SUPPORT THE WORK

GetWiki

Black-body radiation

ARTICLE SUBJECTS
aesthetics  →
being  →
complexity  →
database  →
enterprise  →
ethics  →
fiction  →
history  →
internet  →
knowledge  →
language  →
licensing  →
linux  →
logic  →
method  →
news  →
perception  →
philosophy  →
policy  →
purpose  →
religion  →
science  →
sociology  →
software  →
truth  →
unix  →
wiki  →
ARTICLE TYPES
essay  →
feed  →
help  →
system  →
wiki  →
ARTICLE ORIGINS
critical  →
discussion  →
forked  →
imported  →
original  →
Black-body radiation
[ temporary import ]
please note:
- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
(File:Black body.svg|thumb|303px|As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.)
missing image!
- PlanckianLocus.png -
The color (chromaticity) of black-body radiation depends on reverse the temperature of the black body; the locus of such colors, shown here in CIE 1931 x,y space, is known as the Planckian locus.
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 spectrum and reverse intensity that depends only on the body's temperature, which is assumed for the sake of calculations and theory to be uniform and constant.{{harvnb|Loudon|2000}}, Chapter 1.{{harvnb|Mandel|Wolf|1995}}, Chapter 13.{{harvnb|Kondepudi|Prigogine|1998}}, Chapter 11.{{harvnb|Landsberg|1990}}, Chapter 13.The thermal radiation spontaneously emitted by many ordinary objects can be approximated as black-body radiation. A perfectly insulated enclosure that is in thermal equilibrium internally contains black-body radiation and will emit it through a hole made in its wall, provided the hole is small enough to have negligible effect upon the equilibrium.A black body at room temperature appears black, as most of the energy it radiates is in the infrared spectrum and cannot be perceived by the human eye. Since, by definition, the human eye cannot perceive light waves below the visible frequency, a black body, viewed in the dark at the lowest just faintly visible temperature, subjectively appears grey, even though its objective physical spectrum peak is in the infrared range.Partington, J.R. (1949), p. 466. When it becomes a little hotter, it appears dull red. As its temperature increases further it becomes yellow, white, and ultimately blue-white.Although planets and stars are neither in thermal equilibrium with their surroundings nor perfect black bodies, black-body radiation is used as a first approximation for the energy they emit.BOOK, Introduction to Astronomy and Cosmology, Ian Morison,weblink 48, 0-470-03333-9, 2008, J Wiley & Sons, Black holes are near-perfect black bodies, in the sense that they absorb all the radiation that falls on them. It has been proposed that they emit black-body radiation (called Hawking radiation), with a temperature that depends on the mass of the black hole.BOOK, Modeling black hole evaporation,weblink Chapter 1: Introduction, Alessandro Fabbri, José Navarro-Salas, 1-86094-527-9, 2005, Imperial College Press, The term black body was introduced by Gustav Kirchhoff in 1860.From (Kirchhoff, 1860) (Annalen der Physik und Chemie), p. 277: "Der Beweis, welcher für die ausgesprochene Behauptung hier gegeben werden soll, … vollkommen schwarze, oder kürzer schwarze, nennen." (The proof, which shall be given here for the proposition stated [above], rests on the assumption that bodies are conceivable which in the case of infinitely small thicknesses, completely absorb all rays that fall on them, thus [they] neither reflect nor transmit rays. I will call such bodies "completely black [bodies]" or more briefly "black [bodies]".) See also (Kirchhoff, 1860) (Philosophical Magazine), p. 2. Black-body radiation is also called thermal radiation, cavity radiation, complete radiation or temperature radiation.

