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The joule ( ; symbol: J) is a derived unit of
energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

energy
in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
. It is equal to the energy transferred to (or
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...

work
done on) an object when a
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

force
of one
newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...
acts on that object in the direction of the force's motion through a distance of one
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English ...
(1 newton-metre or N⋅m). It is also the energy dissipated as heat when an
electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...
of one
ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particle In physics ...

ampere
passes through a
resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''Th ...
of one
ohm The ohm (symbol: Ω) is the SI derived unit SI derived units are units of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, ...

ohm
for one second. It is named after the English physicist
James Prescott Joule James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, ...

James Prescott Joule
(1818–1889).


Definition

In terms firstly of base
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system The metric system is a system of measurement A syste ...
and then in terms of other SI units, a joule is defined as :\mathrm, where One joule can also be defined as the following: * The work required to move an
electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectively). Like c ...
of one
coulomb The coulomb (symbol: C) is the International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' ( ...

coulomb
through an
electrical potential difference The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of energy needed to move a unit of from a reference point to the specific point in an electric field. ...

electrical potential difference
of one volt, or one coulomb-volt (C⋅V). This relationship can be used to define the volt. * The work required to produce one watt of
power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, p ...
for one second, or one watt-second (W⋅s) (compare
kilowatt-hour The kilowatt-hour ( SI symbol: kW⋅h or kW h; commonly written as kWh) is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, ...
3.6 megajoules). This relationship can be used to define the watt.


History

The cgs system had been declared official in 1881, at the first
International Electrical CongressThe International Electrical Congress was a series of international meetings, from 1881 - 1904, in the then new field of applied electricity. The first meeting was initiated by the French government, including official national representatives, lead ...
. The
erg The erg is a unit of energy equal to 10−7joule The joule ( ; symbol: J) is a SI derived unit, derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work (physics), work done on) an objec ...
was adopted as its unit of energy in 1882. Wilhelm Siemens, in his inauguration speech as chairman of the
British Association for the Advancement of Science The British Science Association (BSA) is a charity Charity may refer to: Giving * Charitable organization or charity, a non-profit organization whose primary objectives are philanthropy and social well-being * Charity (practice), the practice ...
(23 August 1882) first proposed the ''Joule'' as unit of
heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

heat
, to be derived from the electromagnetic units
Ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particle In physics ...

Ampere
and
Ohm The ohm (symbol: Ω) is the SI derived unit SI derived units are units of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, ...

Ohm
, in cgs units equivalent to . The naming of the unit in honour of
James Prescott Joule James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, ...

James Prescott Joule
(1818–1889), at the time retired but still living (aged 63), is due to Siemens: :"Such a heat unit, if found acceptable, might with great propriety, I think, be called the Joule, after the man who has done so much to develop the dynamical theory of heat." At the second International Electrical Congress, on 31 August 1889, the joule was officially adopted alongside the
watt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...

watt
and the ''quadrant'' (later renamed to
henry Henry may refer to: People *Henry (given name) Henry is a masculine given name derived from Old French Old French (, , ; French language, Modern French: ) was the language spoken in Northern France from the 8th century to the 14th century ...
). Joule died in the same year, on 11 October 1889. At the fourth congress (1893), the "international Ampere" and "international Ohm" were defined, with slight changes in the specifications for their measurement, with the "international Joule" being the unit derived from them. In 1935, the
International Electrotechnical Commission The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization A standards organization, standards body, standards developing organization (SDO), or s ...
(as the successor organisation of the International Electrical Congress) adopted the "
GiorgiGiorgi (; ka, გიორგი, tr) is a Georgians, Georgian masculine Georgian name, given name being the most popular name in Georgia (country), Georgia. It may refer to: Given name * Giorgi Asanidze (born 1975), Georgian weightlifter * Gior ...

Giorgi
system", which by virtue of assuming a defined value for the
magnetic constant Vacuum permeability is the magnetic permeability in a classical vacuum. ''Vacuum permeability'' is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field pro ...
also implied a redefinition of the Joule. The Giorgi system was approved by the
International Committee for Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in ...
in 1946. The joule was now no longer defined based on electromagnetic unit, but instead as the unit of
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...

work
performed by one unit of force (at the time not yet named
newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...
) over the distance of 1
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English ...
. The joule was explicitly intended as the unit of energy to be used in both electromagnetic and mechanical contexts. The ratification of the definition at the ninth
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures The International Bureau of Weights and Measures (fr ...
, in 1948, added the specification that the joule was also to be preferred as the unit of
heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

heat
in the context of
calorimetry upSnellen direct calorimetry chamber, University of Ottawa. Calorimetry is the science or act of measuring changes in ''state variables'' of a body for the purpose of deriving the heat transfer associated with changes of its state due, for exam ...
, thereby officially deprecating the use of the
calorie The calorie is a unit of energy Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a di ...
. This definition was the direct precursor of the joule as adopted in the modern
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
in 1960. The definition of the joule as J=kg⋅m2⋅s−2 has remained unchanged since 1946, but the joule as a derived unit has inherited changes in the definitions of the
second The second (symbol: s, also abbreviated: sec) is the base unit of time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, th ...
(in 1960 and 1967), the
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English ...
(in 1983) and the
kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of " ...
( in 2019).


