The joule ( /ˈdʒuːl/ or sometimes /ˈdʒaʊl/); symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended (or work done) in applying a force of one newton through a distance of one meter (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).^[1][2][3]

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

Failed to parse (Missing texvc executable; please see math/README to configure.): \rm J = {}\rm \frac{kg \cdot m^2}{s^2} = N \cdot m = \rm Pa \cdot m^3={}\rm W \cdot s

where N is the newton, m is the meter, kg is the kilogram, s is the second, Pa is the pascal, and W is the watt.

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). This relationship can be used to define the watt.

Usage[link]

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). When an SI unit is spelled out in English, it should always begin with a lower case letter (joule), except where any word 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[link]

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 as the newton-metre (N·m) is the unit of torque and joules the unit of energy.^[4] Torque and energy are related to each other using the equation

Failed to parse (Missing texvc executable; please see math/README to configure.): E= \tau \theta\

where E is the energy, τ is magnitude of 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.^[4]

Torque and energy have the same dimension because both torque and work (a type of energy) can be calculated by multiplying a force by a distance. However, the details are quite different in the two cases. For torque, the multiplication of force and distance is a vector cross product, while for work it is a dot product. Also, for torque, the distance involved is the length of the lever arm, while for energy it is the distance traveled by the object undergoing the force.

Practical examples[link]

One joule in everyday life is approximately:

• the energy required to lift a small apple one metre straight up. (A mass of about 102 g = ¹⁄_9.81 kg)
• the energy released when that same apple falls one metre to the ground.
• the energy released as heat by a person at rest, every 1/60th of a second.^[5]
• 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 (14 mph).^[6]

Multiples[link]

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

Nanojoule[link]

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.^[7]

Microjoule[link]

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[link]

The millijoule (mJ) is equal to one thousandth of one joule.

Kilojoule[link]

The kilojoule (kJ) is equal to one thousand (10³) joules. Outside of North America, nutrition facts labels are markedly different from those in the United States; in particular, energy is usually expressed in standard kilojoules (kJ) rather than Calories.

One kilojoule per second (1000 watts) is approximately the amount of solar radiation received by one square metre of the Earth in full daylight.^[8]

Megajoule[link]

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

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.^[9]

Terajoule[link]

The terajoule (TJ) is equal to one trillion (10¹²) joules. About 63 terajoules were released by the atomic bomb that exploded over Hiroshima.^[10] The International Space Station, at completion, with a mass of 450,000kg and orbital velocity of 7.7 km/s,^[11] will have a kinetic energy of roughly 13 terajoules.

Petajoule[link]

The petajoule (PJ) is equal to 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[link]

The exajoule (EJ) is equal to 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[link]

The zettajoule (ZJ) is equal to 10²¹ joules. Annual global energy consumption is approximately 0.5 ZJ

Yottajoule[link]

The yottajoule (YJ) is equal to 10²⁴ joules. This is approximately the amount of energy required to heat the entire volume of water on Earth by 1 °Celsius.

Conversions[link]

1 joule is equal to:

• 1×10⁷ ergs (exactly)
• 6.24150974×10¹⁸ eV (electronvolts)
• 0.2390 cal (thermochemical gram calories or small calories)
• 2.3901×10⁻⁴ kcal (thermochemical kilocalories, kilogram calories, large calories or food calories)
• 9.4782×10⁻⁴ BTU (British thermal unit)
• 0.7376 ft·lbf (foot-pounds force)
• 23.7 ft·pdl (foot-poundals)
• 2.7778×10⁻⁷ kilowatt-hour
• 2.7778×10⁻⁴ watt-hour
• 9.8692×10⁻³ litre-atmosphere
• 11.1265 femtograms (mass-energy equivalence)
• 1×10⁻⁴⁴ foe (exactly)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J^[12]
• 1 International Table calorie = 4.1868 J^[12]
• 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

See also[link]

• Conversion of units of energy
• Orders of magnitude (energy)
• Fluence

References[link]

External links[link]

