The Stefan–Boltzmann law, also known as Stefan's law, describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time (also known as the black-body radiant exitance or emissive power), , is directly proportional to the fourth power of the black body's thermodynamic temperature T:

The constant of proportionality σ, called the Stefan–Boltzmann constant or Stefan's constant, derives from other known constants of nature. The value of the constant is
where k is the Boltzmann constant, h is Planck's constant, and c is the speed of light in a vacuum. Thus at 100 K the energy flux is 5.67 W/m2, at 1000 K 56,700 W/m2, etc. The radiance (watts per square metre per steradian) is given by
A body that does not

absorb all incident radiation (sometimes known as a grey body) emits less total energy than a black body and is characterized by an emissivity, :
The irradiance has dimensions of energy flux (energy per time per area), and the SI units of measure are joules per second per square metre, or equivalently, watts per square metre. The SI unit for absolute temperature T is the kelvin. is the emissivity of the grey body; if it is a perfect blackbody, . In the still more general (and realistic) case, the emissivity depends on the wavelength, .
To find the total power radiated from an object, multiply by its surface area, :
Metamaterials may be designed to exceed the Stefan–Boltzmann law.

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  • 1. [Stefan–Boltzmann constant] The Stefan–Boltzmann constant (also Stefan's constant), a physical constant denoted by the Greek letter σ, is the constant of proportionality in the Stefan–Boltzmann law: "the total intensity (physics) radiated over all wavelengths increases as the temperature increases", of a black body which is proportional to the fourth power of the thermodynamic temperature. The theory of
  • 2. [Planck's law] Planck's law describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature. The law is named after Max Planck, who originally proposed it in 1900. It is a pioneering result of modern physics and quantum theory.
  • 3. [Wien's displacement law] Wien's displacement law states that the wavelength distribution of thermal radiation from a black body at any temperature has essentially the same shape as the distribution at any other temperature, except that each wavelength is displaced on the graph. Apart from an overall T4 multiplicative factor, the average thermal energy in each mode with frequency
  • 4. [Emissivity] The emissivity of the surface of a material is its effectiveness in emitting thermal radiation compared to that of a "black body" at the same temperature; emissivity (usually written ε or e) is a simple number that is between 0 and 1. Thermal radiation is light, but for objects near room temperature (20 Celsius) this
  • 5. [Joseph Stefan] Joseph Stefan (Slovene: Jožef Stefan) (24 March 1835 – 7 January 1893) was a Carinthian Slovene physicist, mathematician, and poet of Austrian citizenship.
  • 6. [Black body] A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A white body is one with a "rough surface [that] reflects all incident rays completely and uniformly in all directions."
  • 7. [Dulong–Petit law] The Dulong–Petit law, a thermodynamic rule proposed in 1819 by French physicists Pierre Louis Dulong and Alexis Thérèse Petit, states the classical expression for the molar specific heat capacity of a crystal. Experimentally the two scientists had found that the heat capacity per weight (the mass-specific heat capacity) for a number of substances became close
  • 8. [Radiance] Radiance and spectral radiance are measures of the quantity of radiation that passes through or is emitted from a surface and falls within a given solid angle in a specified direction. They are used in radiometry to characterize diffuse emission and reflection of electromagnetic radiation. In astrophysics, radiance is also used to quantify emission of
  • 9. [Black-body radiation] Black-body radiation is the type of electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body (an opaque and non-reflective body) held at constant, uniform temperature. The radiation has a specific spectrum and intensity that depends only on the temperature of the body.
  • 10. [Thermodynamic temperature] Thermodynamic temperature is the absolute measure of temperature and it is one of the principal parameters of thermodynamics.
    Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, called absolute zero, the particle constituents of matter have minimal motion and can
  • 11. [Ludwig Boltzmann] Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion).
  • 12. [Irradiance] Irradiance is the power of electromagnetic radiation per unit area (radiative flux) incident on a surface. Radiant emittance or radiant exitance is the power per unit area radiated by a surface. The SI units for all of these quantities are watts per square meter (W/m2), while the cgs units are ergs per square centimeter per
  • 13. [Hawking radiation] Hawking radiation is black body radiation that is predicted to be released by black holes, due to quantum effects near the event horizon.
