The joule (/dʒaʊl, dʒuːl/jawl, jool;^{[1]}^{[2]}^{[3]} symbol: J) is a derived unit of energy in the International System of Units.^{[4]} It is equal to the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of the force's motion through a distance of one metre (1 newton metre or N⋅m). 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 (1818–1889).^{[5]}^{[6]}^{[7]}
In terms firstly of base SI units and then in terms of other SI units, a joule is defined below, where kg is the kilogram, m is the metre, s is the second, N is the newton, Pa is the pascal, W is the watt, C is the coulomb, and V is the volt:
The work required to produce one watt of power for one second, or one watt-second (W⋅s) (compare kilowatt-hour – 3.6 megajoules). This relationship can be used to define the watt.
The joule is an named after James Prescott Joule. As with every SI unit named for a person, its symbol starts with an upper case letter (J), but when written out it follows no special casing, following whatever would contextually befit a common noun; i.e., "joule" becomes capitalised at the beginning of a sentence and in titles.
"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."^{[8]}
At the second International Electrical Congress, on 31 August 1889, the joule was officially adopted alongside the watt and the quadrant (later renamed to henry).^{[9]}
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 in 1946. The joule was now no longer defined based on electromagnetic unit, but instead as the unit of work performed by one unit of force (at the time not yet named newton)
over the distance of 1 metre. The joule was explicitly intended as the unit of energy to be used in both electromagnetic and mechanical contexts.^{[10]} 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 the context of calorimetry, thereby officially deprecating the use of the calorie.^{[11]}
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⋅m^{2}⋅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 (in 1983) and the kilogram (in 2019).
A result of this similarity is that the SI unit for torque is the newton metre, which works out algebraically to have the same dimensions as the joule. But they are not interchangeable. The CGPM 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.^{[12]} The use of newton metres for torque and joules for energy is helpful to avoid misunderstandings and miscommunications.^{[12]}
The distinction may be seen also in the fact that energy is a scalar – the dot product of a vector force and a vector displacement. By contrast, torque is a vector – the cross product of a distance vector and a force 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 radians). Since radians are dimensionless, it follows that torque and energy have the same dimensions.
Practical examples
One joule in everyday life represents approximately:
The energy required to lift a medium-sized tomato up 1 metre (3 ft 3 in) (assume the tomato has a mass of approximately 100 grams (3.5 oz)).
The energy released when that same tomato falls back down one metre.
The energy required to accelerate a 1 kg mass at 1 m⋅s^{−2} through a distance of 1 m.
The heat required to raise the temperature of 1 g of water by 0.24 °C.^{[13]}
The typical energy released as heat by a person at rest every 1/60 s (approximately 17 ms).^{[note 1]}
The kinetic energy of a 50 kg human moving very slowly (0.2 m/s or 0.72 km/h).
The kinetic energy of a 56 g tennis ball moving at 6 m/s (22 km/h).^{[14]}
The kinetic energy of an object with mass 1 kg moving at √2 ≈ 1.4 m/s.
The amount of electricity required to light a 1 W LED for 1 s.
Since the joule is also a watt-second and the common unit for electricity sales to homes is the kW⋅h (kilowatt-hour), a kW⋅h is thus 1000 W × 3600 s = 3.6 MJ (megajoules).
The yoctojoule (yJ) is equal to (10^{−24}) of one joule.
Zeptojoule
The zeptojoule (zJ) is equal to one sextillionth (10^{−21}) of one joule. 160 zeptojoules is about one electronvolt. The minimal energy needed to change a bit at around room temperature - approximately 2.75 zJ - is given by the Landauer limit.
Attojoule
The attojoule (aJ) is equal to (10^{−18}) of one joule.
Femtojoule
The femtojoule (fJ) is equal to (10^{−15}) of one joule.
Picojoule
The picojoule (pJ) is equal to one trillionth (10^{−12}) of one joule.
Nanojoule
The nanojoule (nJ) is equal to one billionth (10^{−9}) of one joule. 160 nanojoules is about the kinetic energy of a flying mosquito.^{[15]}
Microjoule
The microjoule (μJ) is equal to one millionth (10^{−6}) of one joule. The Large Hadron Collider (LHC) produces collisions of the microjoule order (7 TeV) per particle.
Millijoule
The millijoule (mJ) is equal to one thousandth (10^{−3}) of a joule.
