Joule

This article is about the unit of energy or work. For other uses, see Joule (disambiguation).

Not to be confused with Juul.

The joule (/dʒuːl/ JOOL, or /dʒaʊl/ JOWL; symbol: J) is the unit of energy in the International System of Units (SI).^[1] It is equal to the amount of work done when a force of one newton displaces a mass through a distance of one metre in the direction of that force. 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).^[2][3][4]

Joule
Intuitive representation of the joule as the work of a motive force
General information
Unit system	SI
Unit of	energy
Symbol	J
Named after	James Prescott Joule
Conversions
1 J in ...	... is equal to ...
SI base units	kg⋅m2⋅s−2
CGS units	1×107 erg
watt-seconds	1 W⋅s
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

Definition

In terms of SI base units and in terms of SI derived units with special names, the joule is defined as^[5]

$${\displaystyle {\begin{alignedat}{3}\mathrm {J} \;&=~\mathrm {kg{\cdot }m^{2}{\cdot }s^{-2}} \\[0.7ex]&=~\mathrm {N{\cdot }m} \\[0.7ex]&=~\mathrm {Pa{\cdot }m^{3}} \\[0.7ex]&=~\mathrm {W{\cdot }s} \\[0.7ex]&=~\mathrm {C{\cdot }V} \\[0.7ex]\end{alignedat}}}$$

Symbol Name J joule kg kilogram m metre s second N newton Pa pascal W watt C coulomb V volt

One joule is also equivalent to any of the following:^[6]

• 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, which is 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.^[7]

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), followed the recommendation of 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.^[10]

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.^[11] 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.^[12] This is the definition declared in the modern International System of Units in 1960.^[13]

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).^[14]

Practical examples

One joule represents (approximately):

• The typical energy released as heat by a person at rest every 1/60 s (~16.6667 ms, basal metabolic rate); about 5,000 kJ (1,200 kcal) / day.
• The amount of electricity required to run a 1 W device for 1 s.
• The energy required to accelerate a 1 kg mass at 1 m/s² through a distance of 1 m.
• The kinetic energy of a 2 kg mass travelling at 1 m/s, or a 1 kg mass travelling at 1.41 m/s.
• The energy required to lift an apple up 1 m, assuming the apple has a mass of 101.97 g.
• The heat required to raise the temperature of 0.239 g of water from 0 °C to 1 °C.^[15]
• 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).^[16]
• The food energy (kcal) in slightly more than half of an ordinary-sized sugar crystal (0.102 mg/crystal).

Multiples

For additional examples, see Orders of magnitude (energy).

SI multiples of joule (J)

Submultiples			Multiples
Value	SI symbol	Name	Value	SI symbol	Name
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
10−27 J	rJ	rontojoule	1027 J	RJ	ronnajoule
10−30 J	qJ	quectojoule	1030 J	QJ	quettajoule
Common multiples are in bold face

zeptojoule

160 zeptojoules is about 1 electronvolt.

The minimal energy needed to change a bit of data in computation at around room temperature – approximately 2.75 zJ – is given by the Landauer limit.^{[citation needed]}

nanojoule

160 nanojoule is about the kinetic energy of a flying mosquito.^[17]

microjoule

The Large Hadron Collider (LHC) produces collisions of the microjoule order (7 TeV) per particle.^{[citation needed]}

kilojoule

Nutritional food labels in most countries express energy in kilojoules (kJ).^[18]

One square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.^[19] A human in a sprint has approximately 3 kJ of kinetic energy,^[20] while a cheetah in a 122 km/h (76 mph) sprint has approximately 20 kJ.^[21] One watt-hour, of electricity or any other form of energy, is 3.6 kJ.

megajoule

The megajoule is approximately the kinetic energy of a one megagram (tonne) vehicle moving at 161 km/h (100 mph).^{[citation needed]}

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.^{[citation needed]}

One kilowatt-hour, of electricity or any other form of energy, is 3.6 MJ.

gigajoule

6 gigajoule is about the chemical energy of combusting 1 barrel (159 L) of petroleum.^[22] 2 GJ is about the Planck energy unit. One megawatt-hour, of electricity or any other form of energy, is 3.6 GJ.

terajoule

The terajoule is about 0.278 GWh (which is often used in energy tables). About 63 TJ of energy was released by Little Boy.^[23] The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7700 m/s,^[24] has a kinetic energy of roughly 13 TJ. In 2017, Hurricane Irma was estimated to have a peak wind energy of 112 TJ.^[25][26] One gigawatt-hour, of electricity or any other form of energy, is 3.6 TJ.

petajoule

210 petajoule is about 50 megatons of TNT, which is the amount of energy released by the Tsar Bomba, the largest man-made explosion ever. One terawatt-hour, of electricity or any other form of energy, is 3.6 PJ.

exajoule

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, and the world final energy consumption was 439 EJ in 2021.^[27] One petawatt-hour of electricity, or any other form of energy, is 3.6 EJ.

zettajoule

The zettajoule is somewhat more than the amount of energy required to heat the Baltic Sea by 1 °C, assuming properties similar to those of pure water.^[28] 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.^{[citation needed]}

yottajoule

The yottajoule is a little less than the amount of energy required to heat the Indian Ocean by 1 °C, assuming properties similar to those of pure water.^[28] The thermal output of the Sun is approximately 400 YJ per second.^[29]

Conversions

Main article: Conversion of units of energy

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

• 1.0×10⁸ erg (exactly)
• 6.24151×10¹⁸ eV
• 9.47817×10⁻³ BTU
• 0.737562 ft⋅lb (foot-pound)
• 23.7304 ft⋅pdl (foot-poundal)

