# Joule

The joule (/dʒuːl/; 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:

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

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.
• 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.
joule
Unit systemSI derived unit
Unit ofEnergy
SymbolJ
Named afterJames Prescott Joule
Conversions
1 J in ...... is equal to ...
SI base units   kgm2s−2
CGS units   1×107 erg
kilowatt hours   2.78×10−7 kW⋅h
kilocalories (thermochemical)   2.390×10−4 kcalth
BTUs   9.48×10−4 BTU
electronvolts   6.24×1018 eV

## Usage

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

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

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

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

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.
• 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.
• 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

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
Yoctojoule
The yoctojoule (yJ) is equal to (10−24) of one joule.
Zeptojoule
The zeptojoule (zJ) is equal to one sextillionth (10−21) of one joule. 160 zeptojoules is about one electronvolt.
Attojoule
The attojoule (aJ) is equal to (10−18) of one joule.
Femtojoule
The femtojoule (fJ) is equal to (10−15) of one joule.
Picojoule
The picojoule (pJ) is equal to one trillionth (10−12) of one joule.
Nanojoule
The nanojoule (nJ) is equal to one billionth (10−9) of one joule. 160 nanojoules is about 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) produces collisions of the microjoule order (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 most countries express energy in kilojoules (kJ).[10]
One square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.[11]
Megajoule
The megajoule (MJ) is equal to one million (106) joules, or approximately the kinetic energy of a one megagram (tonne) vehicle moving at 161 km/h.
The energy required to heat 10 liters of liquid water at constant pressure from 0 °C (32 °F) to 100 °C (212 °F) is approximately 4.2 MJ.
One kilowatt hour of electricity is 3.6 megajoules.
Gigajoule
The gigajoule (GJ) is equal to one billion (109) joules. 6 GJ is about the chemical energy of combusting 1 barrel (159 l) of crude oil.[12] 2 GJ is about the Planck energy unit.
Terajoule
The terajoule (TJ) is equal to one trillion (1012) joules; or about 0.278 GWh (which is often used in energy tables). About 63 TJ of energy was released by the atomic bomb that exploded over Hiroshima.[13] The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7.7 km/s,[14] has a kinetic energy of roughly 13 TJ. In 2017 Hurricane Irma was estimated to have a peak wind energy of 112 TJ.[15][16]
Petajoule
The petajoule (PJ) is equal to one quadrillion (1015) joules. 210 PJ is about 50 megatons of TNT. This is the amount of energy released by the Tsar Bomba, the largest man-made 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 rating of 9.0 on the moment magnitude scale. Yearly U.S. energy consumption amounts to roughly 94 EJ.
Zettajoule
The zettajoule (ZJ) is equal to one sextillion (1021) joules. The human 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 all the water on Earth by 1 °C. The thermal output of the Sun is approximately 400 YJ per second.

## Conversions

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

• 1×107 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 (by way of mass-energy equivalence)
• 1×10−44 foe (exactly)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J[17]
• 1 International Table calorie = 4.1868 J[18]
• 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

## Watt second

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

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.

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

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]