Kilojoule
The kilojoule (kJ) is equal to one thousand (10^{3}) joules. Nutritional food labels in most countries express energy in kilojoules (kJ).^{[16]} One square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.^{[17]}
Megajoule
The megajoule (MJ) is equal to one million (10^{6}) joules, or approximately the kinetic energy of a one megagram (tonne) vehicle moving at 161 km/h. The energy required to heat 10 liters of liquid water at constant pressure from 0 °C (32 °F) to 100 °C (212 °F) is approximately 4.2 MJ. One kilowatt hour of electricity is 3.6 megajoules.
Gigajoule
The gigajoule (GJ) is equal to one billion (10^{9}) joules. 6 GJ is about the chemical energy of combusting 1 barrel (159 l) of crude oil.^{[18]} 2 GJ is about the Planck energy unit.
Terajoule
The terajoule (TJ) is equal to one trillion (10^{12}) joules; or about 0.278 GWh (which is often used in energy tables). About 63 TJ of energy was released by the atomic bomb that exploded over Hiroshima.^{[19]} The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7.7 km/s,^{[20]} has a kinetic energy of roughly 13 TJ. In 2017 Hurricane Irma was estimated to have a peak wind energy of 112 TJ.^{[21]}^{[22]}
Petajoule
The petajoule (PJ) is equal to one quadrillion (10^{15}) joules. 210 PJ is about 50 megatons of TNT which is the amount of energy released by the Tsar Bomba, the largest man-made explosion ever.
The zettajoule (ZJ) is equal to one sextillion (10^{21}) joules. The human annual global energy consumption is approximately 0.5 ZJ.
Yottajoule
The yottajoule (YJ) is equal to one septillion (10^{24}) joules. This is approximately the amount of energy required to heat all the water on Earth by 1 °C. The thermal output of the Sun is approximately 400 YJ per second.
A watt second (also watt-second, symbol W s or W·s) is a derived unit of energy equivalent to the joule.^{[25]} The watt-second is the energy equivalent to the power of one watt 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".
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. An on-camera flash, using a 1000 microfarad capacitor at 300 volts, would be 45 watt-seconds. Studio flashes, using larger capacitors and higher voltages, are in the 200–2000 watt-second range.
${\text{Energy of a flash in joules or watt-seconds}}={\dfrac {1}{2}}\cdot {\text{capacitance of the storage capacitor in farads}}\cdot {\text{working voltage}}^{2}$
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.^{[26]}
^This is called the basal metabolic rate. It corresponds to about 5,000 kJ (1,200 kcal) per day. The kilocalorie (symbol kcal) is also known as the dietary calorie. "At rest" means awake but inactive.
^The American Heritage Dictionary, Second College Edition (1985). Boston: Houghton Mifflin Co., p. 691.
^McGraw-Hill Dictionary of Physics, Fifth Edition (1997). McGraw-Hill, Inc., p. 224.
^"The unit of heat has hitherto been taken variously as the heat required to raise a pound of water at the freezing-point through 1° Fahrenheit or Centigrade, or, again, the heat necessary to raise a kilogramme of water 1° Centigrade. The inconvenience of a unit so entirely arbitrary is sufficiently apparent to justify the introduction of one based on the electro-magnetic system, viz. the heat generated in one second by the current of an Ampère flowing through the resistance of an Ohm. In absolute measure its value is 10^{7} C.G.S. units, and, assuming Joule's equivalent as 42,000,000, it is the heat necessary to raise 0.238 grammes of water 1° Centigrade, or, approximately, the ⅟₁₀₀₀th part of the arbitrary unit of a pound of water raised 1° Fahrenheit and the ⅟₄₀₀₀th of the kilogramme of water raised 1° Centigrade. 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."Carl Wilhelm Siemens, Report of the Fifty-Second Meeting of the British Association for the Advancement of Science. S. 6 f.
^ ^{a}^{b}"Units with special names and symbols; units that incorporate special names and symbols". International Bureau of Weights and Measures. Archived from the original on 28 June 2009. Retrieved 18 March 2015. A derived unit can often be expressed in different ways by combining base units with derived units having special names. Joule, for example, may formally be written newton metre, or kilogram metre squared per second squared. This, however, is an algebraic freedom to be governed by common sense physical considerations; in a given situation some forms may be more helpful than others. In practice, with certain quantities, preference is given to the use of certain special unit names, or combinations of unit names, to facilitate the distinction between different quantities having the same dimension.
^Bonnie Berkowitz; Laris Karklis; Reuben Fischer-Baum; Chiqui Esteban (11 September 2017). "Analysis - How big is Hurricane Irma?". Washington Post. Retrieved 2 November 2017.
^The 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.