Theory

Spectrum

Black-body radiation has a characteristic, continuous frequency spectrum that depends only on the body's temperature,BOOK,weblink 41, §2.3: Thermodynamic equilibrium and black-body radiation, The astrophysics of emission-line stars, Tomokazu Kogure, Kam-Ching Leung, 0-387-34500-0, 2007, Springer,
called the Planck spectrum or Planck's law. The spectrum is peaked at a characteristic frequency that shifts to higher frequencies with increasing temperature, and at room temperature most of the emission is in the infrared region of the electromagnetic spectrum.Wien, W. (1893). Eine neue Beziehung der Strahlung schwarzer Körper zum zweiten Hauptsatz der Wärmetheorie, Sitzungberichte der Königlich-Preußischen Akademie der Wissenschaften (Berlin), 1893, 1: 55–62.Lummer, O., Pringsheim, E. (1899). Die Vertheilung der Energie im Spectrum des schwarzen Körpers, Verhandlungen der Deutschen Physikalischen Gessellschaft (Leipzig), 1899, 1: 23–41.{{harvnb|Planck|1914}} As the temperature increases past about 500 degrees Celsius, black bodies start to emit significant amounts of visible light. Viewed in the dark by the human eye, the first faint glow appears as a "ghostly" grey (the visible light is actually red, but low intensity light activates only the eye's grey-level sensors). With rising temperature, the glow becomes visible even when there is some background surrounding light: first as a dull red, then yellow, and eventually a "dazzling bluish-white" as the temperature rises.Draper, J.W. (1847). On the production of light by heat, London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, series 3, 30: 345–360. weblink{{harvnb|Partington|1949|pages = 466–467, 478}}. When the body appears white, it is emitting a substantial fraction of its energy as ultraviolet radiation. The Sun, with an effective temperature of approximately 5800 K,{{harvnb|Goody|Yung|1989|pages=482, 484}} is an approximate black body with an emission spectrum peaked in the central, yellow-green part of the visible spectrum, but with significant power in the ultraviolet as well.
Black-body radiation provides insight into the thermodynamic equilibrium state of cavity radiation.

