Black body

A black body or blackbody 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."[1]

A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic radiation called black-body radiation. The radiation is emitted according to Planck's law, meaning that it has a spectrum that is determined by the temperature alone (see figure at right), not by the body's shape or composition.

An ideal black body in thermal equilibrium has two notable properties:[2]

  1. 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.
  2. It is a diffuse emitter: 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). 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—of black-body energy levels. By definition, a black body in thermal equilibrium has an emissivity of ε = 1.0. A source with lower emissivity independent of frequency often is referred to as a gray body.[3][4] Construction of black bodies with emissivity as close to one as possible remains a topic of current interest.[5]

In astronomy, the radiation from stars and planets is sometimes characterized in terms of an effective temperature, the temperature of a black body that would emit the same total flux of electromagnetic energy.

Black body
As the temperature of a black body decreases, its intensity also decreases and its peak moves to longer wavelengths. Shown for comparison is the classical Rayleigh–Jeans law and its ultraviolet catastrophe.

Definition

The idea of a black body originally was introduced by Gustav Kirchhoff in 1860 as follows:

...the supposition that bodies can be imagined which, for infinitely small thicknesses, completely absorb all incident rays, and neither reflect nor transmit any. I shall call such bodies perfectly black, or, more briefly, black bodies.[6]

A more modern definition drops the reference to "infinitely small thicknesses":[7]

An ideal body is now defined, called a blackbody. A blackbody allows all incident radiation to pass into it (no reflected energy) and internally absorbs all the incident radiation (no energy transmitted through the body). This is true for radiation of all wavelengths and for all angles of incidence. Hence the blackbody is a perfect absorber for all incident radiation.[8]

Idealizations

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

Black body realization
An approximate realization of a black body as a tiny hole in an insulated enclosure

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.[8] 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 longer 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.[9]

Suppose the cavity is held at a fixed temperature T and the radiation trapped inside the enclosure is at thermal equilibrium 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 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.[9] See the figure in the Introduction for the spectrum as a function of the frequency 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,[10] although the time it takes to do so may be very long.[11] Typically, equilibrium is reached by continual absorption and emission of radiation by material in the cavity or its walls.[12][13][14][15] 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 interactions[16] are usually negligible compared to interactions with matter.[17] Photons are an example of an interacting boson gas,[18] and as described by the H-theorem,[19] 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.[20] 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.[21][22] 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 gray body is one where α, ρ and τ are uniform 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.[23]

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 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.[24][25]

Realizations

A realization of a black body is a real world, physical embodiment. Here are a few.

Cavity with a hole

In 1898, Otto Lummer and Ferdinand Kurlbaum published an account of their cavity radiation source.[26] 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.[27][28] A version described in 1901 had its interior blackened with a mixture of chromium, nickel, and cobalt oxides.[29] See also Hohlraum.

Near-black materials

There is interest in blackbody-like materials for camouflage and radar-absorbent materials for radar invisibility.[30][31] 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.[32] 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 coating will make a body nearly black. An improvement on lamp-black is found in manufactured carbon nanotubes. Nano-porous materials can achieve refractive indices nearly that of vacuum, in one case obtaining average reflectance of 0.045%.[5][33] 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. This absorbs between 98% and 99% of the incoming light in the spectral range from the ultra-violet to the far-infrared regions.[32]

Other examples of nearly perfect black materials are super black, prepared by chemically etching a nickelphosphorus alloy,[34] and vantablack made of carbon nanotubes; both absorb 99.9% of light or more.

Stars and planets

Idealized photosphere
An idealized view of the cross-section of a star. The photosphere contains photons of light nearly in thermal equilibrium, and some escape into space as near-black-body radiation.

A star or planet often is modeled as a black body, and electromagnetic radiation emitted from these bodies as black-body radiation. The figure shows a highly schematic cross-section to illustrate the idea. The photosphere 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.[35]

Effective temperature and color index
Effective temperature of a black body compared with the B-V and U-B color index of main sequence and super giant stars in what is called a color-color diagram.[36]

Using this model the effective 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,[37] with the Sun having an index of +0.648 ± 0.006.[38] 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.[39] 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.[40] For example, the Sun has an effective temperature of 5780 K,[41] which can be compared to the temperature of its photosphere (the region generating the light), which ranges from about 5000 K at its outer boundary with the chromosphere to about 9500 K at its inner boundary with the convection zone approximately 500 km (310 mi) deep.[42]

