Joule

The joule (Template:IPAc-en Template:Respell, or Template:IPAc-en Template:Respell; symbol: J) is the unit of energy in the International System of Units (SI).<ref>Template:SIbrochure8th</ref> In terms of SI base units, one joule corresponds to one kilogram-metre squared per second squared Template:Nowrap One joule is equal to the amount of work done when a force of one newton displaces a body through a distance of one metre in the direction of that force. 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).<ref>American Heritage Dictionary of the English Language, Online Edition (2009). Houghton Mifflin Co., hosted by Yahoo! Education.</ref><ref>The American Heritage Dictionary, Second College Edition (1985). Boston: Houghton Mifflin Co., p. 691.</ref><ref>McGraw-Hill Dictionary of Physics, Fifth Edition (1997). McGraw-Hill, Inc., p. 224.</ref>

Definition

According to the International Bureau of Weights and Measures the joule is defined as "the work done when the point of application of 1 MKS unit of force [newton] moves a distance of 1 metre in the direction of the force."<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

In terms of SI base units and in terms of SI derived units with special names, the joule is defined as<ref>Template:Cite book</ref>

<math display=block>\begin{alignat}{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{alignat}</math>

Symbol Name J joule kg kilogram m metre s second N newton Pa pascal W watt C coulomb V volt

One joule is also equivalent to any of the following:<ref>Template:Citation</ref>

• 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.

Template:SI unit lowercase<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

History

Template:Multiple image 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 Template:Val. The naming of the unit in honour of James Prescott Joule (1818–1889), at the time retired and aged 63, followed the recommendation of 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.<ref>Template:Cite conference</ref>{{#if:|{{#if:|}}

— {{#if:|, in }}Template:Comma separated entries

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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).<ref>Pat Naughtin: A chronological history of the modern metric system, metricationmatters.com, 2009.</ref> 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.<ref>Template:Cite book</ref>

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.<ref>CIPM, 1946, Resolution 2, Definitions of electric units. bipm.org.</ref> 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.<ref>9th CGPM, Resolution 3: Triple point of water; thermodynamic scale with a single fixed point; unit of quantity of heat (joule)., bipm.org.</ref> This is the definition declared in the modern International System of Units in 1960.<ref>Template:SIbrochure</ref>

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).<ref>Template:Cite journal</ref>

Practical examples

One joule represents (approximately):

• The typical energy released as heat by a person at rest every 1/60 s (~Template:Val, basal metabolic rate); about Template:Convert / day.
• The amount of electricity required to run a Template:Val device for Template:Val.
• The energy required to accelerate a Template:Val mass at Template:Val through a distance of Template:Val.
• The kinetic energy of a Template:Val mass travelling at Template:Val, or a Template:Val mass travelling at Template:Val.
• The energy required to lift an apple up 1 m, assuming the apple has a mass of 101.97 g.
• The heat required to raise the temperature of 0.239 g of water from 0 °C to 1 °C.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• The kinetic energy of a Template:Val human moving very slowly (Template:Convert).
• The kinetic energy of a Template:Val tennis ball moving at Template:Convert.<ref>Template:Cite book</ref>
• The food energy (kcal) in slightly more than half of an ordinary-sized sugar crystal (Template:Val/crystal).

Multiples

Template:Vanchor

Template:Convert.Template:Paragraph The minimal energy needed to change a bit of data in computation at around room temperature – approximately Template:Val – is given by the Landauer limit.Template:Citation needed

Template:Vanchor

Template:Val is about the kinetic energy of a flying mosquito.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

Template:Vanchor

The Large Hadron Collider (LHC) produces collisions of the microjoule order (7 TeV) per particle.Template:Citation needed

Template:Vanchor

Nutritional food labels in most countries express energy in kilojoules (kJ).<ref name="Cal vs kJ">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>Template:Paragraph One square metre of the Earth receives about Template:Val of solar radiation every second in full daylight.<ref name=TSI>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> A human in a sprint has approximately 3 kJ of kinetic energy,<ref>Template:Sfrac × 70 kg × (10 m/s)² = 3500 J</ref> while a cheetah in a Template:Val (76 mph) sprint has approximately 20 kJ.<ref>Template:Sfrac × 35 kg × (35 m/s)² = Template:Val</ref> Template:Convert.

Template:Vanchor

The megajoule is approximately the kinetic energy of a one megagram (tonne) vehicle moving at Template:Val (100 mph).Template:Citation neededTemplate:Paragraph The energy required to heat Template:Val of liquid water at constant pressure from Template:Convert to Template:Convert is approximately Template:Val.Template:Citation neededTemplate:Paragraph Template:Convert.

Template:Vanchor

Template:Val is about the chemical energy of combusting Template:Convert of petroleum.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> 2 GJ is about the Planck energy unit. Template:Convert.

Template:Vanchor

The terajoule is about Template:Val (which is often used in energy tables). About Template:Val of energy was released by Little Boy.<ref name="hironaga">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> The International Space Station, with a mass of approximately Template:Val and orbital velocity of Template:Val,<ref name="iss">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> has a kinetic energy of roughly Template:Val. In 2017, Hurricane Irma was estimated to have a peak wind energy of Template:Val.<ref>Template:Cite news</ref><ref>Template:Cite news</ref> Template:Convert.

Template:Vanchor

Template:Val is about Template:Val of TNT, which is the amount of energy released by the Tsar Bomba, the largest man-made explosion ever. Template:Convert.

Template:Vanchor

The 2011 Tōhoku earthquake and tsunami in Japan had Template:Val of energy according to its rating of 9.0 on the moment magnitude scale. Yearly U.S. energy consumption amounts to roughly Template:Val, and the world final energy consumption was Template:Val in 2021.<ref>Template:Cite report</ref> One petawatt-hour of electricity, or any other form of energy, is Template:Convert.

Template:Vanchor

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.<ref name="Volumes of the World's Oceans">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> Human annual world energy consumption is approximately Template:Val. The energy to raise the temperature of Earth's atmosphere 1 °C is approximately Template:Val.Template:Citation needed

Template:Vanchor

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.<ref name="Volumes of the World's Oceans" /> The thermal output of the Sun is approximately Template:Val per second.<ref name="pve">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

Conversions

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} 1 joule is equal to (approximately unless otherwise stated):

• Template:Convert (exactly)
• Template:Convert
• Template:Convert
• Template:Convert (foot-pound)
• Template:Convert (foot-poundal)

Units with exact equivalents in joules include:

• 1 thermochemical calorie = 4.184Template:NbspJ<ref name=FAO>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.</ref>
• 1 International Table calorie = 4.1868Template:NbspJ<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

• 1Template:NbspW⋅h = Template:Convert
• 1Template:NbspkW⋅h = Template:Convert
• 1Template:NbspW⋅s = Template:Val
• 1Template:Nbspton TNT = Template:Convert
• 1Template:Nbspfoe = Template:Val<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

Newton-metre and torque

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} In mechanics, the concept of force (in some direction) has a close analogue in the concept of torque (about some angle):<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Linear	Angular
Force	Torque
Mass	Moment of inertia
Displacement	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 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.<ref name="BIPM2" /> The use of newton-metres for torque but joules for energy is helpful to avoid misunderstandings and miscommunication.<ref name="BIPM2">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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 equationTemplate:Citation needed <math display="block">E = \tau \theta\, ,</math>

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.Template:Citation needed

Watt-second

A watt-second (symbol W s or W⋅s) is a derived unit of energy equivalent to the joule.<ref>Template:SIbrochure8th</ref> 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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

External links

• Template:Wiktionary inline