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The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount 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 ** Working animal, an animal t ...
done when a force of 1 newton displaces a mass through a distance of 1
metre The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...
in the direction of the force applied. It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one 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, mathematician and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). ...
(1818–1889).


Definition

In terms of
SI base units The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all ...
and in terms of SI derived units with special names, the joule is defined as One joule can also be defined by any of the following: * The work required to move an
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
of one coulomb through an 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 most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
for one second, or one watt-second (W⋅s) (compare kilowatt-hour, which is 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 Congress. The erg 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 (23 August 1882) first proposed the ''Joule'' as unit of
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
, to be derived from the electromagnetic units Ampere and 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, mathematician and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). ...
(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 the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James ...
and the ''quadrant'' (later renamed to
henry Henry may refer to: People *Henry (given name) * Henry (surname) * Henry Lau, Canadian singer and musician who performs under the mononym Henry Royalty * Portuguese royalty ** King-Cardinal Henry, King of Portugal ** Henry, Count of Portugal, ...
). 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 (as the successor organisation of the International Electrical Congress) adopted the " Giorgi system", which by virtue of assuming a defined value for the magnetic constant 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 i ...
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 ** Working animal, an animal t ...
performed by one unit of force (at the time not yet named newton) over the distance of 1
metre The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...
. 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, in 1948, added the specification that the joule was also to be preferred as the unit of
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
in the context of
calorimetry In chemistry and thermodynamics, 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 example, to chemical reac ...
, thereby officially deprecating the use of the calorie. This definition was the direct precursor of the joule as adopted in the modern International System of Units 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 (in 1960 and 1967), the
metre The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...
(in 1983) and the kilogram ( 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, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acc ...
of a
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
travelling at , or a mass travelling at . * The energy required to lift a medium-sized tomato up , assuming the tomato has a mass of . * The
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
required to raise the temperature of 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, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acc ...
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

; : is about one electronvolt. The minimal energy needed to change a bit at around room temperature – approximately – is given by the Landauer limit. ; : is about the
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acc ...
of a flying mosquito. ; : The Large Hadron Collider (LHC) produces collisions of the microjoule order (7 TeV) per particle. ; : 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 harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
receives about of
solar radiation Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre ( ...
every second in full daylight. A human in a sprint has approximately 3 kJ of kinetic energy, while a cheetah in a (76 mph) sprint has approximately 20 kJ. One
watt-hour A kilowatt-hour ( unit symbol: kW⋅h or kW h; commonly written as kWh) is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ). Kilowatt-hours are a common bi ...
of electricity is . ; : The megajoule is 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 of electricity is . ; : is about the chemical energy of combusting of
petroleum Petroleum, also known as crude oil, or simply oil, is a naturally occurring yellowish-black liquid mixture of mainly hydrocarbons, and is found in geological formations. The name ''petroleum'' covers both naturally occurring unprocessed crud ...
. 2 GJ is about the Planck energy unit. One megawatt-hour of electricity is . ; : The terajoule is about (which is often used in energy tables). About of energy was released by
Little Boy "Little Boy" was the type of atomic bomb dropped on the Japanese city of Hiroshima on 6 August 1945 during World War II, making it the first nuclear weapon used in warfare. The bomb was dropped by the Boeing B-29 Superfortress ''Enola Gay'' p ...
. The
International Space Station The International Space Station (ISS) is the largest modular space station currently in low Earth orbit. It is a multinational collaborative project involving five participating space agencies: NASA (United States), Roscosmos (Russia), JAXA ( ...
, with a mass of approximately and orbital velocity of , has a
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acc ...
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 on record, followed by Maria two ...
was estimated to have a peak wind energy of . One
gigawatt-hour A kilowatt-hour ( unit symbol: kW⋅h or kW h; commonly written as kWh) is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ). Kilowatt-hours are a common bi ...
of electricity is . ; : is about of TNT, which is the amount of energy released by the Tsar Bomba, the largest man-made explosion ever. One
terawatt-hour A kilowatt-hour ( unit symbol: kW⋅h or kW h; commonly written as kWh) is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ). Kilowatt-hours are a common b ...
of electricity is . ; : The
2011 Tōhoku earthquake and tsunami The occurred at 14:46 JST (05:46 UTC) on 11 March. The magnitude 9.0–9.1 (M) undersea megathrust earthquake had an epicenter in the Pacific Ocean, east of the Oshika Peninsula of the Tōhoku region, and lasted approximately six mi ...
in Japan had of energy according to its rating of 9.0 on the moment magnitude scale. Yearly U.S. energy consumption amounts to roughly . One petawatt-hour of electricity is . ; : The zettajoule is somewhat more than the amount of energy required to heat the
Baltic sea The Baltic Sea is an arm of the Atlantic Ocean that is enclosed by Denmark, Estonia, Finland, Germany, Latvia, Lithuania, Poland, Russia, Sweden and the North and Central European Plain. The sea stretches from 53°N to 66°N latitude and ...
by 1 °C, assuming properties similar to those of pure water. Human annual
world energy consumption World energy supply and consumption is global production and preparation of fuel, generation of electricity, energy transport, and energy consumption. It is a basic part of economic activity. It includes heat, but not energy from food. This art ...
is approximately . The energy to raise the temperature of Earth's atmosphere 1 °C is approximately . ; : The yottajoule is a little less than the amount of energy required to heat the
Indian Ocean The Indian Ocean is the third-largest of the world's five oceanic divisions, covering or ~19.8% of the water on Earth's surface. It is bounded by Asia to the north, Africa to the west and Australia to the east. To the south it is bounded by t ...
by 1 °C, assuming properties similar to those of pure water. The thermal output of the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
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 = 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 =


Newton-metre and torque

In
mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to object ...
, the concept of force (in some direction) has a close analogue in the concept of torque (about some angle): A result of this similarity is that the SI unit for torque is the newton-metre, which works out
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...
ically to have the same
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coor ...
s as the joule, but they are not interchangeable. The General Conference on Weights and Measures has given the unit of 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 quantity – the
dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alge ...
of a force
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
and a displacement vector. By contrast, torque is a vector – the 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 rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...
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 equivalent to the joule. The watt-second is the energy equivalent to the power of one
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James ...
sustained for one second. 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", such as in the rating of photographic electronic flash units.


See also

* Fluence * Reciprocal joules


Notes


References


External links

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