Black holes

A black hole is a region of spacetime from which nothing escapes. Around a black hole there is a mathematically defined surface called an event horizon 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[43] (radiation with a wavelength equal to or larger than the radius of the hole may not be absorbed, so black holes are not perfect black bodies).[44] Physicists believe that to an outside observer, black holes have a non-zero temperature and emit radiation with a nearly perfect black-body spectrum, ultimately evaporating.[45] The mechanism for this emission is related to vacuum fluctuations in which a virtual pair of particles is separated by the gravity of the hole, one member being sucked into the hole, and the other being emitted.[46] The energy distribution of emission is described by Planck's law with a temperature T:

where c is the speed of light, ℏ is the reduced Planck constant, kB is Boltzmann's constant, G is the gravitational constant and M is the mass of the black hole.[47] These predictions have not yet been tested either observationally or experimentally.[48]

Cosmic microwave background radiation

The big bang theory is based upon the cosmological principle, 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".[49] 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.

Radiative cooling

Blackbody peak wavelength exitance vs temperature
Log-log graphs of peak emission wavelength and radiant exitance vs black-body temperature – red arrows show that 5780 K black bodies have 501 nm peak wavelength and 63.3 MW/m² radiant exitance

The integration of Planck's law 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:

where σ is the Stefan–Boltzmann constant, σ ≈ 5.67 × 10−8 W/(m2K4).[50] 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 ε ≤ 1 (P/A = εσT4). The rate of decrease of the temperature of the emitting body can be estimated from the power radiated and the body's heat capacity.[51] This approach is a simplification that ignores details of the mechanisms behind heat redistribution (which may include changing composition, phase transitions 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,[52][53] and the role of other accompanying forms of energy emission, for example, emission of particles like neutrinos.[54]

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.[55] It should be noted that an accurate estimate of size requires some knowledge of the emissivity, particularly its spectral and angular dependence.[56]

