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	kg⋅m^2⋅s^-2
CGS units	1×10^7 erg
kilowatt hours	2.78×10^−7 kW⋅h
kilocalories (thermochemical)	2.390×10^−4 kcalth
BTUs	9.48×10^−4 BTU
electronvolts	6.24×10^18 eV

The joule (/ˈdʒuːl/), symbol J, is a derived unit of energy in the International System of Units.^[1] It is equal to the energy transferred (or work done) to an object when a force of one newton acts on that object in the direction of its 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).^[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:

• 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.

Usage

This SI unit is named after James Prescott Joule. As with every International System of Units (SI) unit named for 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 material using title case. 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-metre (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]

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-metre" in a torque resolves the ambiguity.

Practical examples

One joule in everyday life represents approximately:

• The energy required to lift a medium-size tomato (100 g) 1 meter vertically from the surface of the Earth.^[6]
• The energy released when that same tomato falls back down to the ground.
• The energy required to accelerate a 1 kg mass at 1 m·s⁻² through a 1 m distance in space.
• The heat required to raise the temperature of 1 g of water by 0.24 K.^[7]
• The typical energy released as heat by a person at rest every 1/60 second (approximately 17 ms).^[8]
• 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).^[9]
• 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 watt 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 (kilo) watt × 3600 seconds = 3.6 megajoules (MJ).

Multiples

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

SI multiples for joule (J) Submultiples Multiples Value SI symbol Name Value SI symbol Name 10^−1 J dJ decijoule 10^1 J daJ decajoule 10^−2 J cJ centijoule 10^2 J hJ hectojoule 10^−3 J mJ millijoule 10^3 J kJ kilojoule 10^−6 J µJ microjoule 10^6 J MJ megajoule 10^−9 J nJ nanojoule 10^9 J GJ gigajoule 10^−12 J pJ picojoule 10^12 J TJ terajoule 10^−15 J fJ femtojoule 10^15 J PJ petajoule 10^−18 J aJ attojoule 10^18 J EJ exajoule 10^−21 J zJ zeptojoule 10^21 J ZJ zettajoule 10^−24 J yJ yoctojoule 10^24 J YJ yottajoule Common multiples are in bold face

Zeptojoule

The zeptojoule (zJ) is equal to one sextillionth (10⁻²¹) of one joule. 160 zeptojoules is equivalent to one electronvolt.

Nanojoule

The nanojoule (nJ) is equal to one billionth (10⁻⁹) of one joule. One nanojoule is about 1/160 of the kinetic energy of a flying mosquito.^[10]

Microjoule

The microjoule (μJ) is equal to one millionth (10⁻⁶) of one joule. The Large Hadron Collider (LHC) produce collisions on the order of 1 microjoule (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 some countries express energy in kilojoules (kJ).

One square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.^[11]

Megajoule

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

One kilowatt hour of electricity is 3.6 megajoules.

Gigajoule

The gigajoule (GJ) is equal to one billion (10⁹) joules. 6 GJ is about the amount of potential chemical energy in 160 L (approximately one US standard barrel) of oil, when combusted.^[12]

Terajoule

The terajoule (TJ) is equal to one trillion (10¹²) joules. About 63 TJ of energy was released by the atomic bomb that exploded over Hiroshima.^[13] The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7.7 km/s,^[14] has a kinetic energy of roughly 13 TJ.

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. The human 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 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:

• 1×10⁷ 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
• 23.7 ft·pdl (foot-poundal)
• 2.7778×10⁻⁷ kilowatt-hour
• 2.7778×10⁻⁴ watt-hour
• 9.8692×10⁻³ l·atm (litre-atmosphere)
• 11.1265×10⁻¹⁵ gram (by way of mass-energy equivalence)
• 1×10⁻⁴⁴ foe (exactly)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J^[15]
• 1 International Table calorie = 4.1868 J^[16]
• 1 watt hour = 3600 J (or 3.6 kJ)
• 1 kilowatt hour = 3.6×10⁶ J (or 3.6 MJ)
• 1 watt second = 1 J
• 1 ton TNT = 4.184 GJ

See also

• Conversion of units of energy
• Orders of magnitude (energy)
• Fluence
• International System of Units
• Watt second

Notes and 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
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. "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.
6. "How much is 100 grams?". HealthAliciousNess. Retrieved 2016-03-11.
7. "Units of Heat - BTU, Calorie and Joule". Engineeringtoolbox.com. Retrieved 2013-09-16.
8. 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.
9. Ristinen, Robert A.; Kraushaar, Jack J. (2006). Energy and the Environment (2nd ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0-471-73989-8.
10. CERN - Glossary
11. "Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". Retrieved 2005-10-05.
12. IRS publication
13. 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.
14. "International Space Station Final Configuration" (PDF). European Space Agency. Archived from the original (PDF) on 21 July 2011. Retrieved 18 March 2015.
15. 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.
16. Feynman, Richard (1963). "Physical Units". Feynman's Lectures on Physics. Retrieved 2014-03-07.