• Unit conversion from joule

v t e SI units Base units Ampere · Candela · Kelvin · Kilogram · Metre · Mole · Second Derived units Becquerel · Coulomb · Degree Celsius · Farad · Gray · Henry · Hertz · Joule · Katal · Lumen · Lux · Newton · Ohm · Pascal · Radian · Siemens · Sievert · Steradian · Tesla · Volt · Watt · Weber Accepted for use with SI Dalton (Atomic mass unit) · Astronomical unit · Day · Decibel · Degree Celsius · Degree of arc · Electronvolt · Hectare · Hour · Litre · Minute · Minute of arc · Neper · Second of arc · Tonne Atomic units · Natural units See also SI prefixes · Systems of measurement · Conversion of units · New SI definitions · History of the metric system Book:International System of Units  · Category:SI base units

James Prescott Joule
James Joule – Physicist
Born	(1818-12-24)24 December 1818 Salford, Lancashire, England, UK
Died	11 October 1889(1889-10-11) (aged 70) Sale, Cheshire, England, UK
Citizenship	British
Fields	Physics
Known for	First Law of Thermodynamics
Influences	John Dalton John Davies

James Prescott Joule FRS ( /dʒuːl/;^[1] 24 December 1818 – 11 October 1889) was an English physicist and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). This led to the theory of conservation of energy, which led to the development of the first law of thermodynamics. The SI derived unit of energy, the joule, is named after him. He worked with Lord Kelvin to develop the absolute scale of temperature, made observations on magnetostriction, and found the relationship between the current through resistance and the heat dissipated, now called Joule's law.

Early years[link]

1892 illustration of Joule

The son of Benjamin Joule (1784–1858), a wealthy brewer, and Alice Prescott Joule, James Prescott Joule was born in the house adjoining the Joule Brewery in New Bailey Street, Salford 24 December 1818.^[2] James was tutored at the family home 'Broomhill', Pendlebury, near Salford, until 1834 when he was sent with his elder brother Benjamin, to study with John Dalton at the Manchester Literary and Philosophical Society.^[2] The pair only received two years' education in arithmetic and geometry before Dalton was forced to retire owing to a stroke. However, Dalton's influence made a lasting impression as did that of his associates, chemist William Henry and Manchester engineers Peter Ewart and Eaton Hodgkinson. Joule was subsequently tutored by John Davies. Fascinated by electricity, he and his brother experimented by giving electric shocks to each other and to the family's servants.^[3]

Joule became a manager of the brewery^[4] and took an active role until the sale of the business in 1854. Science was a hobby but he soon started to investigate the feasibility of replacing the brewery's steam engines with the newly invented electric motor. In 1838, his first scientific papers on electricity were contributed to Annals of Electricity, the scientific journal founded and operated by Davies's colleague William Sturgeon. He formulated Joule's laws in 1840^[5] and hoped to impress the Royal Society but found, not for the last time, that he was perceived as a mere provincial dilettante. When Sturgeon moved to Manchester in 1840, Joule and he became the nucleus of a circle of the city's intellectuals. The pair shared similar sympathies that science and theology could and should be integrated. Joule went on to lecture at Sturgeon's Royal Victoria Gallery of Practical Science.^[3]

He went on to realise that burning a pound of coal in a steam engine produced five times as much duty as a pound of zinc consumed in a Grove cell,^[6] an early electric battery.^[7] Joule's common standard of "economical duty" was the ability to raise one pound by a height of one foot, the foot-pound.^[3][8]

Joule was influenced by the thinking of Franz Aepinus and tried to explain the phenomena of electricity and magnetism in terms of atoms surrounded by a "calorific ether in a state of vibration".^[3]

However, Joule's interest diverted from the narrow financial question to that of how much work could be extracted from a given source, leading him to speculate about the convertibility of energy. In 1843 he published results of experiments showing that the heating effect he had quantified in 1841 was due to generation of heat in the conductor and not its transfer from another part of the equipment.^[9] This was a direct challenge to the caloric theory which held that heat could neither be created nor destroyed. Caloric theory had dominated thinking in the science of heat since it was introduced by Antoine Lavoisier in 1783. Lavoisier's prestige and the practical success of Sadi Carnot's caloric theory of the heat engine since 1824 ensured that the young Joule, working outside either academia or the engineering profession, had a difficult road ahead. Supporters of the caloric theory readily pointed to the symmetry of the Peltier-Seebeck effect to claim that heat and current were convertible, at least approximately, by a reversible process.^[3]