See also

References

Citations

  1. ^ Planck 1914, pp. 9–10
  2. ^ Mahmoud Massoud (2005). "§2.1 Blackbody radiation". Engineering thermofluids: thermodynamics, fluid mechanics, and heat transfer. Springer. p. 568. ISBN 978-3-540-22292-7.
  3. ^ The emissivity of a surface in principle depends upon frequency, angle of view, and temperature. However, by definition, the radiation from a gray body is simply proportional to that of a black body at the same temperature, so its emissivity does not depend upon frequency (or, equivalently, wavelength). See Massoud Kaviany (2002). "Figure 4.3(b): Behaviors of a gray (no wavelength dependence), diffuse (no directional dependence) and opaque (no transmission) surface". Principles of heat transfer. Wiley-IEEE. p. 381. ISBN 978-0-471-43463-4. and Ronald G. Driggers (2003). Encyclopedia of optical engineering, Volume 3. CRC Press. p. 2303. ISBN 978-0-8247-4252-2.
  4. ^ Some authors describe sources of infrared radiation with emissivity greater than approximately 0.99 as a black body. See "What is a Blackbody and Infrared Radiation?". Education/Reference tab. Electro Optical Industries, Inc. 2008.
  5. ^ a b Ai Lin Chun (25 Jan 2008). "Carbon nanotubes: Blacker than black". Nature Nanotechnology. doi:10.1038/nnano.2008.29.
  6. ^ Translated by F. Guthrie from Annalen der Physik: 109, 275-301 (1860): G. Kirchhoff (July 1860). "On the relation between the radiating and absorbing powers of different bodies for light and heat". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 20 (130).
  7. ^ The notion of an infinitely thin layer was dropped by Planck. See Planck 1914, p. 10, footnote 2, .
  8. ^ a b Siegel, Robert; Howell, John R. (2002). Thermal Radiation Heat Transfer; Volume 1 (4th ed.). Taylor & Francis. p. 7. ISBN 978-1-56032-839-1.
  9. ^ a b Corrections to the spectrum do arise related to boundary conditions at the walls, curvature, and topology, particularly for wavelengths comparable to the cavity dimensions; see Roger Dale Van Zee; J. Patrick Looney (2002). Cavity-enhanced spectroscopies. Academic Press. p. 202. ISBN 978-0-12-475987-9.
  10. ^ Clement John Adkins (1983). "§4.1 The function of the second law". Equilibrium thermodynamics (3rd ed.). Cambridge University Press. p. 50. ISBN 978-0-521-27456-2.
  11. ^ In simple cases the approach to equilibrium is governed by a relaxation time. In others, the system may 'hang up' in a metastable state, as stated by Adkins (1983) on page 10. For another example, see Michel Le Bellac; Fabrice Mortessagne; Ghassan George Batrouni (2004). Equilibrium and non-equilibrium statistical thermodynamics. Cambridge University Press. p. 8. ISBN 978-0521821438.
  12. ^ The approach to thermal equilibrium of the radiation in the cavity can be catalyzed by adding a small piece of matter capable of radiating and absorbing at all frequencies. See Peter Theodore Landsberg (1990). Thermodynamics and statistical mechanics (Reprint of Oxford University Press 1978 ed.). Courier Dover Publications. p. 209. ISBN 978-0-486-66493-4.
  13. ^ Planck 1914, p. 44, §52
  14. ^ Loudon 2000, Chapter 1
  15. ^ Mandel & Wolf 1995, Chapter 13
  16. ^ Robert Karplus* and Maurice Neuman ,"The Scattering of Light by Light", Phys. Rev. 83, 776–784 (1951)
  17. ^ Ludwig Bergmann; Clemens Schaefer; Heinz Niedrig (1999). Optics of waves and particles. Walter de Gruyter. p. 595. ISBN 978-3-11-014318-8. Because the interaction of the photons with each other is negligible, a small amount of matter is necessary to establish thermodynamic equilibrium of heat radiation.
  18. ^ The fundamental bosons are the photon, the vector bosons of the weak interaction, the gluon, and the graviton. See Allan Griffin; D. W. Snoke; S. Stringari (1996). Bose-Einstein condensation. Cambridge University Press. p. 4. ISBN 978-0-521-58990-1.
  19. ^ Richard Chace Tolman (2010). "§103: Change of H with time as a result of collisions". The principles of statistical mechanics (Reprint of 1938 Oxford University Press ed.). Dover Publications. pp. 455 ff. ISBN 978-0-486-63896-6. ...we can define a suitable quantity H to characterize the condition of a gas which [will exhibit] a tendency to decrease with time as a result of collisions, unless the distribution of the molecules [is already that of] equilibrium. (p. 458)
  20. ^ Paul A. Tipler (1999). "Relative intensity of reflected and transmitted light". Physics for Scientists and Engineers, Parts 1-35; Part 39 (4th ed.). Macmillan. p. 1044. ISBN 978-0-7167-3821-3.
  21. ^ Massoud Kaviany (2002). "Figure 4.3(b) Radiation properties of an opaque surface". Principles of heat transfer. Wiley-IEEE. p. 381. ISBN 978-0-471-43463-4.
  22. ^ BA Venkanna (2010). "§10.3.4 Absorptivity, reflectivity, and transmissivity". Fundamentals of heat and mass transfer. PHI Learning Pvt. Ltd. pp. 385–386. ISBN 978-81-203-4031-2.
  23. ^ Planck 1914, p. 10
  24. ^ Planck 1914, pp. 9–10, §10
  25. ^ Kirchhoff 1860c
  26. ^ Lummer & Kurlbaum 1898
  27. ^ An extensive historical discussion is found in Jagdish Mehra; Helmut Rechenberg (2000). The historical development of quantum theory. Springer. pp. 39 ff. ISBN 978-0-387-95174-4.
  28. ^ Kangro 1976, p. 159
  29. ^ Lummer & Kurlbaum 1901
  30. ^ CF Lewis (June 1988). "Materials keep a low profile" (PDF). Mech. Eng.: 37–41.
  31. ^ Bradley Quinn (2010). Textile Futures. Berg. p. 68. ISBN 978-1-84520-807-3.
  32. ^ a b K. Mizuno; et al. (2009). "A black body absorber from vertically aligned single-walled carbon nanotubes". Proceedings of the National Academy of Sciences. 106 (15): 6044–6077. Bibcode:2009PNAS..106.6044M. doi:10.1073/pnas.0900155106. PMC 2669394. PMID 19339498.
