joule
Energyexact by definition
The joule is the coherent SI unit of energy, work and heat: one newton acting through one metre, which is also one watt for one second and one coulomb through one volt. Its factor is 1 by construction and it is exact, being built from base units with no numerical constant.
| 1 J | 1 J |
Named for James Prescott Joule, whose careful 1840s experiments measuring the heating produced by stirring water established the mechanical equivalent of heat and, with it, the idea that heat and work are the same currency.
About the joule
The joule's importance is that it unified quantities that had been measured in separate units by separate professions. Mechanical work was measured in foot-pounds, heat in calories or BTU, and electrical energy in its own units, and nothing said they were the same thing. Joule's paddle-wheel experiment, in which falling weights stirred water and warmed it by a measurable amount, established a fixed exchange rate between mechanical work and heat. Once that rate was known, one unit could serve for all of them.
The joule's many equivalent forms are a useful check on any energy calculation. It is \(\mathrm{N\,m}\), and \(\mathrm{kg\,m^2\,s^{-2}}\), and \(\mathrm{W\,s}\), and \(\mathrm{C\,V}\), and \(\mathrm{Pa\,m^3}\). That last one is why pressure times volume has units of energy and why the term \(pV\) appears in thermodynamics. For scale, one joule lifts an apple about one metre, a food Calorie is 4184 J, and a kilowatt-hour is 3.6 million J.
One notational trap: the joule and the newton metre are dimensionally identical, but torque is conventionally written in newton metres and never in joules, because torque is a moment rather than an energy. The units match; the physics does not.