# Joule

Joule
 Joule Unit system: SI derived unit Unit of... Energy Symbol: J Named after: James Prescott Joule Unit conversions 1 J in... is equal to... SI base units 1 kg·m2/s2 CGS units 1×107 erg kilocalories 2.39×10−4 kcal

The joule ( /ˈl/ or /ˈl/); symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended (or work done) in applying a force of one newton through a distance of one metre (1 newton metre or N·m), or in passing an electric current of one ampere through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).[1][2][3]

In terms firstly of base SI units and then in terms of other SI units:

$\rm J = {}\rm \frac{kg \cdot m^2}{s^2} = N \cdot m = \rm Pa \cdot m^3={}\rm W \cdot s$

where N is the newton, m is the metre, kg is the kilogram, s is the second, Pa is the pascal, and W is the watt.

One joule can also be defined as:

## Usage

This SI unit is named after James Prescott Joule. As with every SI unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (J). When an SI unit is spelled out in English, it should always begin with a lower case letter (joule), except where any word would be capitalized, such as at the beginning of a sentence or in capitalized material such as a title. Note that "degree Celsius" conforms to this rule because the "d" is lowercase. —Based on The International System of Units, section 5.2.

## Confusion with newton metre

Although the joule has the same dimensions as the newton-metre (1 J = 1 N·m = 1 kg·m2·s−2), these units are not interchangeable as the newton-metre (N·m) is the unit of torque and joules the unit of energy.[4] Torque and energy are related to each other using the equation

$E= \tau \theta\$
where E is the energy, τ is magnitude of the torque, and θ is the angle moved (in radians). Since radians are dimensionless, it follows that torque and energy have the same dimensions.

The use of newton-metres for torque and joules for energy is useful in helping avoid misunderstandings and miscommunications.[4]

Torque and energy have the same dimension because both torque and work (a type of energy) can be calculated by multiplying a force by a distance. However, the details are quite different in the two cases. For torque, the multiplication of force and distance is a vector cross product, while for work it is a dot product. Also, for torque, the distance involved is the length of the lever arm, while for energy it is the distance traveled by the object undergoing the force.

## Practical examples

One joule in everyday life is approximately:

• the energy required to lift a small apple one metre straight up. (A mass of about 102 g = 19.81 kg)
• the energy released when that same apple falls one metre to the ground.
• the energy released as heat by a person at rest, every 1/60th of a second.[5]
• the kinetic energy of a 50 kg human moving very slowly (0.2 m/s).
• the kinetic energy of a tennis ball moving at 23 km/h (14 mph).[6]

## Multiples

For additional examples, see: Orders of magnitude (energy)
Submultiples Multiples Value 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

### Nanojoule

The nanojoule (nJ) is equal to one billionth of one joule. One nanojoule is about 1/160 of the kinetic energy of a flying mosquito.[7]

### Microjoule

The microjoule (μJ) is equal to one millionth of one joule. The Large Hadron Collider (LHC) is expected to produce collisions on the order of 1 microjoule (7 TeV) per particle.

### Millijoule

The millijoule (mJ) is equal to one thousandth of one joule.

### Kilojoule

The kilojoule (kJ) is equal to one thousand (103) joules. Food labels in some countries express food energy in kilojoules.

One kilojoule per second (1000 watts) is approximately the amount of solar radiation received by one square metre of the Earth in full daylight.[8]

### Megajoule

The megajoule (MJ) is equal to one million (106) joules, or approximately the kinetic energy of a one-tonne vehicle moving at 160 km/h (100 mph).

Because 1 watt times one second equals one joule, 1 kilowatt-hour is 1000 watts times 3600 seconds, or 3.6 megajoules.

### Gigajoule

The gigajoule (GJ) is equal to one billion (109) joules. Six gigajoules is about the amount of potential chemical energy in a barrel of oil, when combusted.[9]

### Terajoule

The terajoule (TJ) is equal to one trillion (1012) joules. About 63 terajoules were released by the atomic bomb that exploded over Hiroshima.[10] The International Space Station, at completion, with a mass of 450,000kg and orbital velocity of 7.7 km/s,[11] will have a kinetic energy of roughly 13 terajoules.

### Petajoule

The petajoule (PJ) is equal to 1015 joules. 210 PJ is equivalent to about 50 megatons of TNT. This is the amount of energy released by the Tsar Bomba, the largest man-made nuclear explosion ever.

### Exajoule

The exajoule (EJ) is equal to 1018 joules. The 2011 Tōhoku earthquake and tsunami in Japan had 1.41 EJ of energy according to its 9.0 on the moment magnitude scale. Energy in the United States used per year is roughly 94 EJ.

### Zettajoule

The zettajoule (ZJ) is equal to 1021 joules. Annual global energy consumption is approximately 0.5 ZJ

### Yottajoule

The yottajoule (YJ) is equal to 1024 joules. This is approximately the amount of energy required to heat the entire volume of water on Earth by 1 °Celsius.

