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joule
Intuitive representation of the joule as the work of a motive force
General information
Unit systemSI
Unit ofenergy
SymbolJ
Named afterJames Prescott Joule
Conversions
1 J in ...... is equal to ...
   SI base units   kg⋅m2⋅s−2
   CGS units   1×107 erg
   watt-seconds   1 W⋅s
   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

The joule (/dʒuːl/ JOOL, or /dʒaʊl/ JOWL; symbol: J) is the unit of energy in the International System of Units (SI).[1] In terms of SI base units, one joule corresponds to one kilogram-metre squared per second squared (1 J = 1 kg⋅m2⋅s−2). One joule is equal to the amount of work done when a force of one newton displaces a body through a distance of one metre in the direction of that force. 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]

Definition

[edit]

According to the International Bureau of Weights and Measures the joule is defined as "the work done when the point of application of 1 MKS unit of force [newton] moves a distance of 1 metre in the direction of the force."[5]

In terms of SI base units and in terms of SI derived units with special names, the joule is defined as[6]

Symbol Name
J joule
kg kilogram
m metre
s second
N newton
Pa pascal
W watt
C coulomb
V volt

One joule is also equivalent to any of the following:[7]

  • 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, which is 3.6 megajoules). This relationship can be used to define the watt.

The joule is named after James Prescott Joule. As with every SI unit named after 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.[8]

History

[edit]
In an 1882 British Science Association meeting, Chairman Siemens (left) proposed naming the unit after James Prescott Joule (right).

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 107 erg. The naming of the unit in honour of James Prescott Joule (1818–1889), at the time retired and aged 63, followed the recommendation of 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.[9]

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).[10] 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.[11]

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.[12] 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.[13] This is the definition declared in the modern International System of Units in 1960.[14]

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).[15]

Practical examples

[edit]

One joule represents (approximately):

  • The typical energy released as heat by a person at rest every 1/60 s (~16.6667 ms, basal metabolic rate); about 5,000 kJ (1,200 kcal) / day.
  • The amount of electricity required to run a 1 W device for 1 s.
  • The energy required to accelerate a 1 kg mass at 1 m/s2 through a distance of 1 m.
  • The kinetic energy of a 2 kg mass travelling at 1 m/s, or a 1 kg mass travelling at 1.41 m/s.
  • The energy required to lift an apple up 1 m, assuming the apple has a mass of 101.97 g.
  • The heat required to raise the temperature of 0.239 g of water from 0 °C to 1 °C.[16]
  • 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).[17]
  • The food energy (kcal) in slightly more than half of an ordinary-sized sugar crystal (0.102 mg/crystal).

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
10−27 J rJ rontojoule 1027 J RJ ronnajoule
10−30 J qJ quectojoule 1030 J QJ quettajoule
Common multiples are in bold face
zeptojoule
160 zeptojoules is about 1 electronvolt.
The minimal energy needed to change a bit of data in computation at around room temperature – approximately 2.75 zJ – is given by the Landauer limit.
nanojoule
160 nanojoules is about the kinetic energy of a flying mosquito.[18]
microjoule
The Large Hadron Collider (LHC) produces collisions of the microjoule order (7 TeV) per particle.
kilojoule
Nutritional food labels in most countries express energy in kilojoules (kJ).[19]
One square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.[20] A human in a sprint has approximately 3 kJ of kinetic energy,[21] while a cheetah in a 122 km/h (76 mph) sprint has approximately 20 kJ.[22] One watt-hour, of electricity or any other form of energy, is 3.6 kJ.
megajoule
The megajoule is approximately the kinetic energy of a one megagram (tonne) vehicle moving at 161 km/h (100 mph).
The energy required to heat 10 L 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 or any other form of energy, is 3.6 MJ.
gigajoule
6 gigajoules is about the chemical energy of combusting 1 barrel (159 L) of petroleum.[23] 2 GJ is about the Planck energy unit. One megawatt-hour, of electricity or any other form of energy, is 3.6 GJ.
terajoule
The terajoule is about 0.278 GWh (which is often used in energy tables). About 63 TJ of energy was released by Little Boy.[24] The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7700 m/s,[25] has a kinetic energy of roughly 13 TJ. In 2017, Hurricane Irma was estimated to have a peak wind energy of 112 TJ.[26][27] One gigawatt-hour, of electricity or any other form of energy, is 3.6 TJ.
petajoule
210 petajoules is about 50 megatons of TNT, which is the amount of energy released by the Tsar Bomba, the largest man-made explosion ever. One terawatt-hour, of electricity or any other form of energy, is 3.6 PJ.
exajoule
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, and the world final energy consumption was 439 EJ in 2021.[28] One petawatt-hour of electricity, or any other form of energy, is 3.6 EJ.
zettajoule
The zettajoule is somewhat more than the amount of energy required to heat the Baltic Sea by 1 °C, assuming properties similar to those of pure water.[29] Human annual world energy consumption is approximately 0.5 ZJ. The energy to raise the temperature of Earth's atmosphere 1 °C is approximately 2.2 ZJ.
yottajoule
The yottajoule is a little less than the amount of energy required to heat the Indian Ocean by 1 °C, assuming properties similar to those of pure water.[29] The thermal output of the Sun is approximately 400 YJ per second.[30]