Units with exact equivalents in joules include:

• 1 thermochemical calorie = 4.184 J^[30]
• 1 International Table calorie = 4.1868 J^[31]
• 1 W⋅h = 3,600 J; 3.6 kJ
• 1 kW⋅h = 3.6×10^⁶ J; 3.6 MJ
• 1 W⋅s = 1 J
• 1 ton TNT = 4.184 GJ
• 1 foe = 10⁴⁴ J^[32]

Newton-metre and torque

Main article: Newton-metre

In mechanics, the concept of force (in some direction) has a close analogue in the concept of torque (about some angle):^{[citation needed]}

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 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.^[33] The use of newton-metres for torque but joules for energy is helpful to avoid misunderstandings and miscommunication.^[33]

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^{[citation needed]} $${\displaystyle E=\tau \theta \,,}$$

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.^{[citation needed]}

Watt-second

A watt-second (symbol W s or W⋅s) is a derived unit of energy equivalent to the joule.^[34] 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", such as in the rating of photographic electronic flash units. ^[35]

References

1. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 120, ISBN 92-822-2213-6, archived (PDF) from the original on 2021-06-04, retrieved 2021-12-16
2. American Heritage Dictionary of the English Language, Online Edition (2009). Houghton Mifflin Co., hosted by Yahoo! Education.
3. The American Heritage Dictionary, Second College Edition (1985). Boston: Houghton Mifflin Co., p. 691.
4. McGraw-Hill Dictionary of Physics, Fifth Edition (1997). McGraw-Hill, Inc., p. 224.
5. "NIST Guide to the SI, Chapter 4: The Two Classes of SI Units and the SI Prefixes". NIST. 2016-01-28.
6. Halliday, David; Resnick, Robert (1974), Fundamentals of Physics (revised ed.), New York: Wiley, pp. 516–517, ISBN 0471344311
7. "What Is a Joule? - Chemistry Definition". ThoughtCo. Retrieved 2024-04-07.
8. Siemens, Cal Wilhelm (August 1882). Report of the Fifty-Second Meeting of the British Association for the Advancement of Science. Southampton. pp. 1–33. pp. 6–7: 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 1⁄1000th part of the arbitrary unit of a pound of water raised 1° Fahrenheit and the 1⁄4000th 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.
9. Pat Naughtin: A chronological history of the modern metric system, metricationmatters.com, 2009.
10. Proceedings of the International Electrical Congress. New York: American Institute of Electrical Engineers. 1894.
11. CIPM, 1946, Resolution 2, Definitions of electric units. bipm.org.
12. 9th CGPM, Resolution 3: Triple point of water; thermodynamic scale with a single fixed point; unit of quantity of heat (joule)., bipm.org.
13. The International System of Units (PDF) (9th ed.), International Bureau of Weights and Measures, Dec 2022, ISBN 978-92-822-2272-0
14. "SI Redefinition". NIST. 2018-05-11.
15. "Units of Heat – BTU, Calorie and Joule". Engineering Toolbox. Retrieved 2021-06-14.
16. Ristinen, Robert A.; Kraushaar, Jack J. (2006). Energy and the Environment (2nd ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0-471-73989-8.
17. "Physics – CERN". public.web.cern.ch. Archived from the original on 2012-12-13.
18. "You Say Calorie, We Say Kilojoule: Who's Right?". Archived from the original on 2023-05-15. Retrieved 2 May 2017.
19. "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.
20. ⁠1/2⁠ × 70 kg × (10 m/s)² = 3500 J
21. ⁠1/2⁠ × 35 kg × (35 m/s)² = 21400 J
22. "Energy Units – Energy Explained, Your Guide To Understanding Energy – Energy Information Administration". www.eia.gov.
23. 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.
24. "International Space Station Final Configuration" (PDF). European Space Agency. Archived from the original (PDF) on 21 July 2011. Retrieved 18 March 2015.
25. Bonnie Berkowitz; Laris Karklis; Reuben Fischer-Baum; Chiqui Esteban (11 September 2017). "Analysis – How Big Is Hurricane Irma?". Washington Post. Retrieved 2 November 2017.
26. Rathbone, John-Paul; Fontanella-Khan, James; Rovnick, Naomi (11 September 2017). "A weakened Irma unleashes more damage on Florida coast". Financial Times. New York (Rathbone), Miami (Fontanella-Khan), London (Rovnick). ISSN 0307-1766. Archived from the original on 4 August 2024. Retrieved 11 September 2017.
27. World Energy Outlook 2022 (Report). International Energy Agency. 2022. p. 239. Retrieved 7 September 2023.
28. "Volumes of the World's Oceans from ETOPO1". noaa.gov. National Oceanic and Atmospheric Administration. 19 August 2020. Retrieved 8 March 2022.
29. "The Sun". pveducation.org. Retrieved 22 November 2024.
30. 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.
31. Feynman, Richard (1963). "Physical Units". Feynman's Lectures on Physics. Retrieved 2014-03-07.
32. Marc Herant; Stirling A. Colgate; Willy Benz; Chris Fryer (October 25, 1997). "Neutrinos and Supernovae" (PDF). Los Alamos Sciences. Los Alamos National Laboratory. Archived from the original (PDF) on 2009-01-14. Retrieved 2008-04-23.
33. "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.
34. 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 (PDF) from the original on 2021-06-04, retrieved 2021-12-16
35. "What Is A Watt Second?".

External links

• The dictionary definition of joule at Wiktionary

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