## Notes and references

1. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 120, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
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. ^ a b "Units with special names and symbols; units that incorporate special names and symbols". International Bureau of Weights and Measures. Archived from the original on 28 June 2009. Retrieved 18 March 2015. 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. ^ "Units of Heat – BTU, Calorie and Joule". Engineeringtoolbox.com. Retrieved 2013-09-16.
7. ^ This is called the basal metabolic rate. It corresponds to about 5,000 kJ (1,200 kcal) per day. The kilocalorie (symbol kcal) is also known as the dietary calorie. "At rest" means awake but inactive.
8. ^ Ristinen, Robert A.; Kraushaar, Jack J. (2006). Energy and the Environment (2nd ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0-471-73989-8.
9. ^ "Physics - CERN". public.web.cern.ch. Archived from the original on 2012-12-13.
10. ^ "You Say Calorie, We Say Kilojoule: Who's Right?". Retrieved 2 May 2017.
11. ^ "Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". Archived from the original on 2011-08-22. Retrieved 2005-10-05.
12. ^
13. ^ Malik, John (September 1985). "Report LA-8819: The yields of the Hiroshima and Nagasaki nuclear explosions" (PDF). Los Alamos National Laboratory. Archived from the original (PDF) on 11 October 2009. Retrieved 18 March 2015.
14. ^ "International Space Station Final Configuration" (PDF). European Space Agency. Archived from the original (PDF) on 21 July 2011. Retrieved 18 March 2015.
15. ^ Bonnie Berkowitz; Laris Karklis; Reuben Fischer-Baum; Chiqui Esteban (11 September 2017). "Analysis - How big is Hurricane Irma?". Washington Post. Retrieved 2 November 2017.
16. ^ "Irma unleashes its fury on south Florida", Financial Times, accessed 10-Sept-2017 (subscription required)
17. ^ 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.
18. ^ Feynman, Richard (1963). "Physical Units". Feynman's Lectures on Physics. Retrieved 2014-03-07.
19. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 39–40, 53, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
20. ^
Aughrim County Ground

Aughrim County Ground, known for sponsorship reasons as Joule Park Aughrim, is a GAA stadium in Aughrim, County Wicklow, Ireland. Aughrim County Ground is the name of the home of Gaelic Games for County Wicklow (Gaelic football, Hurling, Camogie, Ladies Football) team. The ground has a capacity of about 10,000. The name "O'Byrne Park" was occasionally used in the past, but this has never been the official name: this mistake that came about because of the Irish name for the local village of Aughrim, "Aughrim of the O'Byrnes" (Eachdhruim Uí Bhroin). Also known locally as "The Pitch", or just "The Field".

Brayton cycle

The Brayton cycle is a thermodynamic cycle named after George Brayton that describes the workings of a constant-pressure heat engine. The original Brayton engines used a piston compressor and piston expander, but more modern gas turbine engines and airbreathing jet engines also follow the Brayton cycle. Although the cycle is usually run as an open system (and indeed must be run as such if internal combustion is used), it is conventionally assumed for the purposes of thermodynamic analysis that the exhaust gases are reused in the intake, enabling analysis as a closed system.

The engine cycle is named after George Brayton (1830–1892), the American engineer who developed it originally for use in piston engines, although it was originally proposed and patented by Englishman John Barber in 1791. It is also sometimes known as the Joule cycle. The reversed Joule cycle uses an external heat source and incorporates the use of a regenerator. One type of Brayton cycle is open to the atmosphere and uses an internal combustion chamber; and another type is closed and uses a heat exchanger.

Electrical resistance and conductance

The electrical resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is electrical conductance, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).

The resistance of an object depends in large part on the material it is made of—objects made of electrical insulators like rubber tend to have very high resistance and low conductivity, while objects made of electrical conductors like metals tend to have very low resistance and high conductivity. This material dependence is quantified by resistivity or conductivity. However, resistance and conductance are extensive rather than bulk properties, meaning that they also depend on the size and shape of an object. For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. All objects show some resistance, except for superconductors, which have a resistance of zero.

The resistance (R) of an object is defined as the ratio of voltage across it (V) to current through it (I), while the conductance (G) is the inverse:

${\displaystyle R={V \over I},\qquad G={I \over V}={\frac {1}{R}}}$

For a wide variety of materials and conditions, V and I are directly proportional to each other, and therefore R and G are constants (although they will depend on the size and shape of the object, the material it is made of, and other factors like temperature or strain). This proportionality is called Ohm's law, and materials that satisfy it are called ohmic materials.

In other cases, such as a transformer, diode or battery, V and I are not directly proportional. The ratio V/I is sometimes still useful, and is referred to as a "chordal resistance" or "static resistance", since it corresponds to the inverse slope of a chord between the origin and an I–V curve. In other situations, the derivative ${\displaystyle {\frac {dV}{dI}}\,\!}$ may be most useful; this is called the "differential resistance".

Heat capacity

.