  33. ^ Zu-Po Yang; et al. (2008). "Experimental observation of an extremely dark material made by a low-density nanotube array". Nano Letters. 8 (2): 446–451. Bibcode:2008NanoL...8..446Y. doi:10.1021/nl072369t. PMID 18181658.
  34. ^ See description of work by Richard Brown and his colleagues at the UK's National Physical Laboratory: Mick Hamer (correspondent) (6 February 2003). "Mini craters key to 'blackest ever black'". New Scientist Magazine Online.
  35. ^ Simon F. Green; Mark H. Jones; S. Jocelyn Burnell (2004). An introduction to the sun and stars. Cambridge University Press. pp. 21–22, 53. ISBN 978-0-521-54622-5. A source in which photons are much more likely to interact with the material within the source than to escape is a condition for the formation of a black-body spectrum
  36. ^ Figure modeled after E. Böhm-Vitense (1989). "Figure 4.9". Introduction to Stellar Astrophysics: Basic stellar observations and data. Cambridge University Press. p. 26. ISBN 978-0-521-34869-0.
  37. ^ David H. Kelley; Eugene F. Milone; Anthony F. (FRW) Aveni (2011). Exploring Ancient Skies: A Survey of Ancient and Cultural Astronomy (2nd ed.). Springer. p. 52. ISBN 978-1-4419-7623-9.
  38. ^ David F Gray (February 1995). "Comparing the sun with other stars along the temperature coordinate". Publications of the Astronomical Society of the Pacific. 107: 120–123. Bibcode:1995PASP..107..120G. doi:10.1086/133525. Retrieved 2012-01-26.
  39. ^ M Golay (1974). "Table IX: U-B Indices". Introduction to astronomical photometry. Springer. p. 82. ISBN 978-90-277-0428-3.
  40. ^ Lawrence Hugh Aller (1991). Atoms, stars, and nebulae (3rd ed.). Cambridge University Press. p. 61. ISBN 978-0-521-31040-6.
  41. ^ Kenneth R. Lang (2006). Astrophysical formulae, Volume 1 (3rd ed.). Birkhäuser. p. 23. ISBN 978-3-540-29692-8.
  42. ^ B. Bertotti; Paolo Farinella; David Vokrouhlický (2003). "Figure 9.2: The temperature profile in the solar atmosphere". New Views of the Solar System. Springer. p. 248. ISBN 978-1-4020-1428-4.
  43. ^ Schutz, Bernard (2004). Gravity From the Group Up: An Introductory Guide to Gravity and General Relativity (1st ed.). Cambridge University Press. p. 304. ISBN 978-0-521-45506-0.
  44. ^ PCW Davies (1978). "Thermodynamics of black holes" (PDF). Rep Prog Phys. 41 (8): 1313–1355. Bibcode:1978RPPh...41.1313D. doi:10.1088/0034-4885/41/8/004. Archived from the original (PDF) on 2013-05-10.
  45. ^ Robert M Wald (2005). "The thermodynamics of black holes". In Andrés Gomberoff; Donald Marolf. Lectures on quantum gravity. Springer Science & Business Media. pp. 1–38. ISBN 978-0-387-23995-8.
  46. ^ Bernard J Carr & Steven B Giddings (2008). "Chapter 6: Quantum black holes". Beyond Extreme Physics: Cutting-edge science. Rosen Publishing Group, Scientific American (COR). p. 30. ISBN 978-1-4042-1402-6.
  47. ^ Valeri P. Frolov; Andrei Zelnikov (2011). "Equation 9.7.1". Introduction to Black Hole Physics. Oxford University Press. p. 321. ISBN 978-0-19-969229-3.
  48. ^ Robert M Wald (2005). "The thermodynamics of black holes (pp. 1–38)". In Andrés Gomberoff; Donald Marolf. Lectures on Quantum Gravity. Springer Science & Business Media. p. 28. ISBN 978-0-387-23995-8. ... no results on black hole thermodynamics have been subject to any experimental or observational tests ...
  49. ^ White, M. (1999). "Anisotropies in the CMB" (PDF). Proceedings of the Los Angeles Meeting, DPF 99. UCLA. See also arXive.org.
  50. ^ "Stefan–Boltzmann constant". NIST reference on constants, units, and uncertainty. Retrieved 2012-02-02.
  51. ^ A simple example is provided by Srivastava M. K. (2011). "Cooling by radiation". The Person Guide to Objective Physics for the IIT-JEE. Pearson Education India. p. 610. ISBN 978-81-317-5513-6.
  52. ^ M Vollmer; K-P Mõllmann (2011). "Figure 1.38: Some examples for temperature dependence of emissivity for different materials". Infrared Thermal Imaging: Fundamentals, Research and Applications. John Wiley & Sons. p. 45. ISBN 978-3-527-63087-5.
  53. ^ Robert Osiander; M. Ann Garrison Darrin; John Champion (2006). MEMS and Microstructures in aerospace applications. CRC Press. p. 187. ISBN 978-0-8247-2637-9.
  54. ^ Krishna Rajagopal; Frank Wilczek (2001). "6.2 Coling by Neutrino Emissions (pp. 2135-2136) – The Condensed Matter Physics of QCD". In Mikhail A. Shifman. At The Frontier of Particle Physics: Handbook of QCD (On the occasion of the 75th birthday of Professor Boris Ioffe). 3. Singapore: World Scientific. pp. 2061–2151. arXiv:hep-ph/0011333v2. CiteSeerX 10.1.1.344.2269. doi:10.1142/9789812810458_0043. ISBN 978-981-02-4969-4. For the first 105–6 years of its life, the cooling of a neutron star is governed by the balance between heat capacity and the loss of heat by neutrino emission. ... Both the specific heat CV and the neutrino emission rate Lν are dominated by physics within T of the Fermi surface. ... The star will cool rapidly until its interior temperature is T < Tc ∼ ∆, at which time the quark matter core will become inert and the further cooling history will be dominated by neutrino emission from the nuclear matter fraction of the star.
  55. ^ Walter Lewin; Warren Goldstein (2011). "X-ray bursters!". For the love of physics. Simon and Schuster. pp. 251 ff. ISBN 978-1-4391-0827-7.
  56. ^ TE Strohmayer (2006). "Neutron star structure and fundamental physics". In John W. Mason. Astrophysics update, Volume 2. Birkhäuser. p. 41. ISBN 978-3-540-30312-1.

