Joule

• 1. Introduction

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  The joule is the unit of energy in the International System of Units, and its symbol is a single letter: J. It hides in plain sight. One joule is roughly the energy to lift an apple a metre into the air, if that apple weighs 101.97 grams. It is also the heat your resting body releases every sixtieth of a second. And it sits at the heart of physics, defined as the work done when a force of one newton pushes a body one metre in the direction of that force. The same quantity measures a tennis ball in flight and the energy of an atomic blast. So how did one small unit come to span a mosquito's flight and the thermal output of the Sun? And why does it carry the name of an English physicist who was 63 and retired when his colleagues chose to honour him?

• 2. What One Joule Is

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  One kilogram-metre squared per second squared. That is the joule expressed in SI base units, written 1 J = 1 kg m2 s-2. The same energy appears when an electric current of one ampere passes through a resistance of one ohm for one second, dissipated as heat. The unit can be approached from electricity rather than mechanics. Moving an electric charge of one coulomb through a potential difference of one volt does exactly one joule of work, a relationship sometimes called the coulomb-volt and used to define the volt. Producing one watt of power for one second yields one joule too, the watt-second, and that relationship can be used to define the watt. For comparison, a kilowatt-hour equals 3.6 megajoules, which is why electricity bills look so much larger than the underlying single-second figures.

• 3. From Erg To Newton

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  The CGS system was declared official in 1881, at the first International Electrical Congress, and the erg became its unit of energy the following year. On the 23rd of August 1882, Wilhelm Siemens used his inauguration speech as chairman of the British Association for the Advancement of Science to propose a heat unit derived from the electromagnetic units ampere and ohm. He suggested its name. Such a heat unit, he said, might with great propriety be called the Joule, after the man who has done so much to develop the dynamical theory of heat. On the 31st of August 1889, at the second International Electrical Congress, the joule was officially adopted alongside the watt and the quadrant, the latter later renamed to henry. James Prescott Joule did not see the unit settle into use for long. He died that same year, on the 11th of October 1889.

• 4. A Definition Rebuilt

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  The fourth congress, in 1893, defined the international ampere and the international ohm, and from them derived an international joule, with slight changes in how each was measured. The whole foundation then shifted. In 1935 the International Electrotechnical Commission, successor to the International Electrical Congress, adopted the Giorgi system, which assumed a defined value for the magnetic constant and so implied a fresh definition of the joule. The International Committee for Weights and Measures approved that system in 1946. From then the joule was no longer pinned to electromagnetic units. It became the work done by one unit of force, not yet named the newton, acting over one metre, intended for both electromagnetic and mechanical use. At the ninth General Conference on Weights and Measures in 1948, the joule was also made the preferred unit of heat in calorimetry, officially deprecating the calorie. That is the definition declared in the modern International System of Units in 1960.

• 5. Inherited Drift

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  J = kg m2 s-2 has not changed since 1946. The formula held even as the units inside it were redefined again and again. The second was redefined in 1960 and again in 1967. The metre was redefined in 1983. The kilogram was redefined in 2019. Each time, the joule quietly inherited the new definition, because it is a derived unit built from those base quantities rather than a standard of its own. A single thermochemical calorie equals exactly 4.184 joules, and an International Table calorie equals exactly 4.1868 joules. The heat needed to raise 0.239 grams of water from 0 degrees Celsius to 1 degree Celsius is about one joule, a small reminder of why the unit once competed with the calorie at all.

• 6. From Mosquito To Sun

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  About 160 zeptojoules is roughly the kinetic energy of a flying mosquito. The Landauer limit, the minimal energy to change a single bit of data near room temperature, sits even lower. At the other extreme, the megajoule is roughly the kinetic energy of a one-tonne vehicle at 100 miles per hour. A human sprinting carries about 3 kilojoules of kinetic energy, while a cheetah at 76 miles per hour carries roughly 20 kilojoules. The Large Hadron Collider produces collisions on the microjoule order, 7 TeV per particle. Larger still, the bomb called Little Boy released about 63 terajoules. The Tsar Bomba, the largest man-made explosion ever, released roughly 50 megatons of TNT. The 2011 Tohoku earthquake and tsunami in Japan, rated 9.0 on the moment magnitude scale, carried about 1.41 of the relevant high-magnitude scale of energy. Hurricane Irma, in 2017, was estimated at a peak wind energy of 112. Higher up the ladder, the zettajoule is somewhat more than the energy needed to heat the Baltic Sea by 1 degree Celsius. World final energy consumption reached 439 in 2021. The yottajoule sits near the energy to heat the Indian Ocean by 1 degree Celsius, and the Sun's thermal output is about 400 such units per second.

• 7. The Look-Alike Unit

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  The newton-metre has exactly the same dimensions as the joule, yet the two are never interchangeable. Torque is measured in newton-metres, energy in joules, and the General Conference on Weights and Measures deliberately gave a special name only to energy. Torque keeps the plain compound name, newton-metre, to avoid misunderstanding. The reason lies deeper than naming. Energy is a scalar, the dot product of a force vector and a displacement vector. Torque is a vector, the cross product of a force vector and a distance vector. They relate through E = the torque magnitude times the angle swept in radians, and since plane angles are dimensionless, the dimensions match. The joule has another twin in name, the watt-second, identical in both units and meaning, yet preferred in specific corners of practice. Photographers rating an electronic flash unit will speak of watt-seconds rather than joules, the same quantity wearing a different label for the trade that uses it.