Joule

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

Joule
Unit system	SI derived unit
Unit of	Energy
Symbol	J
Named after	James Prescott Joule
Conversions
1 J in ...	... is equal to ...
SI base units	1 kg·m2/s2
CGS units	1×107 erg
kilowatt hours	2.78×10−7 kW⋅h
kilocalories	2.39×10−4 kcal
BTUs	9.48×10−4 BTU
electronvolts	6.24×1018 eV

The joule (/ˈdʒuːl/ or sometimes /ˈdʒaʊl/); symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended (or work done) in applying a force of one newton through a distance of one meter (1 newton metre or N·m), or in passing an electric current of one ampere through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).

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

${\rm {J={}{\rm {{\frac {kg\cdot m^{2}}{s^{2}}}=N\cdot m={\rm {Pa\cdot m^{3}={}{\rm {W\cdot s}}}}}}}}$

where N is the newton, m is the meter, kg is the kilogram, s is the second, Pa is the pascal, and W is the watt.

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.
• The work required to produce one watt of power for one second, or one "watt second" (W·s) (compare kilowatt hour). This relationship can be used to define the watt.

Usage

The joule is named after James Prescott Joule. As with every SI unit named for a person, its symbol starts with an upper case letter (J), but when written in full, it follows the rules for capitalisation of a common noun; i.e., joule becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case.

Confusion with newton metre

Main article: newton metre

Although the joule has the same dimensions as the newton-metre (1 J = 1 N·m = 1 kg·m²·s⁻²), these units are not interchangeable as the newton-metre (N·m) is the unit of torque and joules the unit of energy. Torque and energy are related to each other using the equation

$E=\tau \theta \$

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

The use of newton-metres for torque and joules for energy is useful in helping avoid misunderstandings and miscommunications.

Torque and energy have the same dimension because both torque and work (a type of energy) can be calculated by multiplying a force by a distance. However, the details are quite different in the two cases. For torque, the multiplication of force and distance is a vector cross product, while for work it is a dot product. Also, for torque, the distance involved is the length of the lever arm, while for energy it is the distance traveled by the object undergoing the force.

Practical examples

One joule in everyday life is approximately:

• the energy required to lift a small apple one metre straight up. (A mass of about 102 g = 1⁄9.81 kg)
• the energy released when that same apple falls one metre to the ground.
• the energy released as heat by a person at rest, every 1/60th of a second.
• the kinetic energy of a 50 kg human moving very slowly (0.2 m/s).
• the kinetic energy of a tennis ball moving at 23 km/h (14 mph).

Multiples

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 10−27 J rJ rontojoule 1027 J RJ ronnajoule 10−30 J qJ quectojoule 1030 J QJ quettajoule Common multiples are in bold face

Nanojoule

The nanojoule (nJ) is equal to one billionth of one joule. One nanojoule is about 1/160 of the kinetic energy of a flying mosquito.

Microjoule

The microjoule (μJ) is equal to one millionth of one joule. The Large Hadron Collider (LHC) is expected to produce collisions on the order of 1 microjoule (7 TeV) per particle.

Millijoule

The millijoule (mJ) is equal to one thousandth of one joule.

Kilojoule

The kilojoule (kJ) is equal to one thousand (10³) joules. Outside of North America, nutrition facts labels are markedly different from those in the United States; in particular, energy is usually expressed in standard kilojoules (kJ) rather than Calories.

One kilojoule per second (1000 watts) is approximately the amount of solar radiation received by one square metre of the Earth in full daylight.

Megajoule

The megajoule (MJ) is equal to one million (10⁶) joules, or approximately the kinetic energy of a one-tonne vehicle moving at 160 km/h (100 mph).

Because 1 watt times one second equals one joule, 1 kilowatt-hour is 1000 watts times 3600 seconds, or 3.6 megajoules.

Gigajoule

The gigajoule (GJ) is equal to one billion (10⁹) joules. Six gigajoules is about the amount of potential chemical energy in a barrel of oil, when combusted.

Terajoule

The terajoule (TJ) is equal to one trillion (10¹²) joules. About 63 terajoules were released by the atomic bomb that exploded over Hiroshima. The International Space Station, at completion, with a mass of 450,000kg and orbital velocity of 7.7 km/s, will have a kinetic energy of roughly 13 terajoules.

Petajoule

The petajoule (PJ) is equal to 10¹⁵ joules. 210 PJ is equivalent to about 50 megatons of TNT. This is the amount of energy released by the Tsar Bomba, the largest man-made nuclear explosion ever.

Exajoule

The exajoule (EJ) is equal to 10¹⁸ joules. The 2011 Tōhoku earthquake and tsunami in Japan had 1.41 EJ of energy according to its 9.0 on the moment magnitude scale. Energy in the United States used per year is roughly 94 EJ.

Zettajoule

The zettajoule (ZJ) is equal to 10²¹ joules. Annual global energy consumption is approximately 0.5 ZJ

Yottajoule

The yottajoule (YJ) is equal to 10²⁴ joules. This is approximately the amount of energy required to heat the entire volume of water on Earth by 1 °Celsius.

Conversions

Main article: Conversion of units of energy

1 joule is equal to:

• 1×10⁷ ergs (exactly)
• 6.24150974×10¹⁸ eV (electronvolts)
• 0.2390 cal (thermochemical gram calories or small calories)
• 2.3901×10⁻⁴ kcal (thermochemical kilocalories, kilogram calories, large calories or food calories)
• 9.4782×10⁻⁴ BTU (British thermal unit)
• 0.7376 ft⋅lbf (foot-pounds force)
• 23.7 ft⋅pdl (foot-poundals)
• 2.7778×10⁻⁷ kilowatt-hour
• 2.7778×10⁻⁴ watt-hour
• 9.8692×10⁻³ litre-atmosphere
• 11.1265 femtograms (mass-energy equivalence)
• 1×10⁻⁴⁴ foe (exactly)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J
• 1 International Table calorie = 4.1868 J
• 1 watt hour = 3600 J
• 1 kilowatt hour = 3.6×10⁶ J (or 3.6 MJ)
• 1 watt second = 1 J
• 1 ton TNT = 4.184 GJ

See also

• Conversion of units of energy
• Orders of magnitude (energy)
• Fluence

External links

• Unit conversion from joule