Heat capacity or thermal capacity is a physical quantity equal to the ratio of the heat that is added to (or removed from) an object to the resulting temperature change.

The SI unit of heat capacity is joule per kelvin (J/K). However, several other units of measure have been used for this quantity in the past, and are still used in certain contexts.

Heat capacity is an extensive property of matter, meaning that it is proportional to the size of the object. To express the corresponding intensive property of a substance, the heat capacity of a sample is divided by the amount of substance in it.

Either way, the specific heat of a substance, usually denoted by ${\displaystyle c}$, is the amount of heat energy needed to raise the temperature of one unit amount of substance by one unit of temperature.

The specific heat often varies with temperature and state of matter. Liquid water has one of the highest specific heats among common substances, about 4182 J/K/kg at 20°C; but that of ice just below 0°C is only 2093 J/K/kg. The specific heats of iron, granite, oak wood, and hydrogen gas are about 449, 790, 2400, and 14300 J/K/kg, respectively. While a substance is melting or boiling, its specific heat is technically infinite, because the heat goes into changing its state rather than raising its temperature.

The specific heat of a substance, especially a gas, may be significantly lower when it is allowed to expand as it is heated (specific heat at constant pressure) than when is heated in a closed vessel that prevents expansion (specific heat at constant volume). These two values are usually denoted by ${\displaystyle c_{\mathrm {p} }}$ and ${\displaystyle c_{\mathrm {v} }}$, respectively; their quotient ${\displaystyle c_{\mathrm {p} }/c_{\mathrm {v} }}$is the heat capacity ratio.

In some contexts, however, the term specific heat (capacity) may refer to the ratio between the specific heats of a substance at a given temperature and of a reference substance at a reference temperature, such as water at 15°C; much in the fashion of specific gravity.

James Prescott Joule

James Prescott Joule (; 24 December 1818 – 11 October 1889) was an English physicist, mathematician and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). This led to the law of conservation of energy, which in turn led to the development of the first law of thermodynamics. The SI derived unit of energy, the joule, is named after him.

Joule worked with Lord Kelvin to develop an absolute thermodynamic temperature scale, which came to be called the Kelvin scale. Joule also made observations of magnetostriction, and he found the relationship between the current through a resistor and the heat dissipated, which is also called Joule's first law. His experiments about energy transformations were first published in 1843.

Joule-second

The joule-second (J s, or J∙s) is the mathematical product of an SI Derived Unit, the joule (J), and an SI Base Unit, the second (s). The joule-second describes the amount of action occurring in a physical system through a summation of energy (or heat, or work) over time. In mathematical terms, this summation of energy means that the quantity of energy becomes integrated over time to give a number - an answer to the question.

Joule effect

Joule effect and Joule's law are any of several different physical effects discovered or characterized by English physicist James Prescott Joule. These physical effects are not the same, but all are frequently or occasionally referred to in literature as the "Joule effect" or "Joule law" These physical effects include:

"Joule's first law" (Joule heating), a physical law expressing the relationship between the heat generated and current flowing through a conductor.

Joule's second law states that the internal energy of an ideal gas is independent of its volume and pressure, depending only on its temperature.

Magnetostriction, a property of ferromagnetic materials that causes them to change their shape when subjected to a magnetic field.

The Joule–Thomson effect (during Joule expansion), the temperature change of a gas (usually cooling) when it is allowed to expand freely.

The Gough–Joule effect or the Gow–Joule effect, which is the tendency of elastomers to contract if heated while they are under tension.

Joule expansion

The Joule expansion (also called free expansion) is an irreversible process in thermodynamics in which a volume of gas is kept in one side of a thermally isolated container (via a small partition), with the other side of the container being evacuated. The partition between the two parts of the container is then opened, and the gas fills the whole container.

The Joule expansion, treated as a thought experiment involving ideal gases, is a useful exercise in classical thermodynamics. It provides a convenient example for calculating changes in thermodynamic quantities, including the resulting increase in entropy of the universe (entropy production) that results from this inherently irreversible process. An actual Joule expansion experiment necessarily involves real gases; the temperature change in such a process provides a measure of intermolecular forces.

