# Joule

Last updated

joule
Unit system SI
Unit of energy
SymbolJ
Named after James Prescott Joule
Conversions
1 J in ...... is equal to ...
SI base units     kgm 2s −2
CGS units    1×107 erg
watt-seconds    1  Ws
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 ( JOOL, also non-standard JOWL; [1] [2] [3] [4] [5] [ disputed ] symbol: J) is the unit of energy in the International System of Units (SI). [6] It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied. 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). [7] [8] [9]

## Definition

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

{\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}}}
SymbolMeaning
Jjoule
kg kilogram
m metre
s second
N newton
Pa pascal
W watt
C coulomb
V volt

One joule can also be defined by any of the following:

• 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.

## 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), is due to 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." [10]

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). [11] 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. [12]

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. [13] 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. [14] This definition was the direct precursor of the joule as adopted in the modern International System of Units in 1960.

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).

## Practical examples

One joule represents (approximately):

• 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 a medium-sized tomato up 1 metre (3 ft 3 in), assuming the tomato has a mass of 101.97 grams (3.597 oz).
• The heat required to raise the temperature of 0.239 g of water from 0 °C to 1 °C, or from 32 °F to 33.8 °F. [15]
• The typical energy released as heat by a person at rest every 1/60 s (17  ms ). [note 1]
• 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 a sugar crystal (0.102  mg /crystal).

## Multiples

Submultiples Multiples Value SI 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
Zeptojoule
160 zeptojoule is about one electronvolt.
The minimal energy needed to change a bit at around room temperature – approximately 2.75 zJ – is given by the Landauer limit.
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.
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 is 3.6 kilojoules.
Megajoule
The megajoule is approximately the kinetic energy of a one megagram (tonne) vehicle moving at 161  km/h (100 mph).
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 .
One kilowatt-hour of electricity is 3.6 megajoules.
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 is 3.6 gigajoules.
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 is 3.6 terajoules.
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 is 3.6 petajoules.
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. One petawatt-hour of electricity is 3.6 exajoules.
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. [27] 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.
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. [27] The thermal output of the Sun is approximately 400 YJ per second.

## Conversions

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

• 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 (foot-pound)
• 23.7  ft⋅pdl (foot-poundal)
• 2.7778×10−7  kW⋅h (kilowatt-hour)
• 2.7778×10−4 W⋅h (watt-hour)
• 9.8692×10−3 latm (litre-atmosphere)
• 11.1265×10−15  g (by way of mass–energy equivalence)
• 10−44  foe (exactly)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J [28]
• 1 International Table calorie = 4.1868 J [29]
• 1 W⋅h = 3600 J (or 3.6 kJ)
• 1 kW⋅h = 3.6×106 J (or 3.6 MJ)
• 1 W⋅s = 1 J
• 1  ton TNT = 4.184 GJ

## Newton-metre and torque

In mechanics, the concept of force (in some direction) has a close analogue in the concept of torque (about some angle):

LinearAngular
ForceTorque
Mass Moment of inertia
DisplacementAngle

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. [30] The use of newton-metres for torque and joules for energy is helpful to avoid misunderstandings and miscommunications. [30]

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

${\displaystyle E=\tau \theta \,,}$

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.

## Watt-second

A watt-second (symbol W s or W⋅s) is a derived unit of energy equivalent to the joule. [31] 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. [32]

## Notes

1. 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.

## Related Research Articles

The British thermal unit is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United States customary units. The modern SI unit for heat energy is the joule (J); one BTU equals about 1055 J.

The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of one kilogram of water by one degree Celsius. The small calorie or gram calorie was defined as the amount of heat needed to cause the same increase in one gram of water. Thus, 1 large calorie is equal to 1000 small calories.

In physics, energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J).

In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called activity. Power is a scalar quantity.

The joule per mole is the unit of energy per amount of substance in the International System of Units (SI), such that energy is measured in joules, and the amount of substance is measured in moles.

James Prescott Joule was an English physicist, mathematician and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work. This led to the law of conservation of energy, which in turn led to the development of the first law of thermodynamics. The SI derived unit of energy, the joule, is named after him.

A kilowatt-hour is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ). Kilowatt-hours are a common billing unit for electrical energy delivered to consumers by electric utilities.

Food energy is chemical energy that animals derive from their food to sustain their metabolism, including their muscular activity.

Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).

The newton-metre is the unit of torque in the International System of Units (SI). One newton-metre is equal to the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one metre long. The nonstandard notation Nm occurs in some fields.

The foot-pound force is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a force of one pound-force (lbf) through a linear displacement of one foot. The corresponding SI unit is the joule.

The kilocalorie per mole is a unit to measure an amount of energy per number of molecules, atoms, or other similar particles. It is defined as one kilocalorie of energy per one mole of substance. The unit symbol is written kcal/mol or kcal⋅mol−1. As typically measured, one kcal/mol represents a temperature increase of one degree Celsius in one liter of water resulting from the reaction of one mole of reagents.

The following outline is provided as an overview of and topical guide to energy:

Specific energy or massic energy is energy per unit mass. It is also sometimes called gravimetric energy density, which is not to be confused with energy density, which is defined as energy per unit volume. It is used to quantify, for example, stored heat and other thermodynamic properties of substances such as specific internal energy, specific enthalpy, specific Gibbs free energy, and specific Helmholtz free energy. It may also be used for the kinetic energy or potential energy of a body. Specific energy is an intensive property, whereas energy and mass are extensive properties.

Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard suffixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively.

TNT equivalent is a convention for expressing energy, typically used to describe the energy released in an explosion. The tonne of TNT is a unit of energy defined by that convention to be 4.184 gigajoules, which is the approximate energy released in the detonation of a metric ton of TNT. In other words, for each gram of TNT exploded, 4.184 kilojoules of energy is released.

Energy is defined via work, so the SI unit of energy is the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton metre and, in terms of SI base units

The energy efficiency in transport is the useful travelled distance, of passengers, goods or any type of load; divided by the total energy put into the transport propulsion means. The energy input might be rendered in several different types depending on the type of propulsion, and normally such energy is presented in liquid fuels, electrical energy or food energy. The energy efficiency is also occasionally known as energy intensity. The inverse of the energy efficiency in transport, is the energy consumption in transport.

A kinetic energy weapon is a weapon based solely on a projectile's kinetic energy instead of an explosive or any other kind of payload.

The watt is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Watt (1736–1819), an 18th-century Scottish inventor, mechanical engineer, and chemist who improved the Newcomen engine with his own steam engine in 1776. Watt's invention was fundamental for the Industrial Revolution.

## References

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10. "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 11000th part of the arbitrary unit of a pound of water raised 1° Fahrenheit and the 14000th 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."Carl Wilhelm Siemens, Report of the Fifty-Second Meeting of the British Association for the Advancement of Science. S. 6 f.
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18. ${\displaystyle {\tfrac {1}{2}}\cdot 70~{\text{kg}}\cdot \left(10~{\text{m/s}}\right)^{2}=3500~{\text{J}}}$
19. ${\displaystyle {\tfrac {1}{2}}\cdot 35~{\text{kg}}\cdot \left(35~{\text{m/s}}\right)^{2}=21,400~{\text{J}}}$
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• The dictionary definition of joule at Wiktionary