Conversions

[edit]
Main article: Conversion of units of energy

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

  • 1.0×107 erg (exactly)
  • 6.24151×1018 eV
  • 9.47817×10−4 BTU
  • 0.737562 ft⋅lb (foot-pound)
  • 23.7304 ft⋅pdl (foot-poundal)

Units with exact equivalents in joules include:

  • 1 thermochemical calorie = 4.184 J[31]
  • 1 International Table calorie = 4.1868 J[32]
  • 1 W⋅h = 3,600 J; 3.6 kJ
  • 1 kW⋅h = 3.6×10^6 J; 3.6 MJ
  • 1 W⋅s = 1 J
  • 1 ton TNT = 4.184 GJ
  • 1 foe = 1044 J[33]

Newton-metre and torque

[edit]
Main article: Newton-metre

In mechanics, the concept of force (in some direction) has a close analogue in the concept of torque (about some angle):[34][35]

Linear Angular
Force Torque
Mass Moment of inertia
Displacement 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 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.[36] The use of newton-metres for torque but joules for energy is helpful to avoid misunderstandings and miscommunication.[36]

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[citation needed]

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

Watt-second

[edit]

A watt-second (symbol W s or W⋅s) is a derived unit of energy equivalent to the joule.[37] 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", such as in the rating of photographic electronic flash units.[38]

References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Joule

View on Grokipedia
from Grokipedia
The joule (symbol: J) is the derived unit of , work, and in the (SI). It is defined as the amount of work done when a force of one newton is applied over a distance of one in the direction of . In terms of SI base units, the joule is equivalent to one squared per second squared (kg⋅m²⋅s⁻²). Named in honour of the English physicist (1818–1889), who experimentally established the mechanical equivalent of heat through his pioneering work on the interconvertibility of mechanical work and thermal , the unit was adopted by the International Electrical Congress in 1889 and later formalized in the SI system. Joule's contributions, including precise measurements showing that heat is a form of energy rather than a separate fluid (caloric), laid foundational principles for the first law of thermodynamics. The joule is widely used across physics, engineering, and everyday applications to quantify energy transfers, such as in mechanical systems (e.g., kinetic or potential energy), electrical circuits (e.g., power consumption), and thermal processes (e.g., heat capacity). For context, one joule is approximately the energy required to lift an apple (about 100 grams) one metre against Earth's gravity, or the kinetic energy of a 1 kg mass moving at about 1.4 m/s. Common equivalents include: 1 joule ≈ 0.239 calories (the energy to raise 1 gram of water by 1 °C), 1 joule ≈ 9.48 × 10⁻⁴ British thermal units (Btu), and 1 kilowatt-hour (kWh) = 3.6 × 10⁶ joules. Larger multiples like the kilojoule (kJ), megajoule (MJ), and gigajoule (GJ) are employed for scales such as food nutrition, fuel combustion, and electrical billing.

