Joule
Joule | |
---|---|
Unit system | SI derived unit |
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 |
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 (/ˈdʒuːl/), symbol J, is a derived unit of energy in the International System of Units.[1] 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 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:
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
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.
Confusion with newton metre
In mechanics, the concept of force (in some direction) has a close analog in the concept of torque (about some angle):
Linear | Angular |
---|---|
force | torque |
mass | moment of inertia |
distance | 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 CGPM 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.[5] The use of newton metres for torque and joules for energy is helpful to avoid misunderstandings and miscommunications.[5]
The distinction may be seen also in the fact that energy is a scalar – the dot product of a vector force and a vector displacement. By contrast, torque is a vector – the cross product of a distance vector and a force vector. Torque and energy are related to one another by the equation
where E is energy, τ is (the vector magnitude of) torque, and θ is the angle swept (in radians). Since radians are dimensionless, it follows that torque and energy have the same dimensions.
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)
|
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) 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 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] 2 GJ is about the Planck energy unit.
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 latm (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
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png)
- Conversion of units of energy
- Orders of magnitude (energy)
- Fluence
- International System of Units
- Watt second
Notes and references
- ^ 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
- ^ American Heritage Dictionary of the English Language, Online Edition (2009). Houghton Mifflin Co., hosted by Yahoo! Education.
- ^ The American Heritage Dictionary, Second College Edition (1985). Boston: Houghton Mifflin Co., p. 691.
- ^ McGraw-Hill Dictionary of Physics, Fifth Edition (1997). McGraw-Hill, Inc., p. 224.
- ^ 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.
- ^ "How much is 100 grams?". HealthAliciousNess. Retrieved 2016-03-11.
- ^ "Units of Heat - BTU, Calorie and Joule". Engineeringtoolbox.com. Retrieved 2013-09-16.
- ^ 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.
- ^ Ristinen, Robert A.; Kraushaar, Jack J. (2006). Energy and the Environment (2nd ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0-471-73989-8.
- ^ CERN - Glossary
- ^ "Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". Retrieved 2005-10-05.
- ^ IRS publication
- ^ 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.
- ^ "International Space Station Final Configuration" (PDF). European Space Agency. Archived from the original (PDF) on 21 July 2011. Retrieved 18 March 2015.
- ^ 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.
- ^ Feynman, Richard (1963). "Physical Units". Feynman's Lectures on Physics. Retrieved 2014-03-07.