Bibliography

External links

  • Keesey, Lori J. (Dec 12, 2010). "Blacker than black". NASA. Engineers now developing a blacker-than pitch material that will help scientists gather hard-to-obtain scientific measurements... nanotech-based material now being developed by a team of 10 technologists at the NASA Goddard Space Flight Center
Black-body radiation

Black-body radiation is the thermal 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). It has a specific spectrum and intensity that depends only on the body's temperature, which is assumed for the sake of calculations and theory to be uniform and constant.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 infra-red and cannot be perceived by the human eye. Because the human eye cannot perceive light waves at lower frequencies, 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. 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. 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.The term black body was introduced by Gustav Kirchhoff in 1860. Black-body radiation is also called thermal radiation, cavity radiation, complete radiation or temperature radiation.

Brightness temperature

Brightness temperature or radiance temperature is the temperature a black body in thermal equilibrium with its surroundings would have to be to duplicate the observed intensity of a grey body object at a frequency . This concept is used in radio astronomy, planetary science and materials science.

The brightness temperature of a surface is typically determined by an optical measurement, for example using a pyrometer, with the intention of determining the real temperature. As detailed below, the real temperature of a surface can in some cases be calculated by dividing the brightness temperature by the emissivity of the surface. Since the emissivity is a value between 0 and 1, the real temperature will be greater than or equal to the brightness temperature. At high frequencies (short wavelengths) and low temperatures, the conversion must proceed through Planck's law.

The brightness temperature is not a temperature as ordinarily understood. It characterizes radiation, and depending on the mechanism of radiation can differ considerably from the physical temperature of a radiating body (though it is theoretically possible to construct a device which will heat up by a source of radiation with some brightness temperature to the actual temperature equal to brightness temperature). Nonthermal sources can have very high brightness temperatures. In pulsars the brightness temperature can reach 1026 K. For the radiation of a typical helium–neon laser with a power of 60 mW and a coherence length of 20 cm, focused in a spot with a diameter of 10 µm, the brightness temperature will be nearly 14×109 K.[citation needed]


For a black body, Planck's law gives:

where

(the Intensity or Brightness) is the amount of energy emitted per unit surface area per unit time per unit solid angle and in the frequency range between and ; is the temperature of the black body; is Planck's constant; is frequency; is the speed of light; and is Boltzmann's constant.

For a grey body the spectral radiance is a portion of the black body radiance, determined by the emissivity . That makes the reciprocal of the brightness temperature:

At low frequency and high temperatures, when , we can use the Rayleigh–Jeans law:

so that the brightness temperature can be simply written as:

In general, the brightness temperature is a function of , and only in the case of blackbody radiation it is the same at all frequencies. The brightness temperature can be used to calculate the spectral index of a body, in the case of non-thermal radiation.

Candlestick pattern

In technical analysis, a candlestick pattern is a movement in prices shown graphically on a candlestick chart that some believe can predict a particular market movement. The recognition of the pattern is subjective and programs that are used for charting have to rely on predefined rules to match the pattern. There are 42 recognised patterns that can be split into simple and complex patterns.

Color temperature

Not to be confused with warm and cool colors.

The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of a color comparable to that of the light source. Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, horticulture, and other fields. In practice, color temperature is meaningful only for light sources that do in fact correspond somewhat closely to the radiation of some black body, i.e., light in a range going from red to orange to yellow to white to blueish white; it does not make sense to speak of the color temperature of, e.g., a green or a purple light. Color temperature is conventionally expressed in kelvins, using the symbol K, a unit of measure for absolute temperature.

Color temperatures over 5000 K are called "cool colors" (bluish), while lower color temperatures (2700–3000 K) are called "warm colors" (yellowish). "Warm" in this context is an analogy to radiated heat flux of traditional incandescent lighting rather than temperature. The spectral peak of warm-coloured light is closer to infrared, and most natural warm-coloured light sources emit significant infrared radiation. The fact that "warm" lighting in this sense actually has a "cooler" color temperature often leads to confusion.