This type of expansion is named after James Prescott Joule who used this expansion, in 1845, in his study for the mechanical equivalent of heat, but this expansion was known long before Joule e.g. by John Leslie, in the beginning of the 19th century, and studied by Joseph-Louis Gay-Lussac in 1807 with similar results as obtained by Joule.The Joule expansion should not be confused with the Joule-Thompson effect.

Joule heating

Joule heating, also known as Ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor produces heat.

Joule's first law, also known as the Joule–Lenz law, states that the power of heating generated by an electrical conductor is proportional to the product of its resistance and the square of the current:

${\displaystyle P\propto I^{2}R}$

Joule heating affects the whole electric conductor, unlike the Peltier effect which transfers heat from one electrical junction to another.

Joule per mole

The joule per mole (symbol: J·mole−1 or J/mol) is an SI derived unit of energy per amount of material. Energy is measured in joules, and the amount of material is measured in moles. For example, Gibbs free energy is quantified as joules per mole.

Since 1 mole = 6.02214179×1023 particles (atoms, molecules, ions etc.), 1 Joule per mole is equal to 1 Joule divided by 6.02214179×1023 particles, or (6.022×10^23 particles/mole), 1.66054×10−24 Joule per particle. This very small amount of energy is often expressed in terms of a smaller unit such as the electronvolt (eV, see below).

Physical quantities measured in J·mol−1 usually describe quantities of energy transferred during phase transformations or chemical reactions. Division by the number of moles facilitates comparison between processes involving different quantities of material and between similar processes involving different types of materials. The meaning of such a quantity is always context-dependent and, particularly for chemical reactions, is dependent on the (possibly arbitrary) definition of a 'mole' for a particular process.

For convenience and due to the range of magnitudes involved these quantities are almost always reported in kJ·mol−1 rather than in J·mol−1. For example, heats of fusion and vaporization are usually of the order of 10 kJ·mol−1, bond energies are of the order of 100 kJ·mol−1, and ionization energies of the order of 1000 kJ·mol−1.

1 kJ·mol−1 is equal to 0.239 kcal·mol−1 or 1.04×10−2 eV per particle. At room temperature (25 °C, 77 °F, or 298.15 K) 1 kJ·mol−1 is equal to 0.4034  k B T {\displaystyle k_{B}T} .

Joule–Thomson effect

In thermodynamics, the Joule–Thomson effect (also known as the Joule–Kelvin effect, Kelvin–Joule effect) describes the temperature change of a real gas or liquid (as differentiated from an ideal gas) when it is forced through a valve or porous plug while keeping it insulated so that no heat is exchanged with the environment. This procedure is called a throttling process or Joule–Thomson process. At room temperature, all gases except hydrogen, helium and neon cool upon expansion by the Joule–Thomson process when being throttled through an orifice; these three gases experience the same effect but only at lower temperatures. Most liquids such as hydraulic oils will be warmed by the Joule-Thomson throttling process.

The gas-cooling throttling process is commonly exploited in refrigeration processes such as air conditioners, heat pumps, and liquefiers. In hydraulics, the warming effect from Joule-Thomson throttling can be used to find internally leaking valves as these will produce heat which can be detected by thermocouple or thermal-imaging camera. Throttling is a fundamentally irreversible process. The throttling due to the flow resistance in supply lines, heat exchangers, regenerators, and other components of (thermal) machines is a source of losses that limits the performance.

Mechanical equivalent of heat

In the history of science, the mechanical equivalent of heat states that motion and heat are mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat, provided the work done is totally converted to heat energy. The mechanical equivalent of heat was a concept that had an important part in the development and acceptance of the conservation of energy and the establishment of the science of thermodynamics in the 19th century.

Newton metre

The newton metre (also newton-metre, symbol N m or N⋅m) is a unit of torque (also called moment) in the SI system. One newton metre is equal to the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one metre long.