Fundamentals

Definition

The joule (symbol: J) is the derived unit of in the (SI). It is defined as the amount of work done on an object when a force of one newton is applied over a distance of one in the direction of the force. This definition establishes the joule as the coherent SI unit for mechanical work; the symbol J honors the contributions of physicist to the understanding of and . The joule measures not only and work but also related quantities such as and , as well as forms of potential and in physical systems. In terms of SI base units, it is dimensionally equivalent to one times one squared per second squared, expressed as J=kg⋅m2⋅s−2\mathrm{J} = \mathrm{kg \cdot m^2 \cdot s^{-2}}. This equivalence arises from the work W=F⋅dW = F \cdot d, where WW is work in joules, FF is force in newtons (N=kg⋅m⋅s−2\mathrm{N = kg \cdot m \cdot s^{-2}}), and dd is displacement in metres, yielding 1 J=1 N⋅m1 \, \mathrm{J} = 1 \, \mathrm{N \cdot m}.

Expression in Base Units

The joule, as a derived unit in the International System of Units (SI), has the dimensional formula J = kg·m²·s⁻², which combines the base units of mass (kilogram, kg), length (metre, m), and time (second, s) to represent energy or work. This expression arises from the fundamental physical principles of force and displacement, ensuring the unit's direct linkage to the SI's foundational measurements. The derivation begins with Newton's second law of motion, where FF equals mm times aa, so F=m⋅aF = m \cdot a. Substituting the base units yields the newton (N), the SI unit of : N=kg⋅m⋅s−2\mathrm{N} = \mathrm{kg} \cdot \mathrm{m} \cdot \mathrm{s}^{-2}. Work or energy is then defined as applied over a distance, leading to the joule as J=N⋅m=(kg⋅m⋅s−2)⋅m=kg⋅m2⋅s−2J = N \cdot m = (\mathrm{kg} \cdot \mathrm{m} \cdot \mathrm{s}^{-2}) \cdot \mathrm{m} = \mathrm{kg} \cdot \mathrm{m}^2 \cdot \mathrm{s}^{-2}. As a coherent derived unit within the SI, the joule requires no additional numerical constants other than unity in its defining equations, promoting consistency across physical laws that involve , such as those in and . This coherence stems directly from the base unit definitions of the , , and second, allowing seamless integration without conversion factors. In , the joule is realized experimentally through mechanical standards that measure and displacement, often using devices like the to link it to the SI base units via fundamental constants and precise interferometric techniques. These methods ensure the unit's practical accuracy and in laboratories worldwide.

Historical Development

Contributions of James Prescott Joule

James Prescott Joule (1818–1889) was a British and brewer whose self-taught scientific pursuits in the focused on the interplay between , mechanical work, and . Working from his family's brewery in , Joule conducted meticulous experiments to quantify how mechanical energy could produce , building on earlier electrical studies that hinted at energy interconvertibility. Joule's most renowned contribution was the paddle-wheel experiment, first performed around , which directly measured the conversion of mechanical work into . The apparatus consisted of a calorimeter filled with (or other liquids like mercury), containing a with radial arms that churned the fluid when driven by falling weights attached via strings and pulleys. As the weights descended—totaling a drop of about 1260 inches and performing approximately 6067 foot-pounds of work—the paddle's raised the 's by a small but precisely recorded amount, such as 0.56°F. Joule insulated the setup to minimize external loss and corrected for minor inefficiencies, demonstrating that the generated was proportional to the work expended. Through a series of seven refined trials with the paddle-wheel in , Joule calculated the mechanical equivalent of as approximately 772 foot-pounds of work required to raise the temperature of one pound of by 1°F in a . This value, refined across experiments with different fluids and materials (yielding results from 772 to 776 foot-pounds), equated to about 4.18 joules per in modern terms, though Joule expressed it in British units. His findings provided that is not a separate substance but a form of , directly proportional to mechanical : "the quantity of produced by the friction of bodies... is always proportional to the quantity of expended." Joule's experiments fundamentally challenged the prevailing , which posited heat as an indestructible fluid-like entity called caloric, and instead supported the emerging concept of . By quantifying the heat-work relationship, his work influenced the formulation of of , establishing that in various forms—mechanical, thermal, and electrical—is interchangeable and conserved.