    It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after Jacob Bekenstein, who predicted that black holes should have a finite, non-zero temperature and entropy.
  • 14. [Boltzmann constant] The Boltzmann constant (kB or k), named after Ludwig Boltzmann, is a physical constant relating energy at the individual particle level with temperature. It is the gas constant R divided by the Avogadro constant NA:
  • 15. [Polylogarithm] In mathematics, the polylogarithm (also known as Jonquière's function) is a special function Lis(z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or rational functions. In quantum statistics, the polylogarithm function appears as the closed form of integrals
  • 16. [Proportionality (mathematics)] In mathematics, two variables are proportional if a change in one is always accompanied by a change in the other, and if the changes are always related by use of a constant. The constant is called the coefficient of proportionality or proportionality constant.
  • 17. [Planck constant] For the law governing black body radiation, see Planck's law.
    The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of action in quantum mechanics. Published in 1900, it originally described the proportionality constant between the energy (E) of a charged atomic oscillator in the wall of a black
  • 18. [Black hole thermodynamics] In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. Much as the study of the statistical mechanics of black body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle.
  • 19. [Claude Pouillet] Claude Servais Mathias Pouillet (16 February 1790 – 14 June 1868) was a French physicist and a professor of physics at the Sorbonne and member of the French Academy of Science. Succeeding Dulong, he became the fourth holder of the chair of physics at Polytechnique for a brief period of time (1830-1831) but chose to resign, citing health reasons. He was succeeded by César Despretz in 1831 and Gabriel Lamé in 1832.
  • 20. [John Tyndall] John Tyndall FRS (2 August 1820 – 4 December 1893) was a prominent 19th century physicist. His initial scientific fame arose in the 1850s from his study of diamagnetism. Later he made discoveries in the realms of infrared radiation and the physical properties of air. Tyndall also published more than a dozen science books which
  • 21. [Heat engine] In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical energy which can then be used to do mechanical work. It does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat "source" generates thermal energy that brings
  • 22. [Charles Soret] Charles Soret (born 23 September 1854, Geneva, Switzerland; died 4 April 1904) was a Swiss physicist and chemist. He is universally known for his work on thermodiffusion (the so-called Soret effect).
  • 23. [Absorption (electromagnetic radiation)] In physics, absorption of electromagnetic radiation is the way in which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed into internal energy of the absorber, for example thermal energy. The reduction in intensity of a light wave propagating through a medium
  • 24. [Luminosity] In astronomy, luminosity is the total amount of energy emitted by a star, galaxy, or other astronomical object per unit time. It is related to brightness, which is the luminosity of an object in a given spectral region.
  • 25. [Riemann zeta function] The Riemann zeta function or Euler–Riemann zeta function, ζ(s), is a function of a complex variable s that analytically continues the sum of the infinite series , which converges when the real part of s is greater than 1. More general representations of ζ(s) for all s are given below. The Riemann zeta function plays a pivotal role in analytic number theory and has applications in physics, probability theory, and applied statistics.
  • 26. [Kelvin] The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units (SI) and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases
  • 27. [Effective temperature] The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's temperature when the body's emissivity curve (as a function of wavelength) is not known.
  • 28. [Speed of light] The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its value is exactly 299,792,458 metres per second because the length of the metre is defined from this constant and the international standard for time. This is, to three significant figures, 186,000 miles per second,
  • 29. [Dimensionless physical constant] In physics, a dimensionless physical constant, sometimes called fundamental physical constant, is a physical constant that is dimensionless – having no units attached, having a numerical value that is the same under all possible systems of units. A common example is the fine-structure constant α, with approximate value 7.29735257×10−3.
  • 30. [Albedo] Albedo (/ælˈbiːdoʊ/), or reflection coefficient, derived from Latin albedo "whiteness" (or reflected sunlight) in turn from albus "white," is the diffuse reflectivity or reflecting power of a surface. It is the ratio of reflected radiation from the surface to incident radiation upon it. Its dimensionless nature lets it be expressed as a percentage and is measured on a scale from zero for no reflection of a perfectly black surface to 1 for perfect reflection of a white surface.
