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A black body or blackbody is an idealized
physical body In common usage and classical mechanics, a physical object or physical body (or simply an object or body) is a collection of matter within a defined contiguous boundary in three-dimensional space. The boundary must be defined and identified by t ...
that absorbs all incident
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) l ...
, regardless of frequency or angle of incidence. The name "black body" is given because it absorbs all colors of light. A black body also emits
black-body radiation Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spec ...
. In contrast, a white body is one with a "rough surface that reflects all incident rays completely and uniformly in all directions." A black body in
thermal equilibrium Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in ...
(that is, at a constant temperature) emits electromagnetic black-body radiation. The radiation is emitted according to
Planck's law In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature , when there is no net flow of matter or energy between the body and its environment. A ...
, meaning that it has a
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
that is determined by the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
alone (see figure at right), not by the body's shape or composition. An ideal black body in thermal equilibrium has two main properties: #It is an ideal emitter: at every frequency, it emits as much or more thermal radiative energy as any other body at the same temperature. #It is a diffuse emitter: measured per unit area perpendicular to the direction, the energy is radiated isotropically, independent of direction. An approximate realization of a black surface is a hole in the wall of a large insulated enclosure (an
oven upA double oven A ceramic oven An oven is a tool which is used to expose materials to a hot environment. Ovens contain a hollow chamber and provide a means of heating the chamber in a controlled way. In use since antiquity, they have been us ...
, for example). Any light entering the hole is reflected or absorbed at the internal surfaces of the body and is unlikely to re-emerge, making the hole a nearly perfect absorber. When the radiation confined in such an enclosure is in thermal equilibrium, the radiation emitted from the hole will be as great as from any body at that equilibrium temperature. Real materials emit energy at a fraction—called the
emissivity The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation that most commonly includes both visible radiation (light) and infrared radiation, which is ...
—of black-body energy levels. By definition, a black body in thermal equilibrium has an emissivity . A source with a lower emissivity, independent of frequency, is often referred to as a gray body. Constructing black bodies with an emissivity as close to 1 as possible remains a topic of current interest. In
astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, gala ...
star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth ma ...
s and
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a yo ...
s is sometimes characterized in terms of an
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 surface temperature ...
, the temperature of a black body that would emit the same total flux of electromagnetic energy.

# Definition

The idea of a black body originally was introduced by
Gustav Kirchhoff Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coine ...
in 1860 as follows: A more modern definition drops the reference to "infinitely small thicknesses":

# Idealizations

This section describes some concepts developed in connection with black bodies.

## Cavity with a hole

A widely used model of a black surface is a small hole in a cavity with walls that are opaque to radiation. Radiation incident on the hole will pass into the cavity, and is very unlikely to be re-emitted if the cavity is large. The hole is not quite a perfect black surface—in particular, if the wavelength of the incident radiation is greater than the diameter of the hole, part will be reflected. Similarly, even in perfect thermal equilibrium, the radiation inside a finite-sized cavity will not have an ideal Planck spectrum for wavelengths comparable to or larger than the size of the cavity. Suppose the cavity is held at a fixed temperature ''T'' and the radiation trapped inside the enclosure is at
thermal equilibrium Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in ...
with the enclosure. The hole in the enclosure will allow some radiation to escape. If the hole is small, radiation passing in and out of the hole has negligible effect upon the equilibrium of the radiation inside the cavity. This escaping radiation will approximate
black-body radiation Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spec ...
that exhibits a distribution in energy characteristic of the temperature ''T'' and does not depend upon the properties of the cavity or the hole, at least for wavelengths smaller than the size of the hole. See the figure in the Introduction for the
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
as a function of the
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is e ...
of the radiation, which is related to the energy of the radiation by the equation ''E'' = ''hf'', with ''E'' = energy, ''h'' = Planck's constant, ''f'' = frequency. At any given time the radiation in the cavity may not be in thermal equilibrium, but the second law of thermodynamics states that if left undisturbed it will eventually reach equilibrium, although the time it takes to do so may be very long. Typically, equilibrium is reached by continual absorption and emission of radiation by material in the cavity or its walls. Radiation entering the cavity will be " thermalized" by this mechanism: the energy will be redistributed until the ensemble of photons achieves a Planck distribution. The time taken for thermalization is much faster with condensed matter present than with rarefied matter such as a dilute gas. At temperatures below billions of Kelvin, direct photon–photon interactionsRobert Karplus* and Maurice Neuman, "The Scattering of Light by Light", Phys. Rev. 83, 776–784 (1951) are usually negligible compared to interactions with matter. Photons are an example of an interacting
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
gas, and as described by the
H-theorem In classical statistical mechanics, the ''H''-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to decrease in the quantity ''H'' (defined below) in a nearly-ideal gas of molecules. L. Boltzmann,Weitere Studien über das Wä ...
, under very general conditions any interacting boson gas will approach thermal equilibrium.