Black body

All normal (baryonic) matter emits electromagnetic radiation when it has a temperature above absolute zero. The radiation represents a conversion of a body's internal energy into electromagnetic energy, and is therefore called thermal radiation. It is a spontaneous process of radiative distribution of missing image!
- Color temperature black body 800-12200K.svg">thumb|512px|Color of a black body from 800 K to 12200 K. This range of colors approximates the range of colors of stars of different temperatures, as seen or photographed in the night sky.
Conversely all normal matter absorbs electromagnetic radiation to some degree. An object that absorbs all radiation falling on it, at all wavelengths, is called a black body. When a black body is at a uniform temperature, its emission has a characteristic frequency distribution that depends on the temperature. Its emission is called black-body radiation.The concept of the black body is an idealization, as perfect black bodies do not exist in nature.{{harvnb|Planck|1914|page=42}} Graphite and lamp black, with emissivities greater than 0.95, however, are good approximations to a black material. Experimentally, black-body radiation may be established best as the ultimately stable steady state equilibrium radiation in a cavity in a rigid body, at a uniform temperature, that is entirely opaque and is only partly reflective. A closed box of graphite walls at a constant temperature with a small hole on one side produces a good approximation to ideal black-body radiation emanating from the opening.{{harvnb|Wien|1894}}{{harvnb|Planck|1914|page=43}}Black-body radiation has the unique absolutely stable distribution of radiative intensity that can persist in thermodynamic equilibrium in a cavity. In equilibrium, for each frequency the total intensity of radiation that is emitted and reflected from a body (that is, the net amount of radiation leaving its surface, called the spectral radiance) is determined solely by the equilibrium temperature, and does not depend upon the shape, material or structure of the body.BOOK,weblink 107, §4.2.2: Calculation of Planck's law, Passive infrared detection: theory and applications, Joseph Caniou, 0-7923-8532-2, 1999, Springer, For a black body (a perfect absorber) there is no reflected radiation, and so the spectral radiance is entirely due to emission. In addition, a black body is a diffuse emitter (its emission is independent of direction). Consequently, black-body radiation may be viewed as the radiation from a black body at thermal equilibrium.Black-body radiation becomes a visible glow of light if the temperature of the object is high enough. The Draper point is the temperature at which all solids glow a dim red, about {{val|798|u=K}}.BOOK, Radiation heat transfer: a statistical approach, J. R. Mahan, 3rd, Wiley-IEEE, 2002, 978-0-471-21270-6, 58,weblink At {{val|1000|u=K}}, a small opening in the wall of a large uniformly heated opaque-walled cavity (such as an oven), viewed from outside, looks red; at {{val|6000|u=K}}, it looks white. No matter how the oven is constructed, or of what material, as long as it is built so that almost all light entering is absorbed by its walls, it will contain a good approximation to black-body radiation. The spectrum, and therefore color, of the light that comes out will be a function of the cavity temperature alone. A graph of the amount of energy inside the oven per unit volume and per unit frequency interval plotted versus frequency, is called the black-body curve. Different curves are obtained by varying the temperature.Pahoehoe toe.jpg -
Two bodies that are at the same temperature stay in mutual thermal equilibrium, so a body at temperature T surrounded by a cloud of light at temperature T on average will emit as much light into the cloud as it absorbs, following Prevost's exchange principle, which refers to radiative equilibrium. The principle of detailed balance says that in thermodynamic equilibrium every elementary process works equally in its forward and backward sense.de Groot, SR., Mazur, P. (1962). Non-equilibrium Thermodynamics, North-Holland, Amsterdam.{{harvnb|Kondepudi|Prigogine|1998}}, Section 9.4. Prevost also showed that the emission from a body is logically determined solely by its own internal state. The causal effect of thermodynamic absorption on thermodynamic (spontaneous) emission is not direct, but is only indirect as it affects the internal state of the body. This means that at thermodynamic equilibrium the amount of every wavelength in every direction of thermal radiation emitted by a body at temperature T, black or not, is equal to the corresponding amount that the body absorbs because it is surrounded by light at temperature T.When the body is black, the absorption is obvious: the amount of light absorbed is all the light that hits the surface. For a black body much bigger than the wavelength, the light energy absorbed at any wavelength λ per unit time is strictly proportional to the black-body curve. This means that the black-body curve is the amount of light energy emitted by a black body, which justifies the name. This is the condition for the applicability of Kirchhoff's law of thermal radiation: the black-body curve is characteristic of thermal light, which depends only on the temperature of the walls of the cavity, provided that the walls of the cavity are completely opaque and are not very reflective, and that the cavity is in thermodynamic equilibrium.BOOK, Huang, Kerson, Statistical Mechanics, 1967, John Wiley & Sons, New York, 0-471-81518-7, When the black body is small, so that its size is comparable to the wavelength of light, the absorption is modified, because a small object is not an efficient absorber of light of long wavelength, but the principle of strict equality of emission and absorption is always upheld in a condition of thermodynamic equilibrium.In the laboratory, black-body radiation is approximated by the radiation from a small hole in a large cavity, a hohlraum, in an entirely opaque body that is only partly reflective, that is maintained at a constant temperature. (This technique leads to the alternative term cavity radiation.) Any light entering the hole would have to reflect off the walls of the cavity multiple times before it escaped, in which process it is nearly certain to be absorbed. Absorption occurs regardless of the wavelength of the radiation entering (as long as it is small compared to the hole). The hole, then, is a close approximation of a theoretical black body and, if the cavity is heated, the spectrum of the hole's radiation (i.e., the amount of light emitted from the hole at each wavelength) will be continuous, and will depend only on the temperature and the fact that the walls are opaque and at least partly absorptive, but not on the particular material of which they are built nor on the material in the cavity (compare with emission spectrum).The radiance or observed intensity is not a function of direction. Therefore, a black body is a perfect Lambertian radiator.Real objects never behave as full-ideal black bodies, and instead the emitted radiation at a given frequency is a fraction of what the ideal emission would be. The emissivity of a material specifies how well a real body radiates energy as compared with a black body. This emissivity depends on factors such as temperature, emission angle, and wavelength. However, it is typical in engineering to assume that a surface's spectral emissivity and absorptivity do not depend on wavelength, so that the emissivity is a constant. This is known as the gray body assumption.File:Ilc 9yr moll4096.png|thumb|300px|9-year WMAP image (2012) of the cosmic microwave background radiation across the universe.WEB, Gannon, Megan, New 'Baby Picture' of Universe Unveiled,weblink December 21, 2012, (Space.com]], December 21, 2012, JOURNAL, Bennett, C.L., Larson, L., Weiland, J.L., Jarosk, N., Hinshaw, N., Odegard, N., Smith, K.M., Hill, R.S., Gold, B., Halpern, M., Komatsu, E., Nolta, M.R., Page, L., Spergel, D.N., Wollack, E., Dunkley, J., Kogut, A., Limon, M., Meyer, S.S., Tucker, G.S., Wright, E.L., Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results, 1212, 5225, 1212.5225, December 20, 2012, 2013ApJS..208...20B, 10.1088/0067-0049/208/2/20, )With non-black surfaces, the deviations from ideal black-body behavior are determined by both the surface structure, such as roughness or granularity, and the chemical composition. On a "per wavelength" basis, real objects in states of local thermodynamic equilibrium still follow Kirchhoff's Law: emissivity equals absorptivity, so that an object that does not absorb all incident light will also emit less radiation than an ideal black body; the incomplete absorption can be due to some of the incident light being transmitted through the body or to some of it being reflected at the surface of the body.In astronomy, objects such as stars are frequently regarded as black bodies, though this is often a poor approximation. An almost perfect black-body spectrum is exhibited by the cosmic microwave background radiation. Hawking radiation is the hypothetical black-body radiation emitted by black holes, at a temperature that depends on the mass, charge, and spin of the hole. If this prediction is correct, black holes will very gradually shrink and evaporate over time as they lose mass by the emission of photons and other particles.A black body radiates energy at all frequencies, but its intensity rapidly tends to zero at high frequencies (short wavelengths). For example, a black body at room temperature ({{val|300|u=K}}) with one square meter of surface area will emit a photon in the visible range (390–750 nm) at an average rate of one photon every 41 seconds, meaning that for most practical purposes, such a black body does not emit in the visible range.{{citation needed|date=January 2018}}The study of the laws of black bodies and the failure of classical physics to describe them helped establish the foundations of quantum mechanics.