It is also used less commonly as a unit of work, or energy, in which case it is equivalent to the more common and standard SI unit of energy, the joule. In this usage the metre term represents the distance travelled or displacement in the direction of the force, and not the perpendicular distance from a fulcrum as it does when used to express torque. This usage is generally discouraged, since it can lead to confusion as to whether a given quantity expressed in newton metres is a torque or a quantity of energy. However, since torque represents energy transferred or expended per angle of revolution, one newton metre of torque is equivalent to one joule per radian.

Newton metres and joules are dimensionally equivalent in the sense that they have the same expression in SI base units:

${\displaystyle 1\,{\text{N}}{\cdot }\mathrm {m} =1{\frac {{\text{kg}}{\cdot }{\text{m}}^{2}}{{\text{s}}^{2}}}\quad ,\quad 1\,\mathrm {J} =1{\frac {\mathrm {kg} {\cdot }\mathrm {m} ^{2}}{\mathrm {s} ^{2}}}}$

Again, N⋅m and J are distinguished in order to avoid misunderstandings where a torque is mistaken for an energy or vice versa. Similar examples of dimensionally equivalent units include Pa versus J/m3, Bq versus Hz, and ohm versus ohm per square.

Performance per watt

In computing, performance per watt is a measure of the energy efficiency of a particular computer architecture or computer hardware. Literally, it measures the rate of computation that can be delivered by a computer for every watt of power consumed. This rate is typically measured by performance on the LINPACK benchmark when trying to compare between computing systems.

System designers building parallel computers, such as Google's hardware, pick CPUs based on their (other than Green500) performance per watt of power, because the cost of powering the CPU outweighs the cost of the CPU itself.

SI derived unit

SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg m−3), the SI derived unit of density.

The names of SI derived units, when written in full, are in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz"; but the symbol for metre is "m".

The Joule Hotel

The Joule Hotel is a five-star, 164-room hotel developed by Headington Hotels, owned by Timothy Headington. Located at 1530 Main Street, between Akard Street and Ervay Street, the building was constructed in 1927 as the Dallas National Bank Building, and was known later as the SPG Building. At the end of Stone Street Plaza, it is in the Main Street District of downtown Dallas, Texas, and with the Kirby Building, one of two Gothic high-rises in the city.

Its 10th floor pool cantilevers eight feet over the easement below, and was designed by ARCHITEXAS (Architecture, Planning and Historic Preservation, Inc). The interior was designed by Adam Tihany, and the lobby level is home to the CBD Provisions restaurant.From 2005 through 2007, evidence of a fire was discovered during ongoing renovations of the building next to the Joule. According to pictures available at the Dallas Public Library, in 1951, a significant fire occurred at the National Shirt Shop and Manuel's Cleaners, former businesses directly to the East of the Dallas National Bank building.

Units of energy

Because energy is defined via work, the SI unit for energy is the same as the unit of work – the joule (J), named in honor of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton metre and, in terms of SI base units

${\displaystyle 1\ \mathrm {J} =1\ \mathrm {kg} \left({\frac {\mathrm {m} }{\mathrm {s} }}\right)^{2}=1\ {\frac {\mathrm {kg} \cdot \mathrm {m} ^{2}}{\mathrm {s} ^{2}}}}$

An energy unit that is used in atomic physics, particle physics and high energy physics is the electronvolt (eV). One eV is equivalent to 1.60217653×10−19 J.

In spectroscopy the unit cm−1 = 0.000123986 eV is used to represent energy since energy is inversely proportional to wavelength from the equation ${\displaystyle E=h\nu =hc/\lambda }$.

In discussions of energy production and consumption, the units barrel of oil equivalent and ton of oil equivalent are often used. Cubic mile of oil is sometimes used as a unit of energy in discussions of global scale energy economics.

When discussing amounts of energy released in explosions or bolide impact events, the TNT equivalent unit is often used.

Watt

The watt (symbol: W) is a unit of power. In the International System of Units (SI) it is defined as a derived unit of 1 joule per second, and is used to quantify the rate of energy transfer. In dimensional analysis, power is described by ${\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}}$.

Base units
Derived units
with special names
Other accepted units