Adoption and Standardization

The name "joule" for the unit of energy was first proposed in 1882 by William Siemens, president of the British Association for the Advancement of (BAAS), in an address advocating practical units based on the metre-kilogram-second (MKS) system. This proposal aligned with emerging international efforts to standardize units beyond the centimetre-gram-second (CGS) system, where the erg served as the energy unit. The name was adopted by the International Electrical Congress in 1889, shortly after James Prescott Joule's death on October 11 of that year. In 1946, the International Committee for Weights and Measures (CIPM) formally recommended the joule as the MKS unit of or work, defining it as the work done by a force of one newton acting over a distance of one . This recommendation was ratified by the 9th General Conference on Weights and Measures (CGPM) in , which officially adopted the name "joule" (symbol J) and encouraged its use as the international unit for quantity of in , replacing less consistent units. At the same time, the joule supplanted the erg in the MKS system, providing a coherent unit scaled for practical applications (1 J = 10^7 erg). The joule was integrated into the (SI) in 1960 by the 11th CGPM, which established it as a derived unit within the metre-kilogram-second framework, expressed as kg·m²·s⁻². Its definition evolved from reliance on absolute mechanical measurements—tied to physical prototypes like the international kilogram—to a quantum-based standard following the 2019 SI redefinition by the 26th CGPM, which fixed the at exactly 6.626 070 15 × 10^{-34} J·s, thereby anchoring the joule's value to fundamental physical invariants rather than artifacts.

Equivalent Expressions

Mechanical Equivalents

The joule, as a unit of mechanical work and energy, is fundamentally expressed as one newton-meter (N·m), representing the work accomplished when a constant force of one newton acts over a displacement of one meter in the direction of the force. This equivalence underscores the joule's role in quantifying energy transfer through mechanical means, such as lifting an object against or stretching a spring. In broader mechanical contexts, work is defined as the of the vector over the path of displacement: W=∫F⋅dsW = \int \mathbf{F} \cdot d\mathbf{s} where F\mathbf{F} is the applied and dsd\mathbf{s} is the infinitesimal displacement vector. For cases of constant aligned with the displacement, this reduces to the scalar product W=FdW = F d, with FF in newtons and dd in meters, yielding in joules. This formulation is central to , enabling calculations of in systems like colliding objects or rotating mechanisms. Another mechanical equivalent arises in pressure-volume interactions, where 1 J = 1 Pa·m³ (pascal-cubic meter), applicable to thermodynamic processes like gas expansion in a . Here, work is computed as W=∫P dVW = \int P \, dV for varying PP, or W=PΔVW = P \Delta V under constant , linking mechanical to and heat engines. The joule's base-unit form, 1 J = kg·m²·s⁻², further manifests in kinetic expressions, such as 12mv2\frac{1}{2} m v^2, where mass mm is in kilograms, velocity vv in meters per second, highlighting its utility in motion-related energy assessments. In , the joule thus measures work, potential and kinetic energies, providing a metric for physical interactions. The (N·m) is also used for , a distinct with the same dimensions.

Electrical and Thermal Equivalents

In the electrical domain, the joule quantifies energy as the product of electrical potential and charge, such that 1 J = 1 V · C, where V denotes volts and C denotes coulombs. This equivalence stems from the definition of voltage as energy per unit charge. The fundamental relation linking power to energy is given by the equation for electrical power P=VIP = V I, where II is current in amperes; integrating over time yields energy E=Pt=VItE = P t = V I t, expressed in joules when tt is in seconds. This formulation underpins applications in electrical circuits, where the joule measures energy delivered to components, such as in storage devices like batteries or capacitors, and in dissipative processes like resistive heating, known as . In these contexts, the unit facilitates calculations of and capacity in power systems. In the thermal domain, the joule serves as the SI unit for and , directly linking mechanical or electrical work to temperature changes via specific heat capacities. It is related to the through the conversion 1 J ≈ 0.239 cal using the international steam table (cal_IT), with the exact modern value being 1 cal_IT = 4.1868 J, so 1 J = 1 / 4.1868 cal_IT ≈ 0.238846 cal_IT. This equivalence ensures consistency in thermodynamic calculations across energy forms. Contemporary applications extend to cryogenic systems, where the joule quantifies transfers in processes like the Joule-Thomson expansion for cooling gases to low temperatures in and technologies.