## Transmission, absorption, and reflection

A body's behavior with regard to thermal radiation is characterized by its transmission ''τ'', absorption ''α'', and reflection ''ρ''. The boundary of a body forms an interface with its surroundings, and this interface may be rough or smooth. A nonreflecting interface separating regions with different refractive indices must be rough, because the laws of reflection and refraction governed by the Fresnel equations for a smooth interface require a reflected ray when the refractive indices of the material and its surroundings differ. A few idealized types of behavior are given particular names: An opaque body is one that transmits none of the radiation that reaches it, although some may be reflected. That is, ''τ'' = 0 and ''α'' + ''ρ'' = 1. A transparent body is one that transmits all the radiation that reaches it. That is, ''τ'' = 1 and ''α'' = ''ρ'' = 0. A grey body is one where ''α'', ''ρ'' and ''τ'' are constant for all wavelengths. This term also is used to mean a body for which ''α'' is temperature- and wavelength-independent. A white body is one for which all incident radiation is reflected uniformly in all directions: ''τ'' = 0, ''α'' = 0, and ''ρ'' = 1. For a black body, ''τ'' = 0, ''α'' = 1, and ''ρ'' = 0. Planck offers a theoretical model for perfectly black bodies, which he noted do not exist in nature: besides their opaque interior, they have interfaces that are perfectly transmitting and non-reflective.

## Kirchhoff's perfect black bodies

Kirchhoff in 1860 introduced the theoretical concept of a perfect black body with a completely absorbing surface layer of infinitely small thickness, but Planck noted some severe restrictions upon this idea. Planck noted three requirements upon a black body: the body must (i) allow radiation to enter but not reflect; (ii) possess a minimum thickness adequate to absorb the incident radiation and prevent its re-emission; (iii) satisfy severe limitations upon
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
to prevent radiation from entering and bouncing back out. As a consequence, Kirchhoff's perfect black bodies that absorb all the radiation that falls on them cannot be realized in an infinitely thin surface layer, and impose conditions upon scattering of the light within the black body that are difficult to satisfy.

# Realizations

A ''realization'' of a black body refers to a real world, physical embodiment. Here are a few.

## Cavity with a hole

In 1898,
Otto Lummer Otto Richard Lummer (17 July 1860 – 5 July 1925) was a German physicist and researcher. He was born in the city of Gera, Germany. With Leon Arons, Lummer helped to design and build the Arons–Lummer mercury-vapor lamp. Lummer primarily worke ...
and Ferdinand Kurlbaum published an account of their cavity radiation source. Their design has been used largely unchanged for radiation measurements to the present day. It was a hole in the wall of a platinum box, divided by diaphragms, with its interior blackened with iron oxide. It was an important ingredient for the progressively improved measurements that led to the discovery of Planck's law. A version described in 1901 had its interior blackened with a mixture of chromium, nickel, and cobalt oxides. See also
Hohlraum In radiation thermodynamics, a hohlraum (a non-specific German word for a "hollow space" or "cavity") is a cavity whose walls are in radiative equilibrium with the radiant energy within the cavity. This idealized cavity can be approximated in p ...
.

