# Joule

Joule
Unit systemSI derived unit
Unit ofEnergy
SymbolJ
Named afterJames Prescott Joule
Conversions
1 J in ...... is equal to ...
SI base units   kgm2s−2
CGS units   1×107 erg
Watt-seconds   1Ws
kilowatt-hours   2.78×10−7 kW⋅h
kilocalories (thermochemical)   2.390×10−4 kcalth
BTUs   9.48×10−4 BTU
electronvolts   6.24×1018 eV

The joule (/l, l/ jowl, 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]

## Definition

In terms firstly of base SI units and then in terms of other SI units, a joule is defined as

${\displaystyle {\text{J}}={\frac {{\text{kg}}{\cdot }{\text{m}}^{2}}{{\text{s}}^{2}}}={\text{N}}{\cdot }{\text{m}}={\text{Pa}}{\cdot }{\text{m}}^{3}={\text{W}}{\cdot }{\text{s}}={\text{C}}{\cdot }{\text{V}}={\text{Ω}}{\cdot }{\text{A}}^{2}{\cdot }{\text{s}},}$

where

Symbol Meaning
J joule
kg kilogram
m metre
s second
N newton
Pa pascal
W watt
C coulomb
V volt
Ω ohm
A ampere

One joule can also be defined as the following:

• The work required to move an electric charge 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 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 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 in full it follows the rules for capitalisation of a common noun; i.e., "joule" becomes capitalised at the beginning of a sentence and in titles, but is otherwise in lower case.

## 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, to be derived from the electromagnetic units Ampere and Ohm, in cgs units equivalent to 107 erg. The naming of the unit in honour of 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."[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⋅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 (in 1983) and the kilogram (in 2019).

## Practical examples

One joule represents (approximately):

• The energy required to accelerate a kg mass at m/s2 through a distance of m.
• The kinetic energy of a kg mass traveling at m/s.
• The energy required to lift a medium-sized tomato up 1 metre (3 ft 3 in), assume the tomato has a mass of 101.97 grams (3.597 oz).
• The 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.[12]
• The typical energy released as heat by a person at rest every 1/60 s (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).[13]
• The amount of electricity required to run a W device for s.
• The food energy (kcal) in slightly more than half of a sugar crystal (0.102 mg/crystal).

## Multiples

Submultiples Multiples Value SI symbol Name Value 10−1 J dJ decijoule 101 J daJ decajoule 10−2 J cJ centijoule 102 J hJ hectojoule 10−3 J mJ millijoule 103 J kJ kilojoule 10−6 J µJ microjoule 106 J MJ megajoule 10−9 J nJ nanojoule 109 J GJ gigajoule 10−12 J pJ picojoule 1012 J TJ terajoule 10−15 J fJ femtojoule 1015 J PJ petajoule 10−18 J aJ attojoule 1018 J EJ exajoule 10−21 J zJ zeptojoule 1021 J ZJ zettajoule 10−24 J yJ yoctojoule 1024 J YJ yottajoule Common multiples are in bold face
Yoctojoule
The yoctojoule (yJ) is equal to 10−24 joule.
Zeptojoule
The zeptojoule (zJ) is equal to one sextillionth (10−21) of one joule. 160 zJ 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 joule.
Femtojoule
The femtojoule (fJ) is equal to 10−15 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.[14]
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 (103) joules. Nutritional food labels in most countries express energy in kilojoules (kJ).[15]
One square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.[16]
Megajoule
The megajoule (MJ) is equal to one million (106) joules, or approximately the kinetic energy of a one megagram (tonne) vehicle moving at 161 km/h (100 mph).
The energy required to heat 10 L 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 (109) joules. GJ is about the chemical energy of combusting 1 barrel (159 l) of petroleum.[17] 2 GJ is about the Planck energy unit.
Terajoule
The terajoule (TJ) is equal to one trillion (1012) joules; or about 0.278 GWh (which is often used in energy tables). About 63 TJ of energy was released by Little Boy.[18] The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7700 m/s,[19] has a kinetic energy of roughly 13 TJ. In 2017, Hurricane Irma was estimated to have a peak wind energy of 112 TJ.[20][21] 90 TJ is about the amount of energy equivalent to 1 gram of mass.
Petajoule
The petajoule (PJ) is equal to one quadrillion (1015) 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.
Exajoule
The exajoule (EJ) is equal to one quintillion (1018) joules. The 2011 Tōhoku earthquake and tsunami in Japan had 1.41 EJ of energy according to its rating of 9.0 on the moment magnitude scale. Yearly U.S. energy consumption amounts to roughly 94 EJ.
Zettajoule
The zettajoule (ZJ) is equal to one sextillion (1021) joules. Human annual world energy consumption is approximately 0.5 ZJ. The energy to raise the temperature of Earth's atmosphere 1 °C is approximately 2.2 ZJ.
Yottajoule
The yottajoule (YJ) is equal to one septillion (1024) 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.

