Time, and Gravity: The Theory of the Big Bang and Black Holes
(https://books.google.com/books?id=sk5a8ieI91kC&pg=PA113) . University of Chicago
Press. ISBN 9780226870298.

84. Dincer, Ibrahim; Rosen, Marc (2002). Thermal Energy Storage: Systems and Applications (http
s://books.google.com/books?id=EsfcWE5lX40C&pg=PA20) . John Wiley & Sons.
ISBN 9780471495734.

85. Neubauer, Raymond L. (2011). Evolution and the Emergent Self: The Rise of Complexity and
Behavioral Versatility in Nature (https://books.google.com/books?id=5VH_hCSHMCkC&pg=PA
263) . Columbia University Press. pp. 263–266. ISBN 9780231521680.

86. Shahvisi, Arianne (2021). "Entropy Assymetry" (https://books.google.com/books?id=dvc8EAAA

QBAJ&pg=PT626) . In Knox, Eleanor; Wilson, Alastair (eds.). The Routledge Companion to
Philosophy of Physics. Routledge Philosophy Companions. Routledge. ISBN 9781317227137.

87. Baum, F. A.; et al. (December 1959). "Physics of an explosion" (https://apps.dtic.mil/sti/pdfs/A

D0400151.pdf) (PDF). Arlington, VA: Defense Technical Information Center. Retrieved
2025-08-02.

88. Vázquez, A. L.; Corona-Corona, G. (2018). "Period of the Simple Pendulum without Differential
Equations" (https://core.ac.uk/download/pdf/235050526.pdf) (PDF). American Scientific
Research Journal for Engineering, Technology, and Sciences. 40: 125–131. Retrieved
2025-08-02.
89. Rabinowitz, M. (2015). "General derivation of mass-energy relation without electrodynamics or
Einstein's postulates" (https://doi.org/10.4236%2Fjmp.2015.69129) . Journal of Modern
Physics. 6 (9). id. 58717. Bibcode:2015JMPh....6.1243R (https://ui.adsabs.harvard.edu/abs/20
15JMPh....6.1243R) . doi:10.4236/jmp.2015.69129 (https://doi.org/10.4236%2Fjmp.2015.691
29) .

90. Ristinen, Robert A.; et al. (2022). Energy and the Environment (https://books.google.com/book
s?id=o8V6EAAAQBAJ&pg=PA8) (4th ed.). John Wiley & Sons. pp. 8–9.
ISBN 9781119800255.

91. The energy from the rest mass is given by the mass-energy equivalence:
E = mc2 = 1 kg × (3 × 108 m/s)2 = 9 × 1016 J

TNT energy = 4.184 × 109 J/t†

Hence,
E = (9 × 1016 J)/(4.184 × 109 J/t) = 21.5 megatonnes
†: "NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically" (https://www.nis
t.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-ap
pendix-b8) . NIST. February 17, 2022. Retrieved 2025-08-04.

92. Schmidt, G. R.; et al. (September 2000). "Antimatter Requirements and Energy Costs for Near-
Term Propulsion Applications". Journal of Propulsion and Power. 16 (5): 923.
doi:10.2514/2.5661 (https://doi.org/10.2514%2F2.5661) . hdl:2060/19990110316 (https://hd
l.handle.net/2060%2F19990110316) .

93. Eu, Byung Chan; Al-ghoul, Mazen (2018). Chemical Thermodynamics: Reversible And
Irreversible Thermodynamics (https://books.google.com/books?id=uWdhDwAAQBAJ&pg=PT4
5) (Second ed.). World Scientific Publishing Company. ISBN 9789813226074.

94. Avison, John (2014). The World of Physics (https://books.google.com/books?id=DojwZzKAvN

8C&pg=PA414) (2nd ed.). Nelson Thornes. p. 414. ISBN 9780174387336.

95. Luscombe, James (2018). Thermodynamics (https://books.google.com/books?id=fFwPEAAA

QBAJ&pg=PA60) . CRC Press. pp. 60–62. ISBN 9780429017889.

96. Kittel, Charles; Knight, Walter D.; Ruderman, Malvin A. (1965). Berkeley Physics Course. Vol. 1.
McGraw-Hill.

97. The Laws of Thermodynamics (http://www.av8n.com/physics/thermo-laws.htm) . Archived (h

ttps://web.archive.org/web/20061215201900/http://www.av8n.com/physics/thermo-laws.ht
m) 2006-12-15 at the Wayback Machine including careful definitions of energy, free energy, et
cetera.
 98. Feynman, Richard (1964). "Ch. 4: Conservation of Energy" (https://feynmanlectures.caltech.ed
u/I_04.html#Ch4-S1-p2) . The Feynman Lectures on Physics; Volume 1. US: Addison Wesley.
ISBN 978-0-201-02115-8. Archived (https://web.archive.org/web/20220730093042/https://ww
w.feynmanlectures.caltech.edu/I_04.html#Ch4-S1-p2) from the original on 2022-07-30.
Retrieved 2022-05-04.