Cosmic Background Explorer

The Cosmic Background Explorer (COBE ), also referred to as Explorer 66, was a satellite dedicated to cosmology, which operated from 1989 to 1993. Its goals were to investigate the cosmic microwave background radiation (CMB) of the universe and provide measurements that would help shape our understanding of the cosmos.

COBE's measurements provided two key pieces of evidence that supported the Big Bang theory of the universe: that the CMB has a near-perfect black-body spectrum, and that it has very faint anisotropies. Two of COBE's principal investigators, George Smoot and John Mather, received the Nobel Prize in Physics in 2006 for their work on the project. According to the Nobel Prize committee, "the COBE-project can also be regarded as the starting point for cosmology

as a precision science".COBE was followed by two more advanced spacecraft: WMAP operated from 2001-2010 and Planck from 2009-2013.

Cosmic microwave background

All-sky mollweide map of the CMB, created from 9 years of WMAP data

The cosmic microwave background (CMB, CMBR) is electromagnetic radiation as a remnant from an early stage of the universe in Big Bang cosmology. In older literature, the CMB is also variously known as cosmic microwave background radiation (CMBR) or "relic radiation". The CMB is a faint cosmic background radiation filling all space that is an important source of data on the early universe because it is the oldest electromagnetic radiation in the universe, dating to the epoch of recombination. With a traditional optical telescope, the space between stars and galaxies (the background) is completely dark. However, a sufficiently sensitive radio telescope shows a faint background noise, or glow, almost isotropic, that is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1964 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s, and earned the discoverers the 1978 Nobel Prize in Physics.

The discovery of CMB is landmark evidence of the Big Bang origin of the universe. When the universe was young, before the formation of stars and planets, it was denser, much hotter, and filled with a uniform glow from a white-hot fog of hydrogen plasma. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral hydrogen atoms. Unlike the uncombined protons and electrons, these newly conceived atoms could not absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog. Cosmologists refer to the time period when neutral atoms first formed as the recombination epoch, and the event shortly afterwards when photons started to travel freely through space rather than constantly being scattered by electrons and protons in plasma is referred to as photon decoupling. The photons that existed at the time of photon decoupling have been propagating ever since, though growing fainter and less energetic, since the expansion of space causes their wavelength to increase over time (and wavelength is inversely proportional to energy according to Planck's relation). This is the source of the alternative term relic radiation. The surface of last scattering refers to the set of points in space at the right distance from us so that we are now receiving photons originally emitted from those points at the time of photon decoupling.

Precise measurements of the CMB are critical to cosmology, since any proposed model of the universe must explain this radiation. The CMB has a thermal black body spectrum at a temperature of 2.72548±0.00057 K. The spectral radiance dEν/dν peaks at 160.23 GHz, in the microwave range of frequencies, corresponding to a photon energy of about 6.626 × 10−4 eV. Alternatively, if spectral radiance is defined as dEλ/dλ, then the peak wavelength is 1.063 mm (282 GHz, 1.168 x 10−3 eV photons). The glow is very nearly uniform in all directions, but the tiny residual variations show a very specific pattern, the same as that expected of a fairly uniformly distributed hot gas that has expanded to the current size of the universe. In particular, the spectral radiance at different angles of observation in the sky contains small anisotropies, or irregularities, which vary with the size of the region examined. They have been measured in detail, and match what would be expected if small thermal variations, generated by quantum fluctuations of matter in a very tiny space, had expanded to the size of the observable universe we see today. This is a very active field of study, with scientists seeking both better data (for example, the Planck spacecraft) and better interpretations of the initial conditions of expansion. Although many different processes might produce the general form of a black body spectrum, no model other than the Big Bang has yet explained the fluctuations. As a result, most cosmologists consider the Big Bang model of the universe to be the best explanation for the CMB.

The high degree of uniformity throughout the observable universe and its faint but measured anisotropy lend strong support for the Big Bang model in general and the ΛCDM ("Lambda Cold Dark Matter") model in particular. Moreover, the fluctuations are coherent on angular scales that are larger than the apparent cosmological horizon at recombination. Either such coherence is acausally fine-tuned, or cosmic inflation occurred.

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 when the body's emissivity curve (as a function of wavelength) is not known.

When the star's or planet's net emissivity in the relevant wavelength band is less than unity (less than that of a black body), the actual temperature of the body will be higher than the effective temperature. The net emissivity may be low due to surface or atmospheric properties, including greenhouse effect.