## Conversions

1 joule is equal to (approximately unless otherwise stated):

• 107 erg (exactly)
• 6.24150974×1018 eV
• 0.2390 cal (gram calories)
• 2.390×10−4 kcal (food calories)
• 9.4782×10−4 BTU
• 0.7376 ft⋅lb (foot-pound)
• 23.7 ft⋅pdl (foot-poundal)
• 2.7778×10−7 kW⋅h (kilowatt-hour)
• 2.7778×10−4 W⋅h (watt-hour)
• 9.8692×10−3 latm (litre-atmosphere)
• 11.1265×10−15 g (by way of mass-energy equivalence)
• 10−44 foe (exactly)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J[22]
• 1 International Table calorie = 4.1868 J[23]
• 1 W⋅h = 3600 J (or 3.6 kJ)
• 1 kW⋅h = 3.6×106 J (or 3.6 MJ)
• 1 W⋅s = 1 J
• 1 ton TNT = 4.184 GJ

## Newton-metre and torque

In mechanics, the concept of force (in some direction) has a close analogue in the concept of torque (about some angle):

Linear Angular
Force Torque
Mass Moment of inertia
Displacement Angle

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 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.[24] The use of newton-metres for torque and joules for energy is helpful to avoid misunderstandings and miscommunications.[24]

The distinction may be seen also in the fact that energy is a scalar quantity – the dot product of a force vector 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

${\displaystyle E=\tau \theta \ ,}$

where E is energy, τ is (the vector magnitude of) torque, and θ is the angle swept (in radians). 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.[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".[why?]

### 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.

${\displaystyle {\text{Energy of a flash in joules or watt-seconds}}={\dfrac {1}{2}}\cdot {\text{capacitance of the storage capacitor in farads}}\cdot {\text{working voltage}}^{2}}$

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]

## Notes

1. ^ 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.

## References

1. ^ "joule". A new English dictionary on historical principles. The Clarendon press. January 1901. p. 606.CS1 maint: date and year (link)
2. ^ Allen, H. S. (September 1943). "Nature 152, 354 (1943)". Nature. 152 (3856): 354. doi:10.1038/152354a0. S2CID 4182911.
3. ^ Wells, John (2008). Longman Pronunciation Dictionary (3rd ed.). Pearson Longman. ISBN 978-1-4058-8118-0.
4. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 120, ISBN 92-822-2213-6, archived from the original (PDF) on 2017-08-14
5. ^ American Heritage Dictionary of the English Language, Online Edition (2009). Houghton Mifflin Co., hosted by Yahoo! Education.
6. ^ The American Heritage Dictionary, Second College Edition (1985). Boston: Houghton Mifflin Co., p. 691.
7. ^ McGraw-Hill Dictionary of Physics, Fifth Edition (1997). McGraw-Hill, Inc., p. 224.
8. ^ "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 107 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 11000th part of the arbitrary unit of a pound of water raised 1° Fahrenheit and the 14000th 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.
9. ^ Pat Naughtin: A chronological history of the modern metric system., metricationmatters.com, 2009.
10. ^
11. ^
12. ^ "Units of Heat – BTU, Calorie and Joule". Engineering Toolbox. Retrieved 2021-06-14.
13. ^ Ristinen, Robert A.; Kraushaar, Jack J. (2006). Energy and the Environment (2nd ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0-471-73989-8.
14. ^ "Physics – CERN". public.web.cern.ch. Archived from the original on 2012-12-13.
15. ^ "You Say Calorie, We Say Kilojoule: Who's Right?". Retrieved 2 May 2017.
16. ^ "Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". Archived from the original on 2011-08-30. Retrieved 2005-10-05.
17. ^
18. ^ Malik, John (September 1985). "Report LA-8819: The yields of the Hiroshima and Nagasaki nuclear explosions" (PDF). Los Alamos National Laboratory. Archived from the original (PDF) on 11 October 2009. Retrieved 18 March 2015.
19. ^ "International Space Station Final Configuration" (PDF). European Space Agency. Archived from the original (PDF) on 21 July 2011. Retrieved 18 March 2015.
20. ^ Bonnie Berkowitz; Laris Karklis; Reuben Fischer-Baum; Chiqui Esteban (11 September 2017). "Analysis – How big is Hurricane Irma?". Washington Post. Retrieved 2 November 2017.
21. ^ "Irma unleashes its fury on south Florida", Financial Times, accessed 10-Sept-2017 (subscription required)
22. ^ 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.
23. ^ Feynman, Richard (1963). "Physical Units". Feynman's Lectures on Physics. Retrieved 2014-03-07.
24. ^ 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.
25. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 39–40, 53, ISBN 92-822-2213-6, archived from the original (PDF) on 2017-08-14
26. ^