## Near-black materials

There is interest in blackbody-like materials for
camouflage Camouflage is the use of any combination of materials, coloration, or illumination for concealment, either by making animals or objects hard to see, or by disguising them as something else. Examples include the leopard's spotted coat, the b ...
and radar-absorbent materials for radar invisibility. They also have application as solar energy collectors, and infrared thermal detectors. As a perfect emitter of radiation, a hot material with black body behavior would create an efficient infrared heater, particularly in space or in a vacuum where convective heating is unavailable. They are also useful in telescopes and cameras as anti-reflection surfaces to reduce stray light, and to gather information about objects in high-contrast areas (for example, observation of planets in orbit around their stars), where blackbody-like materials absorb light that comes from the wrong sources. It has long been known that a
lamp-black Carbon black (subtypes are acetylene black, channel black, furnace black, lamp black and thermal black) is a material produced by the incomplete combustion of coal and coal tar, vegetable matter, or petroleum products, including fuel oil, fluid ...
coating will make a body nearly black. An improvement on lamp-black is found in manufactured
carbon nanotube A scanning tunneling microscopy image of a single-walled carbon nanotube Rotating single-walled zigzag carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with diameters typically measured in nanometers. ''Single-wall carbon nan ...
s. Nano-porous materials can achieve refractive indices nearly that of vacuum, in one case obtaining average reflectance of 0.045%. In 2009, a team of Japanese scientists created a material called nanoblack which is close to an ideal black body, based on vertically aligned single-walled
carbon nanotubes A scanning tunneling microscopy image of a single-walled carbon nanotube Rotating single-walled zigzag carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with diameters typically measured in nanometers. ''Single-wall carbon nan ...
. This absorbs between 98% and 99% of the incoming light in the spectral range from the ultra-violet to the far-infrared regions. Other examples of nearly perfect black materials are super black, prepared by chemically etching a
nickel Nickel is a chemical element with symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive but large pieces are slow to ...
phosphorus Phosphorus is a chemical element with the symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but because it is highly reactive, phosphorus is never found as a free element on Ea ...
alloy An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductilit ...
, vertically aligned carbon nanotube arrays (like
VantaBlack Vantablack is a brand name for a class of super-black coatings with total hemispherical reflectances (THR) below 1.5% in the visible spectrum. The coatings were invented by Ben Jensen, who first publicly unveiled them in July 2014, and commerci ...
) and flower carbon nanostructures; all absorb 99.9% of light or more.

## Stars and planets

A star or planet often is modeled as a black body, and electromagnetic radiation emitted from these bodies as
black-body radiation Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spec ...
. The figure shows a highly schematic cross-section to illustrate the idea. The
photosphere The photosphere is a star's outer shell from which light is radiated. The term itself is derived from Ancient Greek roots, φῶς, φωτός/''phos, photos'' meaning "light" and σφαῖρα/''sphaira'' meaning "sphere", in reference to it ...
of the star, where the emitted light is generated, is idealized as a layer within which the photons of light interact with the material in the photosphere and achieve a common temperature ''T'' that is maintained over a long period of time. Some photons escape and are emitted into space, but the energy they carry away is replaced by energy from within the star, so that the temperature of the photosphere is nearly steady. Changes in the core lead to changes in the supply of energy to the photosphere, but such changes are slow on the time scale of interest here. Assuming these circumstances can be realized, the outer layer of the star is somewhat analogous to the example of an enclosure with a small hole in it, with the hole replaced by the limited transmission into space at the outside of the photosphere. With all these assumptions in place, the star emits black-body radiation at the temperature of the photosphere. Using this model the
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 surface temperature ...
of stars is estimated, defined as the temperature of a black body that yields the same surface flux of energy as the star. If a star were a black body, the same effective temperature would result from any region of the spectrum. For example, comparisons in the ''B'' (blue) or ''V'' (visible) range lead to the so-called ''B-V'' color index, which increases the redder the star, with the Sun having an index of +0.648 ± 0.006. Combining the ''U'' (ultraviolet) and the ''B'' indices leads to the ''U-B'' index, which becomes more negative the hotter the star and the more the UV radiation. Assuming the Sun is a type G2 V star, its ''U-B'' index is +0.12. The two indices for two types of most common star sequences are compared in the figure (diagram) with the effective surface temperature of the stars if they were perfect black bodies. There is a rough correlation. For example, for a given ''B-V'' index measurement, the curves of both most common sequences of star (the main sequence and the supergiants) lie below the corresponding black-body ''U-B'' index that includes the ultraviolet spectrum, showing that both groupings of star emit less ultraviolet light than a black body with the same ''B-V'' index. It is perhaps surprising that they fit a black body curve as well as they do, considering that stars have greatly different temperatures at different depths. For example, the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
has an effective temperature of 5780 K, which can be compared to the temperature of its
photosphere The photosphere is a star's outer shell from which light is radiated. The term itself is derived from Ancient Greek roots, φῶς, φωτός/''phos, photos'' meaning "light" and σφαῖρα/''sphaira'' meaning "sphere", in reference to it ...
(the region generating the light), which ranges from about 5000 K at its outer boundary with the
chromosphere A chromosphere ("sphere of color") is the second layer of a star's atmosphere, located above the photosphere and below the solar transition region and corona. The term usually refers to the Sun's chromosphere, but not exclusively. In the ...
to about 9500 K at its inner boundary with the
convection zone A convection zone, convective zone or convective region of a star is a layer which is unstable due to convection. Energy is primarily or partially transported by convection in such a region. In a radiation zone, energy is transported by radiation ...
approximately deep.

