This article is about the unit of energy. For other uses, see Joule (disambiguation)

The joule (; symbol: J) is a derived unit of energy in the International System of Units.[1] 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 its 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).[2][3][4]

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

J = kg ⋅ m 2 s 2 = N ⋅ m = Pa ⋅ m 3 = W ⋅ s = C ⋅ V , {\displaystyle {\text{J}}={\frac {{\text{kg}}{\cdot }{\text{m}}^{2}}{{\text{s}}^{2}}}={\text{N}}{\cdot }{\text{m}}={\text{Pa}}{\cdot }{\text{m}}^{3}={\text{W}}{\cdot }{\text{s}}={\text{C}}{\cdot }{\text{V}},}

where kg is the kilogram, m is the metre, s is the second, N is the newton, Pa is the pascal, W is the watt, C is the coulomb, and V is the volt.

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.

(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.

Usage [ edit ]

This SI unit is named after James Prescott Joule. As with every International System of Units (SI) unit named for a person, the first letter of its symbol is upper case (J). However, when an SI unit is spelled out in English, it is treated as a common noun and should always begin with a lower case letter (joule)—except in a situation where any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case.

Exception of newton metre [ edit ]

In mechanics, the concept of force (in some direction) has a close analog in the concept of torque (about some angle):

Linear Angular Force Torque Mass Moment of inertia Displacement (sometimes position) 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 CGPM 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.[5] The use of newton metres for torque and joules for energy is helpful to avoid misunderstandings and miscommunications.[5]

The distinction may be seen also in the fact that energy is a scalar – the dot product of a vector force and a vector displacement. By contrast, torque is a vector – the cross product of a distance vector and a force vector. Torque and energy are related to one another by the equation

E = τ θ , {\displaystyle E=\tau \theta \ ,}

where E is energy, τ is (the vector magnitude of) torque, and θ is the angle swept (in radians). Since radians are dimensionless, it follows that torque and energy have the same dimensions.

Practical examples [ edit ]

One joule in everyday life represents approximately:

The energy required to lift a medium-sized tomato up 1 metre (3 ft 3 in) (assume the tomato has a mass of approximately 100 grams (3.5 oz)).

The energy released when that same tomato falls back down one metre.

The energy required to accelerate a 1 kg mass at 1 m⋅s −2 through a distance of 1 m.

through a distance of 1 m. The heat required to raise the temperature of 1 g of water by 0.24 °C. [6]

The typical energy released as heat by a person at rest every 1/60 s (approximately 17 ms). [7]

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). [8]

The kinetic energy of an object with mass 1 kg moving at √ 2 ≈ 1.4 m/s.

≈ 1.4 m/s. The amount of electricity required to light a 1 W LED for 1 s.

Since the joule is also a watt-second and the common unit for electricity sales to homes is the kW⋅h (kilowatt-hour), a kW⋅h is thus 1000 W × 3600 s = 3.6 MJ (megajoules).

Multiples [ edit ]

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

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

Conversions [ edit ]

1 joule is equal to (approximately unless otherwise stated):

7000100000000000000♠ 1 × 10 7 erg 10

7000100000001488094♠ 6.241 509 74 × 10 18 eV 6.24110

6999999976000000000♠ 0.2390 0.2390 cal

6999999976000000000♠ 2.390 × 10 −4 kcal 2.39010

7000100000303823028♠ 9.4782 × 10 −4 BTU 9.478210

6999737600000000000♠ 0.7376 0.7376 ft⋅lb

6999998720609223173♠ 23.7 23.7 ft⋅pdl

6993277780000000000♠ 2.7778 × 10 −7 kW⋅h 2.777810

6996277780000000000♠ 2.7778 × 10 −4 W⋅h 2.777810

6999999996690000000♠ 9.8692 × 10 −3 l⋅atm 9.869210

6983111265000000000♠ 11.1265 × 10 −15 g 11.126510 mass-energy equivalence)

mass-energy equivalence) 7000100000000000000♠ 1 × 10−44 foe 10

Units defined exactly in terms of the joule include:

1 thermochemical calorie = 4.184 J [17]

J 1 International Table calorie = 4.1868 J [18]

J 1 W⋅h = 3600 J (or 3.6 kJ)

W⋅h = 3600 J (or 3.6 kJ) 1 kW⋅h = 7006360000000000000♠ 3.6 × 10 6 J (or 3.6 MJ)

kW⋅h = (or 3.6 MJ) 1 W⋅s = 7000100000000000000♠ 1 J

W⋅s = 1 ton TNT = 7009418400000000000♠ 4.184 GJ

Watt second [ edit ]

A watt second (also watt-second, symbol W s or W·s) is a derived unit of energy equivalent to the joule.[19] 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 [ edit ]

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. An on-camera flash, using a 1000 microfarad capacitor at 300 volts, would be 45 watt-seconds. Studio flashes, using larger capacitors and higher voltages, are in the 200–2000 watt-second range.

Energy of a flash in joules or watt-seconds = 1 2 ⋅ capacitance of the storage capacitor in farads ⋅ working voltage 2 {\displaystyle {\text{Energy of a flash in joules or watt-seconds}}={\dfrac {1}{2}}\cdot {\text{capacitance of the storage capacitor in farads}}\cdot {\text{working voltage}}^{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.[20]

See also [ edit ]