The mechanical equivalent of heat[link]

Joule wrote in his 1845 paper:

... the mechanical power exerted in turning a magneto-electric machine is converted into the heat evolved by the passage of the currents of induction through its coils; and, on the other hand, that the motive power of the electro-magnetic engine is obtained at the expense of the heat due to the chemical reactions of the battery by which it is worked.^[10]

Joule's Heat Apparatus, 1845

Joule here adopts the language of vis viva (energy), possibly because Hodgkinson had read a review of Ewart's On the measure of moving force to the Literary and Philosophical Society in April 1844.

Further experiments and measurements by Joule led him to estimate the mechanical equivalent of heat as 838 ft·lbf of work to raise the temperature of a pound of water by one degree Fahrenheit.^[11] He announced his results at a meeting of the chemical section of the British Association for the Advancement of Science in Cork in 1843 and was met by silence.

Joule was undaunted and started to seek a purely mechanical demonstration of the conversion of work into heat. By forcing water through a perforated cylinder, he was able to measure the slight viscous heating of the fluid. He obtained a mechanical equivalent of 770 ft·lbf/Btu (4.14 J/cal). The fact that the values obtained both by electrical and purely mechanical means were in agreement to at least one order of magnitude was, to Joule, compelling evidence of the reality of the convertibility of work into heat.

Joule now tried a third route. He measured the heat generated against the work done in compressing a gas. He obtained a mechanical equivalent of 823 ft·lbf/Btu (4.43 J/cal).^[12] In many ways, this experiment offered the easiest target for Joule's critics but Joule disposed of the anticipated objections by clever experimentation. However, his paper was rejected by the Royal Society and he had to be content with publishing in the Philosophical Magazine. In the paper he was forthright in his rejection of the caloric reasoning of Carnot and Émile Clapeyron, but his theological motivations also became evident:

I conceive that this theory ... is opposed to the recognised principles of philosophy because it leads to the conclusion that vis viva may be destroyed by an improper disposition of the apparatus: Thus Mr Clapeyron draws the inference that 'the temperature of the fire being 1000 °C to 2000 °C higher than that of the boiler there is an enormous loss of vis viva in the passage of the heat from the furnace to the boiler.' Believing that the power to destroy belongs to the Creator alone I affirm ... that any theory which, when carried out, demands the annihilation of force, is necessarily erroneous.

In 1845, Joule read his paper On the mechanical equivalent of heat to the British Association meeting in Cambridge.^[13] In this work, he reported his best-known experiment, involving the use of a falling weight, in which gravity does the mechanical work, to spin a paddle-wheel in an insulated barrel of water which increased the temperature. He now estimated a mechanical equivalent of 819 ft·lbf/Btu (4.41 J/cal).

In 1850, Joule published a refined measurement of 772.692 ft·lbf/Btu (4.159 J/cal), closer to twentieth century estimates.^[14]

Reception and priority[link]

Joule's apparatus for measuring the mechanical equivalent of heat

For the controversy over priority with Mayer, see Mechanical equivalent of heat: Priority

Much of the initial resistance to Joule's work stemmed from its dependence upon extremely precise measurements. He claimed to be able to measure temperatures to within ¹⁄₂₀₀ of a degree Fahrenheit (3 mK). Such precision was certainly uncommon in contemporary experimental physics but his doubters may have neglected his experience in the art of brewing and his access to its practical technologies.^[15] He was also ably supported by scientific instrument-maker John Benjamin Dancer.

However, in Germany, Hermann Helmholtz became aware both of Joule's work and the similar 1842 work of Julius Robert von Mayer. Though both men had been neglected since their respective publications, Helmholtz's definitive 1847 declaration of the conservation of energy credited them both.