99. Byers, Nina (December 1996). "E. Noether's Discovery of the Deep Connection Between
Symmetries and Conservation Laws" (https://web.archive.org/web/20110514080739/http://w
ww.physics.ucla.edu/~cwp/articles/noether.asg/noether.html) . UCLA Physics & Astronomy.
Archived from the original (http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.ht
ml) on 2011-05-14. Retrieved 2010-12-12.

100. "Time Invariance" (http://ptolemy.eecs.berkeley.edu/eecs20/week9/timeinvariance.html) .

EECS20N. Ptolemy Project. Archived (https://web.archive.org/web/20110717210455/http://pt
olemy.eecs.berkeley.edu/eecs20/week9/timeinvariance.html) from the original on 2011-07-
17. Retrieved 2010-12-12.

101. Schmitz, Wouter (2019). Particles, Fields and Forces: A Conceptual Guide to Quantum Field
Theory and the Standard Model (https://books.google.com/books?id=wXeUDwAAQBAJ&pg=P
A245) . The Frontiers Collection. Springer. p. 245. ISBN 9783030128784.

102. Wigner, E. P. (1997). "On the Time–Energy Uncertainty Relation" (http://link.springer.com/10.10

07/978-3-662-09203-3_58) . In Wightman, Arthur S. (ed.). Part I: Particles and Fields. Part II:
Foundations of Quantum Mechanics. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 538–
548. doi:10.1007/978-3-662-09203-3_58 (https://doi.org/10.1007%2F978-3-662-09203-3_5
8) . ISBN 978-3-642-08179-8.

103. Desai, Bipin R. (2010). Quantum Mechanics with Basic Field Theory (https://books.google.co
m/books?id=cScBCJ6wLpYC&pg=PA65) . Cambridge University Press. p. 63–66.
ISBN 9780521877602.

104. Braibant, Sylvie; Giacomelli, Giorgio; Spurio, Maurizio (2011). Particles and Fundamental
Interactions: An Introduction to Particle Physics (https://books.google.com/books?id=0Pp-f0G
9_9sC&pg=PA101) . Undergraduate Lecture Notes in Physics. Springer Science & Business
Media. ISBN 9789400724631.

105. Madou, Marc J. (2011). Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and
Nanotechnology (https://books.google.com/books?id=sRvSBQAAQBAJ&pg=PA542) . CRC
Press. p. 542. ISBN 9781439895344.
106. Volokitin, A. I.; Persson, B. N. J. (2007). "Theory of Noncontact Friction". In Gnecco, Enrico;
Meyer, Ernst (eds.). Fundamentals of Friction and Wear on the Nanoscale (https://books.googl
e.com/books?id=v2Pe5thhNiwC&pg=PA394) . NanoScience and Technology. Springer
Science & Business Media. p. 394. ISBN 9783540368076.

107. Scully, M.; Sokolov, A.; Svidzinsky, A. (2018). "Virtual photons: From the Lamb shift to black
holes" (https://www.fonlo.org/2018/additionalreading/Scully-Marlan/OPN-VirtualPhotonsBH.p
df) (PDF). Optics and Photonics News. 29 (2): 34–40. doi:10.1364/OPN.29.2.000034 (http
s://doi.org/10.1364%2FOPN.29.2.000034) . Retrieved 2025-08-04.

108. Jaffe, Robert L.; Taylor, Washington (2018). The Physics of Energy (https://books.google.com/
books?id=drZDDwAAQBAJ&pg=PA611) . Cambridge University Press. p. 611. ISBN 978-1-107-
01665-1.

109. Borel, Lucien; Favrat, Daniel (2010). Thermodynamics and Energy Systems Analysis: From
Energy to Exergy (https://books.google.com/books?id=bnyCpHkqQ_0C&pg=PA16) .
Engineering Sciences. EPFL Press. ISBN 978-1-4398-3516-6.

110. Rathakrishnan, Ethirajan (2019). Applied Gas Dynamics (https://books.google.com/books?id=e

saKDwAAQBAJ&pg=PA12) (2nd ed.). John Wiley & Sons. pp. 12–13. ISBN 9781119500384.