Applications

Practical Examples

In , a fundamental example of work expressed in joules is the required to lift a 1 kg 1 meter against Earth's gravity, where the acceleration due to gravity is approximately 9.8 m/s². The work done is calculated as W=mghW = m g h, yielding W=1 kg×9.8 m/s2×1 m=9.8 JW = 1 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 1 \, \text{m} = 9.8 \, \text{J}. This illustrates how the joule quantifies gravitational potential in everyday lifting tasks. For , consider a 1 kg object moving at 1 m/s; its energy is KE=12mv2=12×1 kg×(1 m/s)2=0.5 JKE = \frac{1}{2} m v^2 = \frac{1}{2} \times 1 \, \text{kg} \times (1 \, \text{m/s})^2 = 0.5 \, \text{J}. Similarly, the stored in a compressed spring follows U=12kx2U = \frac{1}{2} k x^2, where kk is the spring constant and xx is the compression ; for a spring with k=200 N/mk = 200 \, \text{N/m} compressed by 0.1 m, U=12×200 N/m×(0.1 m)2=1 JU = \frac{1}{2} \times 200 \, \text{N/m} \times (0.1 \, \text{m})^2 = 1 \, \text{J}. A practical engineering example is the muzzle energy of a 9 mm bullet, which represents the kinetic energy imparted upon firing. Typical 9 mm ammunition has a bullet mass of about 8 grams (0.008 kg) and a muzzle velocity of around 350 m/s. The kinetic energy is KE=12mv2=12×0.008 kg×(350 m/s)2≈490 JKE = \frac{1}{2} m v^2 = \frac{1}{2} \times 0.008 \, \text{kg} \times (350 \, \text{m/s})^2 \approx 490 \, \text{J}, often rounded to approximately 500 J for standard loads. This value highlights the joule's role in quantifying impact energies in ballistics. In thermal applications, consider the energy dissipated as in a bulb's filament. A standard 100 W incandescent bulb consumes electrical power at a rate of 100 J/s, meaning that in 1 second of operation, it converts 100 J into and , with the majority heating the tungsten filament to incandescence. For modern , battery capacity provides a relatable example of stored electrical in joules. A typical lithium-ion battery operates at 3.7 V nominal voltage with a capacity of 3000 mAh (3 Ah). To convert to joules, first find the charge in coulombs: Q=3 Ah×3600 s/h=10,800 CQ = 3 \, \text{Ah} \times 3600 \, \text{s/h} = 10{,}800 \, \text{C}; then, is E=VQ=3.7 V×10,800 C≈40,000 JE = V Q = 3.7 \, \text{V} \times 10{,}800 \, \text{C} \approx 40{,}000 \, \text{J} (or about 11 Wh). This conversion underscores how joules scale to represent portable in devices.

Use in Specific Fields

In nutrition, the joule serves as a standard unit for measuring dietary energy, with recommendations often expressed in kilojoules (kJ) or megajoules (MJ) to quantify daily intake needs. The (WHO), in collaboration with the (FAO), defines energy requirements for adults based on factors like age, sex, and physical activity level, typically ranging from 7 to 12 MJ per day for moderately active individuals. For instance, the conversion between traditional caloric units and joules is precise, where 1 kilocalorie (kcal) equals exactly 4.184 kJ, allowing nutrition labels and guidelines to align SI standards with legacy systems. This adoption promotes global consistency, as WHO guidelines emphasize limiting free sugars to less than 10% of total energy intake, calculated in kJ to support policies. In meteorology, the joule quantifies extreme atmospheric energy releases, such as in lightning strikes, where a typical cloud-to-ground bolt dissipates approximately 1 gigajoule (GJ) of electrical energy over its path. This scale highlights the joule's utility in assessing storm impacts, as the total energy—often 1 to 10 GJ per strike—can power a 100-watt bulb for months but is too brief and unpredictable for practical harnessing. Similarly, wind energy assessments use joules to evaluate kinetic energy flux, with global wind power potential estimated in terajoules (TJ) annually, informing renewable forecasts and climate models. Astronomy employs the joule to describe radiative and gravitational energy fluxes across cosmic scales. The solar constant, representing the average energy flux from the Sun at , measures about 1.36 kJ per square meter per second, providing a baseline for calculations in . In black hole physics, energy scales reach immense proportions, such as the from merging s releasing up to 5 × 10^{47} J—equivalent to several solar masses converted via E = mc²—detected by observatories like to probe dynamics. In engineering, particularly energy systems, the joule evaluates through volumetric , with typically containing around 32 MJ per liter, guiding combustion engine design and emissions standards. This metric enables comparisons across fuels, where higher MJ/L values indicate greater range per volume, influencing automotive and applications without delving into combustion mechanics. At the quantum level, the joule underpins calculations via E = hν, where h is Planck's constant (6.626 × 10^{-34} J·s) and ν is , expressing discrete packets in processes like photoelectric emission and . This formulation, integral to , scales from individual photons (e.g., visible light at ~10^{-19} J) to macroscopic fields, bridging microscopic interactions with observable phenomena. In battery contexts, it aligns with storage rated in watt-hours convertible to joules, emphasizing charge-discharge efficiency.