Practical examples

One joule represents (approximately): * The amount of electricity required to run a device for . * The energy required to accelerate a mass at through a distance of . * The
kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
of a
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
traveling at . * The energy required to lift a medium-sized tomato up , assuming the tomato has a mass of . * The
heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

heat
required to raise the temperature 0.239 g of water from 0 °C to 1 °C, or from 32 °F to 33.8 °F. * The typical energy released as heat by a person at rest every 1/60 s (). * The
kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
of a human moving very slowly (). * The kinetic energy of a tennis ball moving at . * The food energy (kcal) in slightly more than half of a sugar crystal (/crystal).


Multiples

; : The yoctojoule (yJ) is equal to . ; : The zeptojoule (zJ) is equal to one sextillionth () of one joule. is about one
electronvolt In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular suc ...
. The minimal energy needed to change a bit at around room temperature – approximately – is given by the
Landauer limit Landauer's principle is a physical principle pertaining to the lower theoretical A theory is a rational type of abstract thinking about a phenomenon A phenomenon (; plural phenomena) is an observable fact or event. The term came into its m ...
. ; : The attojoule (aJ) is equal to . ; : The femtojoule (fJ) is equal to . ; : The picojoule (pJ) is equal to one trillionth () of one joule. ; : The nanojoule (nJ) is equal to one billionth () of one joule. is about the
kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
of a flying mosquito. ; : The microjoule (μJ) is equal to one millionth () of one joule. The
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle collider A collider is a type of particle accelerator , a synchrotron collider type particle accelerator at Fermi National Accelerator Laboratory (Fermilab) ...
(LHC) produces collisions of the microjoule order (7 TeV) per particle. ; : The millijoule (mJ) is equal to one thousandth () of a joule. ; : The kilojoule (kJ) is equal to one thousand () joules. Nutritional food labels in most countries express energy in kilojoules (kJ). One square metre of the
Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...

Earth
receives about of
solar radiation Solar irradiance is the power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one j ...
every second in full daylight. A human in a sprint has approximately 3kJ of kinetic energy, while a cheetah in a 70mph sprint has approximately 20kJ. ; : The megajoule (MJ) is equal to one million () joules, or approximately the kinetic energy of a one megagram (tonne) vehicle moving at (100 mph). The energy required to heat of liquid water at constant pressure from to is approximately . One
kilowatt-hour The kilowatt-hour ( SI symbol: kW⋅h or kW h; commonly written as kWh) is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, ...
of electricity is . ; :The gigajoule (GJ) is equal to one billion () joules. is about the
chemical energy Chemical energy is the energy of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects th ...
of combusting of
petroleum Petroleum, also known as crude oil and oil, is a naturally occurring, yellowish-black liquid A liquid is a nearly incompressible In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric process, isoc ...

petroleum
. 2 GJ is about the Planck energy unit. ; :The terajoule (TJ) is equal to one trillion () joules; or about (which is often used in energy tables). About of energy was released by
Little Boy "Little Boy" was the codename for the type of atomic bomb A nuclear weapon (also known as an atom bomb, atomic bomb, nuclear bomb or nuclear warhead, and colloquially as an A-bomb or nuke) is an explosive device that derives its destructi ...

Little Boy
. The
International Space Station The International Space Station (ISS) is a Modular design, modular space station (habitable satellite, artificial satellite) in low Earth orbit. It is a multinational collaborative project involving five participating space agencies: NASA (Uni ...

International Space Station
, with a mass of approximately and orbital velocity of , has a
kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
of roughly . In 2017,
Hurricane Irma Hurricane Irma was an extremely powerful Cape Verde hurricane that caused widespread destruction across its path in September 2017. Irma was the first Category 5 hurricane to strike the Leeward Islands french: Îles-Sous-le-Vent , im ...

Hurricane Irma
was estimated to have a peak wind energy of . is about the amount of energy equivalent to of mass. ; : The petajoule (PJ) is equal to one quadrillion () joules. is about of TNT which is the amount of energy released by the
Tsar Bomba The Tsar Bomba (), (code name: ''Ivan'' or ''Vanya''), also known by the alphanumerical designation AN602, was a hydrogen bomb, hydrogen aerial bomb, and the most powerful nuclear weapon ever created and tested. Tsar Bomba was developed in the ...
, the largest man-made explosion ever. ; : The exajoule (EJ) is equal to one quintillion () joules. The
2011 Tōhoku earthquake and tsunami The occurred at 14:46 JST (05:46 UTC) on 11 March. The magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object ...
in Japan had of energy according to its rating of 9.0 on the
moment magnitude scale The moment magnitude scale (MMS; denoted explicitly with or Mw, and generally implied with use of a single M for magnitude) is a measure of an earthquake An earthquake (also known as a quake, tremor or temblor) is the shaking of the surfa ...
. Yearly U.S. energy consumption amounts to roughly . ; :The zettajoule (ZJ) is equal to one sextillion () joules. Human annual
world energy consumption World energy supply and consumption is global production and preparation of fuel A fuel is any material that can be made to react with other substances so that it releases energy as thermal energy Thermal radiation in visible light can be se ...