Also in 1847, another of Joule's presentations at the British Association in Oxford was attended by George Gabriel Stokes, Michael Faraday, and the precocious and maverick William Thomson, later to become Lord Kelvin, who had just been appointed professor of natural philosophy at the University of Glasgow. Stokes was "inclined to be a Joulite" and Faraday was "much struck with it" though he harboured doubts. Thomson was intrigued but sceptical.

Unanticipated, Thomson and Joule met later that year in Chamonix. Joule married Amelia Grimes on 18 August and the couple went on honeymoon. Marital enthusiasm notwithstanding, Joule and Thomson arranged to attempt an experiment a few days later to measure the temperature difference between the top and bottom of the Cascade de Sallanches waterfall, though this subsequently proved impractical.

Though Thomson felt that Joule's results demanded theoretical explanation, he retreated into a spirited defence of the Carnot-Clapeyron school. In his 1848 account of absolute temperature, Thomson wrote that "the conversion of heat (or caloric) into mechanical effect is probably impossible, certainly undiscovered"^[16] – but a footnote signalled his first doubts about the caloric theory, referring to Joule's "very remarkable discoveries". Surprisingly, Thomson did not send Joule a copy of his paper but when Joule eventually read it he wrote to Thomson on 6 October, claiming that his studies had demonstrated conversion of heat into work but that he was planning further experiments. Thomson replied on the 27th, revealing that he was planning his own experiments and hoping for a reconciliation of their two views. Though Thomson conducted no new experiments, over the next two years he became increasingly dissatisfied with Carnot's theory and convinced of Joule's. In his 1851 paper, Thomson was willing to go no further than a compromise and declared "the whole theory of the motive power of heat is founded on ... two ... propositions, due respectively to Joule, and to Carnot and Clausius".

As soon as Joule read the paper he wrote to Thomson with his comments and questions. Thus began a fruitful, though largely epistolary, collaboration between the two men, Joule conducting experiments, Thomson analysing the results and suggesting further experiments. The collaboration lasted from 1852 to 1856, its discoveries including the Joule-Thomson effect, and the published results did much to bring about general acceptance of Joule's work and the kinetic theory.

Kinetic theory[link]

James Prescott Joule

Kinetics is the science of motion. Joule was a pupil of Dalton and it is no surprise that he had learned a firm belief in the atomic theory, even though there were many scientists of his time who were still sceptical. He had also been one of the few people receptive to the neglected work of John Herapath on the kinetic theory of gases. He was further profoundly influenced by Peter Ewart's 1813 paper On the measure of moving force.

Joule perceived the relationship between his discoveries and the kinetic theory of heat. His laboratory notebooks reveal that he believed heat to be a form of rotational, rather than translational motion.

Joule could not resist finding antecedents of his views in Francis Bacon, Sir Isaac Newton, John Locke, Benjamin Thompson (Count Rumford) and Sir Humphry Davy. Though such views are justified, Joule went on to estimate a value for the mechanical equivalent of heat of 1034 foot-pound from Rumford's publications. Some modern writers have criticised this approach on the grounds that Rumford's experiments in no way represented systematic quantitative measurements. In one of his personal notes, Joule contends that Mayer's measurement was no more accurate than Rumford's, perhaps in the hope that Mayer had not anticipated his own work. Joule is attributed with explaining the Green Flash phenomenon in a letter to the Manchester Literary and Philosophical Society in 1869.

Honours[link]

A statue of Joule in the Manchester Town Hall

Joule's gravestone in Brooklands cemetery, Sale

Joule died at home in Sale^[17] and is buried in Brooklands cemetery there. The gravestone is inscribed with the number "772.55", his climacteric 1878 measurement of the mechanical equivalent of heat, and with a quotation from the Gospel of John, "I must work the works of him that sent me, while it is day: the night cometh, when no man can work" (9:4). The Wetherspoon's public house in Sale, the town of his death, is named after him.