## Conversions

1 joule is equal to:

• 1×107 ergs (exactly)
• 6.24150974×1018 eV (electronvolts)
• 0.2390 cal (thermochemical gram calories or small calories)
• 2.3901×10−4 kcal (thermochemical kilocalories, kilogram calories, large calories or food calories)
• 9.4782×10−4 BTU (British thermal unit)
• 0.7376 ft·lbf (foot-pounds force)
• 23.7 ft·pdl (foot-poundals)
• 2.7778×10−7 kilowatt-hour
• 2.7778×10−4 watt-hour
• 9.8692×10−3 litre-atmosphere
• 11.1265 femtograms (mass-energy equivalence)
• 1×10−44 foe (exactly)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J[12]
• 1 International Table calorie = 4.1868 J[12]
• 1 watt hour = 3600 J
• 1 kilowatt hour = 3.6×106 J (or 3.6 MJ)
• 1 watt second = 1 J
• 1 ton TNT = 4.184 GJ

## References

1. ^ American Heritage Dictionary of the English Language, Online Edition (2009). Houghton Mifflin Co., hosted by Yahoo! Education.
2. ^ The American Heritage Dictionary, Second College Edition (1985). Boston: Houghton Mifflin Co., p. 691.
3. ^ McGraw-Hill Dictionary of Physics, Fifth Edition (1997). McGraw-Hill, Inc., p. 224.
4. ^ a b From the official SI website: "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."
5. ^ This is called the basal metabolic rate. It corresponds to about 1200 kilocalories (also called dietary calories) per day. "At rest" means awake but inactive.
6. ^ Ristinen, Robert A.; Kraushaar, Jack J. (2006). Energy and the Environment (2nd ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0471739898.
7. ^ CERN - Glossary
8. ^
9. ^ IRS publication
10. ^ Los Alamos National Laboratory report LA-8819, The yields of the Hiroshima and Nagasaki nuclear explosions by John Malik, September 1985. Available online at http://www.mbe.doe.gov/me70/manhattan/publications/LANLHiroshimaNagasakiYields.pdf
11. ^ International Space Station Fact Sheet
12. ^ a b 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.

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### Look at other dictionaries:

• joule — joule …   Dictionnaire des rimes

• joule — [ ʒul ] n. m. • 1882; nom d un physicien ♦ Phys. Unité de mesure de travail, d énergie et de quantité de chaleur (symb. J), correspondant au travail d une force d un newton se déplaçant d un mètre dans la direction de la force. Une calorie vaut… …   Encyclopédie Universelle

• Joule — [dʒ̮u:l], das; [s], : Maßeinheit für die Energie (z. B. des Energieumsatzes des menschlichen Körpers; 1 Kalorie = 4,186 Joule): ein Glas Vollmilch hat 167 Joule. * * * Joule 〈[dʒaʊl] od. [ʒu:l] n.; s, ; 〉 Maßeinheit, SI Einheit der Energie,… …   Universal-Lexikon

• JOULE (J. P.) — Joule compte parmi les plus importants fondateurs de la thermodynamique. Parvenu en 1843 à donner une formulation stricte du principe de la conservation de l’énergie, il entreprit de quantifier les relations entre chaleur et travail au moyen… …   Encyclopédie Universelle

• joule — JOULE, jouli, s.m. Unitate de măsură a energiei, egală cu lucrul mecanic efectuat de forţa de un newton, când punctul ei de aplicaţie se deplasează cu un metru în direcţia şi în sensul forţei. [pr.: jul] – Din fr., enlg. joule. Trimis de cata, 13 …   Dicționar Român

• joule — (j[=oo]l), n. [From the distinguished English physicist, James Prescott Joule (1818 1889).] (Physics.) A unit of work which is equal to 10^{7} ergs (the unit of work in the C. G. S. system of units), and is equivalent to one watt second, the… …   The Collaborative International Dictionary of English

• Joule — se refiere a: Julio o joule (con símbolo J), unidad del Sistema Internacional para energía y trabajo. James Prescott Joule, físico inglés, en honor al cual se denominó la unidad anterior. El efecto Joule, relativo a la energía que disipa un… …   Wikipedia Español

• joule — [dʒuːl ǁ dʒuːl, dʒaʊl] written abbreviation J noun [countable] a unit of energy, work done, or quantity of heat * * * joule UK US /dʒuːl/ noun [C] (WRITTEN ABBREVIATION J) MEASURES ► …   Financial and business terms

• Joule — [von DIN u. anderen Organisationen festgelegte Aussprache nur dʒu:l, sonst auch dʒaul] das; [s], <nach dem engl. Physiker James Prescott Joule, 1818 1889> Maßeinheit für die Energie (z. B. den Energieumsatz des Körpers; 1 cal = 4,186… …   Das große Fremdwörterbuch

• Joule — 〈 [dʒaʊl] od. [ʒu:l] n.; Gen.: od. s, Pl.: ; Zeichen: J〉 Maßeinheit der Energie, 1 J = 1 Newtonmeter (Nm) = 1 Wattsekunde (Ws) = 0,102 Kilopondmeter (kpm) = 0,238 Kalorien (cal) = 1 m2kg/s2 [Etym.: nach dem engl. Physiker James Prescott Joule,… …   Lexikalische Deutsches Wörterbuch

• Joule — [nach DIN: ds̶c̶h̶u̱l, sonst auch: ds̶c̶h̶a̲u̲l; nach dem engl. Physiker J.JouleP. Joule, 1818 1889] s; [s], : Maßeinheit der Arbeit, Energie und Wärmemenge (z. B. für den Energiewert der aufgenommenen Nahrung; dafür bisher ↑Kalorie); Zeichen J… …   Das Wörterbuch medizinischer Fachausdrücke