111. I. Klotz, R. Rosenberg, Chemical Thermodynamics – Basic Concepts and Methods, 7th ed.,
Wiley (2008), p. 39

112. Kittel and Kroemer (1980). Thermal Physics. New York: W. H. Freeman. ISBN 978-0-7167-1088-
2.

113. Chen, Long-Qing (2022). Thermodynamic Equilibrium and Stability of Materials (https://books.
google.com/books?id=82RXEAAAQBAJ&pg=PA30) . Springer Nature. pp. 30–31.
ISBN 9789811386916.

114. Dill, Ken; Bromberg, Sarina (2010). Molecular Driving Forces: Statistical Thermodynamics in
Biology, Chemistry, Physics, and Nanoscience (https://books.google.com/books?id=1gYPBAA
AQBAJ&pg=PA212) (2nd ed.). Garland Science. pp. 212–213. ISBN 978-1-1366-7299-6.

115. Onsager, L. (1931). "Reciprocal relations in irreversible processes" (https://doi.org/10.1103%2F

PhysRev.37.405) . Physical Review. 37 (4): 405–26. Bibcode:1931PhRv...37..405O (https://ui.
adsabs.harvard.edu/abs/1931PhRv...37..405O) . doi:10.1103/PhysRev.37.405 (https://doi.or
g/10.1103%2FPhysRev.37.405) .
116. Martyushev, L. M.; Seleznev, V. D. (2006). "Maximum entropy production principle in physics,
chemistry and biology". Physics Reports. 426 (1): 1–45. Bibcode:2006PhR...426....1M (https://
ui.adsabs.harvard.edu/abs/2006PhR...426....1M) . doi:10.1016/j.physrep.2005.12.001 (http
s://doi.org/10.1016%2Fj.physrep.2005.12.001) .

117. Belkin, A.; Hubler, A.; Bezryadin, A. (2015). "Self-Assembled Wiggling Nano-Structures and the
Principle of Maximum Entropy Production" (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4
321171) . Scientific Reports. 5 (1): 8323. Bibcode:2015NatSR...5.8323B (https://ui.adsabs.har
vard.edu/abs/2015NatSR...5.8323B) . doi:10.1038/srep08323 (https://doi.org/10.1038%2Fsr
ep08323) . PMC 4321171 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4321171) .
PMID 25662746 (https://pubmed.ncbi.nlm.nih.gov/25662746) .

Further reading

Alekseev, G. N. (1986). Energy and Entropy (https://archive.org/details/EnergyAndEntropy) .

Moscow, Russia: Mir Publishers.

The Biosphere (A Scientific American Book), San Francisco, California, W. H. Freeman and
Company, 1970.ISBN 0-7167-0945-7. This book, originally a 1970 Scientific American issue,
covers virtually every major concern and concept since debated regarding materials and energy
resources, population trends, and environmental degradation.

Crowell, Benjamin (2011). "ch. 11" (http://www.lightandmatter.com/lm) . Light and Matter.

Fullerton, California: Light and Matter. Archived (https://web.archive.org/web/20110519093054/h
ttp://lightandmatter.com/lm/) from the original on 2011-05-19. Retrieved 2017-04-12.

Energy and Power (A Scientific American Book), San Francisco, California, W. H. Freeman and
Company, 1971.ISBN 0-7167-0938-4.

Ross, John S. (23 April 2002). "Work, Power, Kinetic Energy" (http://www.physnet.org/modules/pd
f_modules/m20.pdf) (PDF). Project PHYSNET. Michigan State University. Archived (https://web.
archive.org/web/20110426160837/http://www.physnet.org/modules/pdf_modules/m20.pdf)
(PDF) from the original on 26 April 2011. Retrieved 10 April 2009.

Santos, Gildo M. "Energy in Brazil: a historical overview," The Journal of Energy History (2018),
online (http://www.energyhistory.eu/en/panorama/energy-brazil-historical-overview) .Archived (h
ttps://web.archive.org/web/20190209180117/http://www.energyhistory.eu/en/panorama/energy-
brazil-historical-overview) 2019-02-09 at the Wayback Machine

Smil, Vaclav (2008). Energy in nature and society: general energetics of complex systems.
Cambridge, Massachusetts: MIT Press. ISBN 978-0-262-19565-2.
 Walding, Richard; Rapkins, Greg; Rossiter, Glenn (1999). New Century Senior Physics. Melbourne,
Australia: Oxford University Press. ISBN 978-0-19-551084-3.

Journals
The Journal of Energy History / Revue d'histoire de l'énergie (JEHRHE), 2018– (http://www.energy
history.eu/en)

External links

Differences between Heat and Thermal energy (http://www.biocab.org/Heat.html) (Archived (htt

ps://web.archive.org/web/20160827224418/http://www.biocab.org/Heat.html) 2016-08-27 at
the Wayback Machine) – BioCab