# Joule

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 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 kilowatt hours 2.78×10−7 kW⋅h kilocalories 2.39×10−4 kcal BTUs 9.48×10−4 BTU electronvolts 6.24×1018 eV

The joule ( or sometimes ), symbol J, is a derived unit of energy, work, or amount of heat in the International System of Units.[1] 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).[2][3][4]

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

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

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.

One joule can also be defined as:

## Usage

This SI unit is named after James Prescott Joule. As with every International System of Units (SI) unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (J). However, when an SI unit is spelled out in English, it should always begin with a lower case letter (joule), except in a situation where any word in that position 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

In angular mechanics, torque is analogous to the linear Newtonian mechanics parameter of force, moment of inertia to mass, and angle to distance. Energy is the same in both systems. Thus, although the joule has the same dimensions as the newton-meter (1 J = 1 N·m = 1 kg·m2·s−2), these units 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 the unit of torque is known as the newton-metre (N·m) - a compound name derived from its constituent parts.[5] Torque and energy are related to each other using the equation

$E= \tau \theta\$

where E is the energy, τ is 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.[5] Another solution to this problem is to name the unit of angle, such that the unit of torque is called joule per radian.

An additional solution is to realize that joules are scalars - they are the dot product of a vector force and a vector displacement whereas torque is a vector. Torque is the cross product of a distance vector and a force vector. Drawing a traditional vector arrow over "newton-meter" in a torque resolves the ambiguity.

## Practical examples

One joule in everyday life represents approximately:

• the energy required to lift a small apple (with a mass of approximately 100 g) vertically through one meter of air.
• the energy released when that same apple falls one meter to the ground.
• the heat required to raise the temperature of 1 g of water by 0.24 K.[6]
• the typical energy released as heat by a person at rest, every 1/60th of a second.[7]
• 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 (6.4 m/s).[8]
• the kinetic energy of 1 kg moving √2 m/s.

Since the joule is also a watt-second and the common unit for electricity sales to homes is the kWh (kilowatt-hour), a kWh is thus 1000 (kilo) x 3600 seconds = 3.6 MJ (megajoules).

## 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.[9]

### 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 a joule.

### Kilojoule

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

One kilojoule per second (1 kilowatt) is approximately the amount of solar radiation received by one square metre of the Earth in full daylight.[10]

### Megajoule

The megajoule (MJ) is equal to one million (106) joules, or approximately the kinetic energy of a one-ton 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.[11]

### Terajoule

The terajoule (TJ) is equal to one trillion (1012) joules. About 63 terajoules were released by the atomic bomb that exploded over Hiroshima.[12] The International Space Station, with a mass of approximately 450,000 kg and orbital velocity of 7.7 km/s,[13] has a kinetic energy of roughly 13.34 terajoules.

### Petajoule

The petajoule (PJ) is equal to one quadrillion (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 one quintillion (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 one sextillion (1021) joules. Annual global energy consumption is approximately 0.5 ZJ.

### Yottajoule

The yottajoule (YJ) is equal to one septillion (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:

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J[14]
• 1 International Table calorie = 4.1868 J[15]
• 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

## Notes and references

1. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 120, ISBN 92-822-2213-6
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. ^ 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."
6. ^ "Units of Heat - BTU, Calorie and Joule". Engineeringtoolbox.com. Retrieved 2013-09-16.
7. ^ 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.
8. ^ Ristinen, Robert A.; Kraushaar, Jack J. (2006). Energy and the Environment (2nd ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0-471-73989-8.
9. ^ CERN - Glossary
10. ^ "Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". Retrieved 2005-10-05.
11. ^ IRS publication
12. ^ 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
13. ^ International Space Station Fact Sheet
14. ^ 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.
15. ^ Feynman, Richard (1963). "Physical Units". Feynman's Lectures on Physics. Retrieved 2014-03-07.