Joule

joule
Unit system	SI
Unit of	energy
Symbol	J
Named after	James Prescott Joule
Conversions
1 J in ...	... is equal to ...
SI base units	kg⋅m2⋅s−2
CGS units	1×107 erg
watt-seconds	1 W⋅s
kilowatt-hours	≈2.78×10−7 kW⋅h
kilocalories (thermochemical)	2.390×10−4 kcalth
BTUs	9.48×10−4 BTU

The joule (pronounced /ˈdʒuːl/, JOOL or /ˈdʒaʊl/ JOWL; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of one newton displaces a mass 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).

Definition

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

[math]\displaystyle{ \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 Meaning J joule 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.

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."

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). 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.

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. 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. 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 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.
• The typical energy released as heat by a person at rest every 1/60 s (17 ms).
• 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).
• The food energy (kcal) in slightly more than half of an ordinary-sized sugar crystal (0.102 mg/crystal).

Multiples

SI multiples of joule (J)

Submultiples				Multiples
Value	SI symbol	Name		Value	SI symbol	Name
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

Nanojoule

160 nanojoule is about the kinetic energy of a flying mosquito.

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 l⋅atm (litre-atmosphere)
• 11.1265×10⁻¹⁵ g⋅c² (by way of mass–energy equivalence)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J
• 1 International Table calorie = 4.1868 J
• 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
• 1 foe = 10⁴⁴ J

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):

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. The use of newton-metres for torque but joules for energy is helpful to avoid misunderstandings and miscommunication.

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 [math]\displaystyle{ 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.

Watt-second

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