## Black holes

A
black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...
is a region of
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
from which nothing escapes. Around a black hole there is a mathematically defined surface called an
event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact obj ...
that marks the point of no return. It is called "black" because it absorbs all the light that hits the horizon, reflecting nothing, making it almost an ideal black body (radiation with a wavelength equal to or larger than the diameter of the hole may not be absorbed, so black holes are not perfect black bodies). Physicists believe that to an outside observer, black holes have a non-zero temperature and emit
black-body radiation Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spec ...
, radiation with a nearly perfect black-body spectrum, ultimately evaporating. The mechanism for this emission is related to vacuum fluctuations in which a
virtual pair A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbat ...
of particles is separated by the gravity of the hole, one member being sucked into the hole, and the other being emitted. The energy distribution of emission is described by
Planck's law In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature , when there is no net flow of matter or energy between the body and its environment. A ...
with a temperature ''T'': :$T=\frac \ ,$ where ''c'' is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, ℏ is the
reduced Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
, ''k''B is the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
, ''G'' is the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in th ...
and ''M'' is the mass of the black hole. These predictions have not yet been tested either observationally or experimentally.

The Big Bang theory is based upon the
cosmological principle In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throu ...
, which states that on large scales the Universe is homogeneous and isotropic. According to theory, the Universe approximately a second after its formation was a near-ideal black body in thermal equilibrium at a temperature above 1010 K. The temperature decreased as the Universe expanded and the matter and radiation in it cooled. The cosmic microwave background radiation observed today is "the most perfect black body ever measured in nature". It has a nearly ideal Planck spectrum at a temperature of about 2.7 K. It departs from the perfect isotropy of true black-body radiation by an observed anisotropy that varies with angle on the sky only to about one part in 100,000.

The integration of
Planck's law In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature , when there is no net flow of matter or energy between the body and its environment. A ...
over all frequencies provides the total energy per unit of time per unit of surface area radiated by a black body maintained at a temperature ''T'', and is known as the
Stefan–Boltzmann law The Stefan–Boltzmann 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 ...
: :$P/A = \sigma T^4 \ ,$ where ''σ'' is the Stefan–Boltzmann constant, To remain in thermal equilibrium at constant temperature ''T'', the black body must absorb or internally generate this amount of power ''P'' over the given area ''A''. The cooling of a body due to thermal radiation is often approximated using the Stefan–Boltzmann law supplemented with a "gray body"
emissivity The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation that most commonly includes both visible radiation (light) and infrared radiation, which is ...
(). The rate of decrease of the temperature of the emitting body can be estimated from the power radiated and the body's
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity i ...
. This approach is a simplification that ignores details of the mechanisms behind heat redistribution (which may include changing composition,
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
s or restructuring of the body) that occur within the body while it cools, and assumes that at each moment in time the body is characterized by a single temperature. It also ignores other possible complications, such as changes in the emissivity with temperature, and the role of other accompanying forms of energy emission, for example, emission of particles like neutrinos. If a hot emitting body is assumed to follow the Stefan–Boltzmann law and its power emission ''P'' and temperature ''T'' are known, this law can be used to estimate the dimensions of the emitting object, because the total emitted power is proportional to the area of the emitting surface. In this way it was found that X-ray bursts observed by astronomers originated in neutron stars with a radius of about 10 km, rather than black holes as originally conjectured. An accurate estimate of size requires some knowledge of the emissivity, particularly its spectral and angular dependence.

*
Kirchhoff's law of thermal radiation In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium. It is a special case of Onsager ...
*
Vantablack Vantablack is a brand name for a class of super-black coatings with total hemispherical reflectances (THR) below 1.5% in the visible spectrum. The coatings were invented by Ben Jensen, who first publicly unveiled them in July 2014, and commerci ...
, a substance produced in 2014 and among the blackest known *
Planckian locus In physics and color science, the Planckian locus or black body locus is the path or ''locus'' that the color of an incandescent black body would take in a particular chromaticity space as the blackbody temperature changes. It goes from deep ...
, black body incandescence in a given chromaticity space

# References

## Bibliography

* * * a translation of ''Frühgeschichte der Quantentheorie (1899–1913)'', Physik Verlag, Mosbach/Baden. * * * * Translated by Guthrie, F. as * * * * * * * * * * * * * * *