Multiples and Submultiples

Common Multiples

The kilojoule (kJ), equivalent to 10³ joules, is commonly used to express moderate quantities in everyday and scientific contexts, such as nutritional content on food labels where daily intake might range from 8,000 to 12,000 kJ for an average adult, and the energy released in small explosions like that of 1 gram of TNT, which yields approximately 4.184 kJ. The megajoule (MJ), or 10⁶ joules, scales up to larger energy transfers, including the energy in fuels—such as a full 50-liter tank containing roughly 1,600 MJ based on an of about 44 MJ/kg—and the typical discharge of a lightning bolt, which releases between 1,000 and 5,000 MJ. At the gigajoule (GJ) level, representing 10⁹ joules, measurements apply to substantial annual budgets, like the average U.S. household's total consumption of approximately 170 GJ per year across , heating, and other sources as of 2022. SI prefixes extend to even larger multiples of the joule for specialized applications, particularly in and cosmology, though prefixes beyond - are infrequently used in practical due to the immense scales involved. The following table summarizes the standard decimal multiples from kilo- to yotta-, including their factors and representative examples:
PrefixSymbolFactorExample Use Case
kilo-k10³Food energy intake (e.g., 10 kJ per serving)
mega-M10⁶Lightning bolt energy (e.g., 2,000 MJ)
giga-G10⁹Annual energy use (e.g., 170 GJ as of 2022)
tera-T10¹²Large (e.g., 0.02 TJ per ton of primary production)
peta-P10¹⁵Global daily energy supply (e.g., ~1,600 PJ as of 2024)
exa-E10¹⁸Annual (e.g., 600 EJ as of 2024)
zetta-Z10²¹ output of the Sun per day (e.g., ~3.3 × 10^{10} ZJ)
yotta-Y10²⁴Total absorbed by annually (e.g., 3.85 YJ)
These prefixes adhere to the definitions in the SI Brochure published by the International Bureau of Weights and Measures (BIPM), which standardizes them for all base and derived units like the joule to ensure consistency across scientific and technical fields; in practice, multiples above tera- are mostly theoretical or reserved for planetary and cosmic scales due to challenges.