Emissivity

The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation and it may include both visible radiation (light) and infrared radiation, which is not visible to human eyes. The thermal radiation from very hot objects (see photograph) is easily visible to the eye. Quantitatively, emissivity is the ratio of the thermal radiation from a surface to the radiation from an ideal black surface at the same temperature as given by the Stefan–Boltzmann law. The ratio varies from 0 to 1. The surface of a perfect black body (with an emissivity of 1) emits thermal radiation at the rate of approximately 448 watts per square metre at room temperature (25 °C, 298.15 K); all real objects have emissivities less than 1.0, and emit radiation at correspondingly lower rates.Emissivities are important in several contexts:

insulated windows. – Warm surfaces are usually cooled directly by air, but they also cool themselves by emitting thermal radiation. This second cooling mechanism is important for simple glass windows, which have emissivities close to the maximum possible value of 1.0. "Low-E windows" with transparent low emissivity coatings emit less thermal radiation than ordinary windows. In winter, these coatings can halve the rate at which a window loses heat compared to an uncoated glass window.

solar heat collectors. – Similarly, solar heat collectors lose heat by emitting thermal radiation. Advanced solar collectors incorporate selective surfaces that have very low emissivities. These collectors waste very little of the solar energy through emission of thermal radiation.

thermal shielding. – For the protection of structures from high surface temperatures, such as reusable spacecraft or hypersonic aircraft, high emissivity coatings (HECs), with emissivity values near 0.9, are applied on the surface of insulating ceramics . This facilitates radiative cooling and protection of the underlying structure and is an alternative to ablative coatings, used in single-use reentry capsules.

planetary temperatures. – The planets are solar thermal collectors on a large scale. The temperature of a planet's surface is determined by the balance between the heat absorbed by the planet from sunlight, heat emitted from its core, and thermal radiation emitted back into space. Emissivity of a planet is determined by the nature of its surface and atmosphere.

temperature measurements. – Pyrometers and infrared cameras are instruments used to measure the temperature of an object by using its thermal radiation; no actual contact with the object is needed. The calibration of these instruments involves the emissivity of the surface that's being measured.

Flame

A flame (from Latin flamma) is the visible, gaseous part of a fire. It is caused by a highly exothermic reaction taking place in a thin zone. Very hot flames are hot enough to have ionized gaseous components of sufficient density to be considered plasma.

Max Planck

Max Karl Ernst Ludwig Planck, ForMemRS (German: [ˈplaŋk]; English: ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.Planck made many contributions to theoretical physics, but his fame as a physicist rests primarily on his role as the originator of quantum theory, which revolutionized human understanding of atomic and subatomic processes. In 1948 the German scientific institution the Kaiser Wilhelm Society (of which Planck was twice president) was renamed the Max Planck Society (MPS). The MPS now includes 83 institutions representing a wide range of scientific directions.

Melting point

The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at a standard pressure such as 1 atmosphere or 100 kPa.

When considered as the temperature of the reverse change from liquid to solid, it is referred to as the freezing point or crystallization point. Because of the ability of some substances to supercool, the freezing point is not considered as a characteristic property of a substance. When the "characteristic freezing point" of a substance is determined, in fact the actual methodology is almost always "the principle of observing the disappearance rather than the formation of ice", that is, the melting point.

Planck's law

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.At the end of the 19th-century, physicists were unable to explain why the observed spectrum of black body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories. In 1900, Max Planck empirically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. This resolved the problem of the ultraviolet catastrophe predicted by classical physics.

It was a pioneering insight of modern physics and is of fundamental importance to quantum theory.

Planck constant

The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.

At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories. In 1900, Max Planck empirically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, h, from the experimental measurements, and that constant is named in his honor. In 1905, the value E was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called a photon.

Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram (IPK), that had defined the kilogram since 1889. The new definition was unanimously approved at the General Conference on Weights and Measures (CGPM) on 16 November 2018 as part of the 2019 redefinition of SI base units. For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.62607015×10−34 J⋅s exactly. The kilogram was the last SI base unit to be re-defined by a fundamental physical property to replace a physical artefact.

Planetary equilibrium temperature

The planetary equilibrium temperature is a theoretical temperature that a planet would be at when considered simply as if it were a black body being heated only by its parent star. In this model, the presence or absence of an atmosphere (and therefore any greenhouse effect) is not considered, and one treats the theoretical black body temperature as if it came from an idealized surface of the planet.

Other authors use different names for this concept, such as equivalent blackbody temperature of a planet, or the effective radiation emission temperature of the planet. Similar concepts include the global mean temperature, global radiative equilibrium, and global-mean surface air temperature, which includes the effects of global warming.