Further explanation

According to the Classical Theory of Radiation, if each Fourier mode of the equilibrium radiation ( in an otherwise empty cavity with perfectly reflective walls) is considered as a degree of freedom capable of exchanging energy, then, according to the equipartition theorem of classical physics, there would be an equal amount of energy in each mode. Since there are an infinite number of modes, this would imply infinite heat capacity , as well as an nonphysical spectrum of emitted radiation that grows without bound with increasing frequency, a problem known as the ultraviolet catastrophe.In the longer wavelengths this deviation is not so noticeable, as h nu and nh nu are very small. In the shorter wavelengths of the ultraviolet range, however, classical theory predicts the energy emitted tends to infinity, hence the ultraviolet catastrophe. As all possible vibrational modes (including those whose energy less than h nu-The quantum of energy), the energy summed to infinity. The theory even predicted that all bodies would emit most of their energy in the ultraviolet range, clearly contradicted by the experimental data which showed a different peak wavelength at different temperatures. (see also wiens law) (File:Black body.svg|thumb|303px|As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.)Instead, in the quantum treatment of this problem ,the numbers of the energy modes are quantized, attenuating the spectrum at high frequency in agreement with experimental observation and resolving the catastrophe. The modes that had more energy than the thermal energy of the substance itself were not considered , and by quantization - modes having infinitesimally little energy were excluded. Thus for shorter wavelengths very few modes(having energy more than h nu) were allowed, supporting the data that the energy emitted is reduced for wavelengths less than the wavelength of the observed peak of emission.Notice that there are two factors responsible for the shape of the graph. Firstly, longer wavelengths have a larger number of modes associated with them. Secondly, shorter wavelengths have more energy associated per mode. The two factors combined give the characteristic maximum wavelength .Calculating the black-body curve was a major challenge in theoretical physics during the late nineteenth century. The problem was solved in 1901 by Max Planck in the formalism now known as Planck's law of black-body radiation.JOURNAL, Planck, Max, Max_Planck, Ueber das Gesetz der Energieverteilung im Normalspectrum, On the law of the distribution of energy in the normal spectrum, Annalen der Physik, 4th series, 4, 3, 553–563, 1901,weblink German, 10.1002/andp.19013090310, 1901AnP...309..553P, By making changes to Wien's radiation law (not to be confused with Wien's displacement law) consistent with thermodynamics and electromagnetism, he found a mathematical expression fitting the experimental data satisfactorily. Planck had to assume that the energy of the oscillators in the cavity was quantized, i.e., it existed in integer multiples of some quantity. Einstein built on this idea and proposed the quantization of electromagnetic radiation itself in 1905 to explain the photoelectric effect. These theoretical advances eventually resulted in the superseding of classical electromagnetism by quantum electrodynamics. These quanta were called photons and the black-body cavity was thought of as containing a gas of photons. In addition, it led to the development of quantum probability distributions, called Fermi–Dirac statistics and Bose–Einstein statistics, each applicable to a different class of particles, fermions and bosons.The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan–Boltzmann law. So, as temperature increases, the glow color changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue. It will never become invisible—indeed, the radiation of visible light increases monotonically with temperature.BOOK, Landau, L. D., E. M. Lifshitz, Statistical Physics, 3rd Edition Part 1, 1996, Butterworth–Heinemann, Oxford, 0-521-65314-2, The Stefan–Boltzmann law also says that the total radiant heat energy emitted from a surface is proportional to the fourth power of its absolute temperature. The law was formulated by Josef Stefan in 1879 and later derived by Ludwig Boltzmann. The formula {{nowrap|1=E = σT4}} is given, where E is the radiant heat emitted from a unit of area per unit time, T is the absolute temperature, and {{nowrap|1=σ = {{val|5.670367|e=-8|u=W·m−2⋅K−4}}}} is the Stefan–Boltzmann constant.ENCYCLOPEDIA, Stefan-Boltzmann law, Encyclopædia Britannica,weblink 2019,