world energy consumption
is approximately . The energy to raise the temperature of Earth's atmosphere 1 °C is approximately . ; :The yottajoule (YJ) is equal to one septillion () joules. This is approximately the amount of energy required to heat by 1 °C. The thermal output of the
Sun The Sun is the star A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many othe ...

Sun
is approximately per second.


Conversions

1 joule is equal to (approximately unless otherwise stated): * (exactly) * * (gram calories) * (food calories) * * (foot-pound) * (foot-poundal) * (kilowatt-hour) * (watt-hour) * (litre-atmosphere) * (by way of mass-energy equivalence) * (exactly) Units defined exactly in terms of the joule include: * 1 thermochemical
calorie The calorie is a unit of energy Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a di ...
= 4.184JThe adoption of joules as units of energy
FAO/WHO Ad Hoc Committee of Experts on Energy and Protein, 1971. A report on the changeover from calories to joules in nutrition.
* 1 International Table calorie = 4.1868J * 1W⋅h = 3600J (or 3.6kJ) * 1kW⋅h = (or 3.6MJ) * 1W⋅s = * 1
ton TNT TNT equivalent is a convention for expressing energy, typically used to describe the energy released in an explosion. The is a unit of energy As energy In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ ...
=


Newton-metre and torque

In
mechanics Mechanics (Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximat ...

mechanics
, the concept of
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

force
(in some direction) has a close analogue in the concept of
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. The concept originated with the studies ...

torque
(about some angle): A result of this similarity is that the SI unit for torque is the
newton-metre The newton-metre (also newton metre or newton meter; symbol N⋅m or N m) is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of acti ...

newton-metre
, which works out
algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with number theory, geometry and mathematical analysis, analysis. In its most ge ...

algebra
ically to have the same
dimension In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
s as the joule, but are not interchangeable. The
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures The International Bureau of Weights and Measures (fr ...
has given the unit of
energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

energy
the name ''joule'', but has not given the unit of torque any special name, hence it is simply the newton-metre (N⋅m) – a compound name derived from its constituent parts. The use of newton-metres for torque and joules for energy is helpful to avoid misunderstandings and miscommunications. The distinction may be seen also in the fact that energy is a
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers *Scalar (physics), a physical quantity that can be described by a single element of a number field such as ...
quantity – the
dot product In mathematics, the dot product or scalar productThe term ''scalar product'' is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space. is an algebraic operation that takes two equal-length seque ...
of a force
vector Vector may refer to: Biology *Vector (epidemiology) In epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and risk factor, determinants of health and disease conditions in defined pop ...
and a displacement vector. By contrast, torque is a vector – the
cross product In , the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a on two s in a three-dimensional (named here E), and is denoted by the symbol \times. Given two and , the cross produc ...

cross product
of a force vector and a distance vector. Torque and energy are related to one another by the equation E = \tau \theta\, , where ''E'' is energy, ''τ'' is (the vector magnitude of) torque, and ''θ'' is the angle swept (in
radian The radian, denoted by the symbol \text, is the SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric sy ...

radian
s). Since plane angles are dimensionless, it follows that torque and energy have the same dimensions.


Watt-second

A watt-second (symbol W s or W·s) is a derived unit of
energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

energy
equivalent to the joule. The watt-second is the energy equivalent to the power of one
watt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...

watt
sustained for one
second The second (symbol: s, also abbreviated: sec) is the base unit of time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, th ...
. While the watt-second is equivalent to the joule in both units and meaning, there are some contexts in which the term "watt-second" is used instead of "joule".


Photography

In photography, the unit for flashes is the watt-second. A flash can be rated in watt-seconds (e.g., 300 W⋅s) or in joules (different names for the same thing), but historically, the term "watt-second" has been used and continues to be used. :\text = \dfrac \cdot \text \cdot \text^2 The energy rating a flash is given is not a reliable benchmark for its light output because there are numerous factors that affect the energy conversion efficiency. For example, the construction of the tube will affect the efficiency, and the use of reflectors and filters will change the usable light output towards the subject. Some companies specify their products in "true" watt-seconds, and some specify their products in "nominal" watt-seconds.


See also

*
Fluence In radiometry Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as oppo ...
* Reciprocal joules


Notes


References


External links

* {{Footer energy James Prescott Joule SI derived units Units of energy