  • 31. [Solar radius] Solar radius is a unit of distance used to express the size of stars in astronomy equal to the current radius of the Sun:
    The solar radius is approximately 695,500 kilometres (432,450 miles) or about 110 times the radius of the Earth, or 10 times the average radius of Jupiter. It varies slightly from pole to equator due to its rotation, which induces an oblateness of order 10 parts per million. See 1 gigametre for similar distances.
  • 32. [Methods of contour integration] In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.
    One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods.
  • 33. [Joule] The joule (/ˈdʒuːl/ or sometimes /ˈdʒaʊl/), symbol J, is a derived unit of energy, work, or amount of heat 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 metre (1 newton metre or N·m), or in
  • 34. [Spherical coordinate system] In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.
  • 35. [Thermodynamics] Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work. It defines macroscopic variables, such as internal energy, entropy, and pressure, that partly describe a body of matter or radiation. It states that the behavior of those variables is subject to general constraints, that are common to
  • 36. [International System of Units] The International System of Units (abbreviated SI from French: Le Système international d'unités) is the modern form of the metric system and is the world's most widely used system of measurement, used in both everyday commerce and science. It comprises a coherent system of units of measurement built around seven base units, 22 named and
  • 37. [Metamaterial] Metamaterials are artificial materials engineered to have properties that may not be found in nature. They are assemblies of multiple individual elements fashioned from conventional microscopic materials such as metals or plastics, but the materials are usually arranged in repeating patterns. Metamaterials gain their properties not from their composition, but from their exactingly-designed structures. Their
  • 38. [Black hole] A black hole is a region of spacetime from which gravity prevents anything, including light, from escaping. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon. Although crossing the
  • 39. [Light] Light is radiant energy, usually referring to electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light is usually defined as having a wavelength in the range of 400 nanometres (nm), or 400×10−9 m, to 700 nanometres – between the infrared, with longer wavelengths and the
  • 40. [Celsius] Celsius, also known as centigrade, is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale as well as a unit to indicate a temperature interval, a
  • 41. [Methane] Methane (/ˈmɛθeɪn/ or /ˈmiːθeɪn/) is a chemical compound with the chemical formula CH
    4 (one atom of carbon and four atoms of hydrogen). It is the simplest alkane and the main component of natural gas. The relative abundance of methane makes it an attractive fuel, though capturing and storing it may pose challenges due to

  • 42. [Energy] In physics, energy is a property of objects, transferable among them via fundamental interactions, which can be converted in form but not created or destroyed. The joule is the SI unit of energy, based on the amount transferred to an object by the mechanical work of moving it 1 metre against a force of 1 newton.
  • 43. [Sun] The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields. It has a diameter of about 1,392,684 km (865,374 mi), around 109 times that of Earth, and its mass (1.989×1030 kilograms, approximately 330,000 times the mass of Earth) accounts
  • 44. [Taylor series] In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
  • 45. [Differentiable function] In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain. As a result, the graph of a differentiable function must have a non-vertical tangent line at each point in its domain, be relatively smooth, and cannot contain any breaks, bends, or cusps.
  • 46. [Atmosphere of Earth] The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention (greenhouse effect), and reducing temperature extremes between day and night (the diurnal temperature variation).
  • 47. [Convex hull] In mathematics, the convex hull or convex envelope of a set X of points in the Euclidean plane or Euclidean space is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape formed by a rubber band stretched around X.
  • 48. [Watt] The watt (symbol: W) is a derived unit of power in the International System of Units (SI), named after the Scottish engineer James Watt (1736–1819). The unit, defined as one joule per second, measures the rate of energy conversion or transfer.
  • 49. [Greenhouse gas] A greenhouse gas (sometimes abbreviated GHG) is a gas in an atmosphere that absorbs and emits radiation within the thermal infrared range. This process is the fundamental cause of the greenhouse effect. The primary greenhouse gases in the Earth's atmosphere are water vapor, carbon dioxide, methane, nitrous oxide, and ozone. Greenhouse gases greatly affect the
  • 50. [Time] Time is a dimension and measure in which events can be ordered from the past through the present into the future, and also the measure of durations of events and the intervals between them. Time has long been a major subject of study in religion, philosophy, and science, but defining it in a manner applicable
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