Common Submultiples

Submultiples of the joule are defined using SI decimal prefixes to express fractions of the unit, enabling precise measurement of energy at progressively smaller scales in fields such as , , chemistry, and quantum physics. These prefixes are essential for describing phenomena from short pulses to atomic and subatomic interactions, where energies are too small to conveniently express in joules alone. The system standardizes notation, with each prefix representing a ^{-3}, as established by the International Bureau of Weights and Measures (BIPM). The millijoule (mJ), equivalent to 10^{-3} J, is frequently used for the energy delivered in short pulses, such as those in lasers for applications like and material processing. For instance, 100-nanosecond Er-doped lasers have achieved millijoule pulse energies at 1.55 μm . The microjoule (µJ), or 10^{-6} J, appears in for energy per operation in pulsed systems and in high-repetition-rate lasers for scientific instrumentation. Mode-locked vertical-external-cavity surface-emitting semiconductor disk lasers have produced pulses approaching microjoule energies, compressed to 711 fs durations with megawatt peak powers. The nanojoule (nJ), 10^{-9} J, is relevant for energy scales in and advanced , including mode-locked outputs. Polarization-maintaining, all-fiberized thulium-doped fiber lasers have demonstrated dissipative solitons at nanojoule energy levels operating at 1876 nm. Smaller submultiples, starting from the picojoule (pJ, 10^{-12} J), are critical for quantifying energies in molecular bonds and quantum events. These extend down to the yoctojoule (yJ, 10^{-24} J), used in for ultra-low-energy processes like those involving photons, whose average energy is approximately 3.7 × 10^{-23} J. The femtojoule (fJ, 10^{-15} J) and attojoule (aJ, 10^{-18} J) particularly suit atomic-scale applications, such as electron transitions with energies around 10^{-18} J, equivalent to several electronvolts (where 1 eV = 1.602 × 10^{-19} J). The following table summarizes common submultiples of the joule, including their factors and representative applications in microscopic and atomic contexts:
PrefixUnit SymbolFactorRepresentative Application
milli-mJ10^{-3}Laser pulses in fiber-based LIDAR systems
micro-µJ10^{-6}Pulses in mode-locked lasers
nano-nJ10^{-9}Outputs from thulium-doped mode-locked lasers
pico-pJ10^{-12}Switching energies in photonic integrated circuits
femto-fJ10^{-15}Gate operations in nanoscale devices
atto-aJ10^{-18}Single molecular bond dissociation or atomic transitions
yocto-yJ10^{-24}Quantum events in , e.g., low-energy photons in cosmic backgrounds

Clarifications and Distinctions

Relation to Newton-Metre

The joule (J) is defined in the (SI) as the work done when a force of one newton is applied over a distance of one in the direction of the force, establishing the direct equivalence 1 J=1 N⋅m1 \, \mathrm{J} = 1 \, \mathrm{N \cdot m} for linear mechanical work or energy transfer. This equivalence holds because the joule quantifies scalar energy, derived from the product of force and displacement along the line of action. However, the unit (N·m) is also the SI unit for , or moment of , which represents the rotational equivalent of applied perpendicular to a lever arm. Unlike the joule, which specifically denotes , in N·m measures the tendency to cause without implying unless multiplied by an angular displacement; the SI explicitly specifies N·m for rather than the joule to avoid confusion, as the joule is never used to express . In rotational contexts, the energy or work associated with torque is given by W=τθW = \tau \theta, where τ\tau is in N·m and θ\theta is the in , yielding units of joules since one radian is dimensionless. Thus, while dimensionally identical, a standalone N·m value for torque does not equate to a joule of energy; for instance, applying a 1 N·m over 1 radian transfers 1 J, but the torque itself remains a vectorial moment distinct from scalar . A common misconception arises from assuming all instances of N·m represent joules, overlooking the contextual distinction: torque involves vector cross products (force perpendicular to radius), whereas work in joules is a scalar path integral. This separation ensures clarity in applications like , where torque magnitudes are reported in N·m to emphasize rotational effect rather than .

Relation to Watt-Second

The joule is numerically equivalent to the watt-second, meaning 1 J = 1 W·s. This equivalence arises because the watt (W) is defined as one joule per second (J/s), representing power as the rate of energy transfer. In fundamental terms, energy in joules is the time of power in watts. For constant power, this simplifies to E=P⋅tE = P \cdot t, where EE is energy in joules, PP is power in watts, and tt is time in seconds. More generally, power is the time of energy, P=dEdtP = \frac{dE}{dt}, so integrating yields E=∫P dtE = \int P \, dt, with the result in joules. This relation underscores the joule as the SI unit for energy derived from power over time. Although the watt-second is sometimes used in electrical engineering contexts for its intuitive connection to power and time, it carries no distinction in magnitude from the joule and is not a preferred SI name. The joule remains the standard SI unit for all energy measurements. In renewable energy assessments, conversions from watt-hours (Wh) to joules are common, such as 1 Wh = 3,600 J, to align metrics with SI conventions.

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