Equations

Planck's law of black-body radiation

Planck's law states that{{harvnb|Rybicki|Lightman|1979|p=22}}
B_nu(nu, T) = frac{2hnu^3}{c^2}frac{1}{e^{hnu/kT} - 1},
where
Bν(T) is the spectral radiance (the power per unit solid angle and per unit of area normal to the propagation) density of frequency ν radiation per unit frequency at thermal equilibrium at temperature T. h is the Planck constant; c is the speed of light in a vacuum; k is the Boltzmann constant; ν is the frequency of the electromagnetic radiation; T is the absolute temperature of the body.
For a black body surface the spectral radiance density (defined per unit of area normal to the propagation) is independent of the angle theta of emission with respect to the normal. However, this means that, following Lambert's cosine law, B_nu(T) cos theta is the radiance density per unit area of emitting surface as the surface area involved in generating the radiance is increased by a factor 1/cos theta with respect to an area normal to the propagation direction. At oblique angles, the solid angle spans involved do get smaller, resulting in lower aggregate intensities.

Wien's displacement law

Wien's displacement law shows how the spectrum of black-body radiation at any temperature is related to the spectrum at any other temperature. If we know the shape of the spectrum at one temperature, we can calculate the shape at any other temperature. Spectral intensity can be expressed as a function of wavelength or of frequency.A consequence of Wien's displacement law is that the wavelength at which the intensity per unit wavelength of the radiation produced by a black body is at a maximum, lambda_max, is a function only of the temperature:
lambda_max = frac{b}{T},
where the constant b, known as Wien's displacement constant, is equal to {{val|2.897771955|e=-3|u=m K}}.WEB, Wien wavelength displacement law constant,weblink The NIST Reference on Constants, Units, and Uncertainty, NIST, February 8, 2019, Planck's law was also stated above as a function of frequency. The intensity maximum for this is given by
nu_max = T times 5.879 times 10^{10} mathrm{Hz}/mathrm{K}.
WEB
, Nave
, Dr. Rod
, Wien's Displacement Law and Other Ways to Characterize the Peak of Blackbody Radiation
, HyperPhysics
,
,weblink
,
,
Provides 5 variations of Wien's displacement law

Stefan–Boltzmann law

By integrating B_nu(T) over the frequency the integrated radiance L is
L=frac{2pi^5}{15} frac{k^4 T^4}{c^2h^3} frac{1}{pi}=:sigma T^4 frac{1}{pi}
by using int_0^infty dx, frac{x^3}{e^x - 1}=frac{pi^4}{15} with x equiv frac{hnu}{k T} and with sigma equiv frac{2pi^5}{15} frac{k^4}{c^2h^3}=5.670373 times 10^{-8} frac{W}{m^2 K^4} being the Stefan–Boltzmann constant. The radiance L is then
sigma T^4 frac{cos theta}{pi}
per unit of emitting surface.On a side note, at a distance d, the intensity dI per area dA of radiating surface is the useful expression
dI=sigma T^4 frac{costheta}{pi d^2}dA
when the receiving surface is perpendicular to the radiation.By subsequently integrating over the solid angle Omega (where theta

- content above as imported from Wikipedia
- "Black-body radiation" does not exist on GetWiki (yet)
- time: 2:10am EDT - Sun, Sep 15 2019
[ this remote article is provided by Wikipedia ]
LATEST EDITS [ see all ]
GETWIKI 09 JUL 2019
Eastern Philosophy
History of Philosophy
GETWIKI 09 MAY 2016
GETWIKI 18 OCT 2015
M.R.M. Parrott
Biographies
GETWIKI 20 AUG 2014
GETWIKI 19 AUG 2014
CONNECT