• Fellow of the Royal Society, (1850);
  • Royal Medal, (1852);
  • Copley Medal (1870);
• President of Manchester Literary and Philosophical Society, (1860);
• President of the British Association for the Advancement of Science, (1872, 1887);
• Honorary degrees:
  • LL.D., Trinity College Dublin, (1857);
  • DCL, University of Oxford, (1860);
  • LL.D., University of Edinburgh, (1871).
• He received a civil list pension of £200 per annum in 1878 for services to science;
• Albert Medal of the Royal Society of Arts, (1880).
• There is a memorial to Joule in the north choir aisle of Westminster Abbey, though he is not buried there, contrary to what some biographies state.
• A statue by Alfred Gilbert, stands in Manchester Town Hall, opposite that of Dalton.

Selected writings[link]

• Joule, J. P. (1963). The Scientific Papers of James Prescott Joule. London: Dawsons of Pall Mall. 

Notes[link]

Further reading[link]

• Bottomley, J. T. (1882). "James Prescott Joule". Nature 26 (678): 617–620. Bibcode 1882Natur..26..617B. DOI:10.1038/026617a0. 
• Cardwell, D. S. L. (1991). James Joule: A Biography. Manchester college Press. ISBN 0-7190-3479-5. 
• Forrester, J. (1975). "Chemistry and the Conservation of Energy: The Work of James Prescott Joule". Studies in the History and Philosophy of Science 6 (4): 273–313. DOI:10.1016/0039-3681(75)90025-4. 
• Fox, R, "James Prescott Joule, 1818–1889", in North, J. (1969). Mid-nineteenth-century scientists. Elsevier. pp. 72–103. ISBN 0-7190-3479-5. 
• Reynolds, Osbourne (1892). Memoir of James Prescott Joule. Manchester, England: Manchester Literary and Philosophical Society. http://books.google.com/?id=Zs93x6asUPgC&pg=PA154&dq=joule. Retrieved 15 March 2008. 
• Sibum, H. O. (1995). "Reworking the mechanical value of heat: instruments of precision and gestures of accuracy in early Victorian England". Studies in History and Philosophy of Science 26: 73–106. DOI:10.1016/0039-3681(94)00036-9. 
• Smith, C. (1998). The Science of Energy: A Cultural History of Energy Physics in Victorian Britain. London: Heinemann. ISBN 0-485-11431-3. 
• Smith, Crosbie, "Joule, James Prescott", on the website of the Oxford Dictionary of National Biography (subscription or UK public library membership required), http://dx.doi.org/10.1093/ref:odnb/15139 . The first edition of this text is available as an article on Wikisource:  "Joule, James Prescott". Dictionary of National Biography. London: Smith, Elder & Co. 1885–1900. 
• Smith, C. & Wise, M.N. (1989). Energy and Empire: A Biographical Study of Lord Kelvin. Cambridge University Press. ISBN 0-521-26173-2. 
• Steffens, H.J. (1979). James Prescott Joule and the Concept of Energy. Watson. ISBN 0-88202-170-2. 
• Walker, James (1950). Physics 4th Edition. Pearson. ISBN 978-0-321-54163-5. 

External links[link]

Wikimedia Commons has media related to: James Prescott Joule (category)

Wikisource has original works written by or about: James Prescott Joule

• Classic papers of 1845 and 1847 at ChemTeam website On the Mechanical Equivalent of Heat and On the Existence of an Equivalent Relation between Heat and the ordinary Forms of Mechanical Power
• Joule's water friction apparatus at London Science Museum
• Some Remarks on Heat and the Constitution of Elastic Fluids, Joule's 1851 estimate of the speed of a gas molecule.
• University of Manchester material on Joule – includes photographs of Joule's house and gravesite
•  "Joule, John Prescott". Dictionary of National Biography. London: Smith, Elder & Co. 1885–1900. 
• "Dr. Joule". Electrical Engineer (London: Biggs & Co) (18 October): 311–312. 1889. http://books.google.com/?id=PQsAAAAAMAAJ&pg=PA311&lpg=PA311&dq=James+Joule+obituary. Retrieved 16 May 2008. - obituary with brief comment on Joule's family
• Joule Physics Laboratory at the University of Salford