Joule

The joule ( ; symbol: J) is a derived unit of

energy

in the International System of Units. It is equal to the energy transferred to (or

work

done on) an object when a

force

of one newton acts on that object in the direction of the force's motion through a distance of one metre (1 newton-metre or N⋅m). 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 firstly of base SI units and then in terms of other SI units, a joule is defined as

:$\mathrm,$

where

One joule can also be defined as 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 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 .
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 device for .
* The energy required to accelerate a mass at through a distance of .
* The kinetic energy of a mass traveling at .
* The energy required to lift a medium-sized tomato up , assuming the tomato has a mass of .
* The

heat

required to raise the temperature 0.239 g of water from 0 °C to 1 °C, or from 32 °F to 33.8 °F.
* The typical energy released as heat by a person at rest every 1/60 s ().
* The kinetic energy of a human moving very slowly ().
* The kinetic energy of a tennis ball moving at .
* The food energy (kcal) in slightly more than half of a sugar crystal (/crystal).

Multiples

; : The yoctojoule (yJ) is equal to .
; : The zeptojoule (zJ) is equal to one sextillionth () of one joule. is about one electronvolt. The minimal energy needed to change a bit at around room temperature – approximately – is given by the Landauer limit.
; : The attojoule (aJ) is equal to .
; : The femtojoule (fJ) is equal to .
; : The picojoule (pJ) is equal to one trillionth () of one joule.
; : The nanojoule (nJ) is equal to one billionth () of one joule. is about the kinetic energy of a flying mosquito.
; : The microjoule (μJ) is equal to one millionth () of one joule. The Large Hadron Collider (LHC) produces collisions of the microjoule order (7 TeV) per particle.
; : The millijoule (mJ) is equal to one thousandth () of a joule.
; : The kilojoule (kJ) is equal to one thousand () joules. Nutritional food labels in most countries express energy in kilojoules (kJ). One square metre of the

Earth

receives about of solar radiation every second in full daylight. A human in a sprint has approximately 3kJ of kinetic energy, while a cheetah in a 70mph sprint has approximately 20kJ.
; : The megajoule (MJ) is equal to one million () joules, or approximately the kinetic energy of a one megagram (tonne) vehicle moving at (100 mph). The energy required to heat of liquid water at constant pressure from to is approximately . One kilowatt-hour of electricity is .
; :The gigajoule (GJ) is equal to one billion () joules. is about the chemical energy of combusting of

petroleum

. 2 GJ is about the Planck energy unit.
; :The terajoule (TJ) is equal to one trillion () joules; or about (which is often used in energy tables). About of energy was released by

Little Boy

. The

International Space Station

, with a mass of approximately and orbital velocity of , has a kinetic energy of roughly . In 2017,

Hurricane Irma

was estimated to have a peak wind energy of . is about the amount of energy equivalent to of mass.
; : The petajoule (PJ) is equal to one quadrillion () joules. is about of TNT which is the amount of energy released by the Tsar Bomba, the largest man-made explosion ever.
; : The exajoule (EJ) is equal to one quintillion () joules. The 2011 Tōhoku earthquake and tsunami in Japan had of energy according to its rating of 9.0 on the moment magnitude scale. Yearly U.S. energy consumption amounts to roughly .
; :The zettajoule (ZJ) is equal to one sextillion () joules. Human annual

world energy consumption

is approximately . The energy to raise the temperature of Earth's atmosphere 1 °C is approximately .
; :The yottajoule (YJ) is equal to one septillion () joules. This is approximately the amount of energy required to heat

all the water on Earth

by 1 °C. The thermal output of the

Sun

is approximately per second.

Conversions

1 joule is equal to (approximately unless otherwise stated):
* (exactly)
*
* (gram calories)
* (food calories)
*
* (foot-pound)
* (foot-poundal)
* (kilowatt-hour)
* (watt-hour)
* (litre-atmosphere)
* (by way of mass-energy equivalence)
* (exactly)

Units defined exactly in terms of the joule include:
* 1 thermochemical calorie = 4.184JThe 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.
* 1 International Table calorie = 4.1868J
* 1W⋅h = 3600J (or 3.6kJ)
* 1kW⋅h = (or 3.6MJ)
* 1W⋅s =
* 1ton TNT =

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):

A result of this similarity is that the SI unit for torque is the

newton-metre

, which works out

algebra

ically to have the same dimensions as the joule, but 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 and joules for energy is helpful to avoid misunderstandings and miscommunications.

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
$E = \tau \theta\, ,$

where ''E'' is energy, ''τ'' is (the vector magnitude of) torque, and ''θ'' is the angle swept (in

radian

s). 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".

Photography

In photography, the unit for flashes is the watt-second. A flash can be rated in watt-seconds (e.g., 300 W⋅s) or in joules (different names for the same thing), but historically, the term "watt-second" has been used and continues to be used.

:$\text = \dfrac \cdot \text \cdot \text^2$

The energy rating a flash is given is not a reliable benchmark for its light output because there are numerous factors that affect the energy conversion efficiency. For example, the construction of the tube will affect the efficiency, and the use of reflectors and filters will change the usable light output towards the subject. Some companies specify their products in "true" watt-seconds, and some specify their products in "nominal" watt-seconds.

See also

* Fluence
* Reciprocal joules

Notes

References

External links

*

{{Footer energy

James Prescott Joule
SI derived units
Units of energy