# Joule

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

{{#invoke:Hatnote|hatnote}} Template:Infobox Unit The joule (Template:IPAc-en or sometimes Template:IPAc-en), symbol J, is a derived unit of energy, work, or amount of heat in the International System of Units.[1] It is equal to the energy transferred (or work done) when applying a force of one newton through a distance of one metre (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).[2][3][4]

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

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

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:

## Confusion with newton-metre

{{#invoke:main|main}} In angular mechanics, torque is analogous to the linear Newtonian mechanics parameter of force, moment of inertia to mass, and angle to distance. Energy is the same in both systems. Thus, 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: the CGPM has given the unit of energy the name "joule", but has not given the unit of torque any special name, hence the unit of torque is known as the newton-metre (N·m) - a compound name derived from its constituent parts.[5] Torque and energy are related to each other using the equation

${\displaystyle E=\tau \theta \ }$

where E is the energy, τ is 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.[5]

An additional solution is to realize that joules are scalars – they are the dot product of a vector force and a vector displacement whereas torque is a vector. Torque is the cross product of a distance vector and a force vector. Drawing a traditional vector arrow over "newton-metre" in a torque resolves the ambiguity.

## Practical examples

One joule in everyday life represents approximately:

• the energy required to lift a small apple (with a mass of approximately 100 g) vertically through one metre of air.
• the energy released when that same apple falls one metre to the ground.
• the energy required to accelerate a 1 kg mass at 1 m·s−2 through a 1 m distance in space.
• the heat required to raise the temperature of 1 g of water by 0.24 K.[6]
• the typical energy released as heat by a person at rest every 1/60 second (approximately 17 ms).[7]
• the kinetic energy of a 50 kg human moving very slowly (Template:Convert).
• the kinetic energy of a 56 g tennis ball moving at Template:Convert.[8]
• the kinetic energy of an object with mass 1 kg moving at √2 ≈ 1.4 m/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 (kilo) × 3600 seconds = 3.6 MJ (megajoules).

## Multiples

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

### Nanojoule

The nanojoule (nJ) is equal to one billionth (10-9) of one joule. One nanojoule is about 1/160 of the kinetic energy of a flying mosquito.[9]

### Microjoule

The microjoule (μJ) is equal to one millionth (10-6) 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 (10-3) of a joule.

### Kilojoule

The kilojoule (kJ) is equal to one thousand (103) joules. Nutritional food labels in certain countries express energy in kilojoules (kJ).

One kilojoule per second (1 kilowatt) is approximately the amount of solar radiation received by one square metre of the Earth in full daylight.[10]

### Megajoule

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

Because 1 watt times 1 second equals 1 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. 6 GJ is about the amount of potential chemical energy in a barrel of oil, when combusted.[11]

### Terajoule

The terajoule (TJ) is equal to one trillion (1012) joules. About 63 TJ of energy was released by the atomic bomb that exploded over Hiroshima.[12] The International Space Station, with a mass of approximately 450,000 kg and orbital velocity of 7.7 km/s,[13] has a kinetic energy of roughly 13 TJ.

### Petajoule

The petajoule (PJ) is equal to one quadrillion (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 one quintillion (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 one sextillion (1021) joules. Annual global energy consumption is approximately 0.5 ZJ.

### Yottajoule

The yottajoule (YJ) is equal to one septillion (1024) joules. This is approximately the amount of energy required to heat the entire volume of water on Earth by 1 °C. The thermal output of the Sun is approximately 400 YJ per second.

## Conversions

{{#invoke:main|main}} 1 joule is equal to:

Units defined exactly in terms of the joule include:

## Notes and references

1. Template:SIbrochure8th
2. American Heritage Dictionary of the English Language, Online Edition (2009). Houghton Mifflin Co., hosted by Yahoo! Education.
3. The American Heritage Dictionary, Second College Edition (1985). Boston: Houghton Mifflin Co., p. 691.
4. McGraw-Hill Dictionary of Physics, Fifth Edition (1997). McGraw-Hill, Inc., p. 224.
5. From the official SI website: "A derived unit can often be expressed in different ways by combining base units with derived units having special names. Joule, for example, may formally be written newton metre, or kilogram metre squared per second squared. This, however, is an algebraic freedom to be governed by common sense physical considerations; in a given situation some forms may be more helpful than others. In practice, with certain quantities, preference is given to the use of certain special unit names, or combinations of unit names, to facilitate the distinction between different quantities having the same dimension."
6. Template:Cite web
7. This is called the basal metabolic rate. It corresponds to about Template:Convert per day. The kilocalorie (symbol kcal) is also known as the dietary calorie. "At rest" means awake but inactive.
8. {{#invoke:citation/CS1|citation |CitationClass=book }}
9. CERN - Glossary
10. Template:Cite web
11. IRS publication
12. Los Alamos National Laboratory report LA-8819, The yields of the Hiroshima and Nagasaki nuclear explosions by John Malik, September 1985. Available online at http://www.mbe.doe.gov/me70/manhattan/publications/LANLHiroshimaNagasakiYields.pdf
13. International Space Station Fact Sheet
14. The 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.
15. Template:Cite web