Radiation

In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:

electromagnetic radiation, such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma radiation (γ)

particle radiation, such as alpha radiation (α), beta radiation (β), and neutron radiation (particles of non-zero rest energy)

acoustic radiation, such as ultrasound, sound, and seismic waves (dependent on a physical transmission medium)

gravitational radiation, radiation that takes the form of gravitational waves, or ripples in the curvature of spacetime.Radiation is often categorized as either ionizing or non-ionizing depending on the energy of the radiated particles. Ionizing radiation carries more than 10 eV, which is enough to ionize atoms and molecules, and break chemical bonds. This is an important distinction due to the large difference in harmfulness to living organisms. A common source of ionizing radiation is radioactive materials that emit α, β, or γ radiation, consisting of helium nuclei, electrons or positrons, and photons, respectively. Other sources include X-rays from medical radiography examinations and muons, mesons, positrons, neutrons and other particles that constitute the secondary cosmic rays that are produced after primary cosmic rays interact with Earth's atmosphere.

Gamma rays, X-rays and the higher energy range of ultraviolet light constitute the ionizing part of the electromagnetic spectrum. The word "ionize" refers to the breaking of one or more electrons away from an atom, an action that requires the relatively high energies that these electromagnetic waves supply. Further down the spectrum, the non-ionizing lower energies of the lower ultraviolet spectrum cannot ionize atoms, but can disrupt the inter-atomic bonds which form molecules, thereby breaking down molecules rather than atoms; a good example of this is sunburn caused by long-wavelength solar ultraviolet. The waves of longer wavelength than UV in visible light, infrared and microwave frequencies cannot break bonds but can cause vibrations in the bonds which are sensed as heat. Radio wavelengths and below generally are not regarded as harmful to biological systems. These are not sharp delineations of the energies; there is some overlap in the effects of specific frequencies.The word radiation arises from the phenomenon of waves radiating (i.e., traveling outward in all directions) from a source. This aspect leads to a system of measurements and physical units that are applicable to all types of radiation. Because such radiation expands as it passes through space, and as its energy is conserved (in vacuum), the intensity of all types of radiation from a point source follows an inverse-square law in relation to the distance from its source. Like any ideal law, the inverse-square law approximates a measured radiation intensity to the extent that the source approximates a geometric point.

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 per unit time (also known as the black-body radiant emittance) 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, is derived from other known physical constants. 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. 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 radiant emittance 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, :

Wavelength- and subwavelength-scale particles, metamaterials, and other nanostructures are not subject to ray-optical limits and may be designed to exceed the Stefan–Boltzmann law.

Thermal radiation

Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation. Particle motion results in charge-acceleration or dipole oscillation which produces electromagnetic radiation.

The infrared radiation emitted by animals that is detectable with an infrared camera, and the cosmic microwave background radiation, are all examples of thermal radiation.

If a radiation-emitting object meets the physical characteristics of a black body in thermodynamic equilibrium, the radiation is called blackbody radiation. Planck's law describes the spectrum of blackbody radiation, which depends solely on the object's temperature. Wien's displacement law determines the most likely frequency of the emitted radiation, and the Stefan–Boltzmann law gives the radiant intensity.Thermal radiation is also one of the fundamental mechanisms of heat transfer.

Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and 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, absolute zero, the particle constituents of matter have minimal motion and can become no colder. In the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy. Thermodynamic temperature is often also called absolute temperature, for two reasons: one, proposed by Kelvin, that it does not depend on the properties of a particular material; two that it refers to an absolute zero according to the properties of the ideal gas.

The International System of Units specifies a particular scale for thermodynamic temperature. It uses the kelvin scale for measurement and selects the triple point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically. The Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a practical means of estimating the thermodynamic temperature to a very high degree of accuracy.

Roughly, the temperature of a body at rest is a measure of the mean of the energy of the translational, vibrational and rotational motions of matter's particle constituents, such as molecules, atoms, and subatomic particles. The full variety of these kinetic motions, along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these, make up the total internal energy of a substance. Internal energy is loosely called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings, or by the substance upon the surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a "degree of freedom". At equilibrium, each degree of freedom will have on average the same energy: where is the Boltzmann constant, unless that degree of freedom is in the quantum regime. The internal degrees of freedom (rotation, vibration, etc.) may be in the quantum regime at room temperature, but the translational degrees of freedom will be in the classical regime except at extremely low temperatures (fractions of kelvins) and it may be said that, for most situations, the thermodynamic temperature is specified by the average translational kinetic energy of the particles.

Wien's displacement law
Not to be confused with Wien distribution law.

Wien's displacement law states that the black body radiation curve for different temperature peaks at a wavelength is inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness of black body radiation as a function of wavelength at any given temperature. However, it had been discovered by Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black body radiation toward shorter wavelengths as temperature increases.

Formally, Wien's displacement law states that the spectral radiance of black body radiation per unit wavelength, peaks at the wavelength λmax given by:

where T is the absolute temperature in kelvins. b is a constant of proportionality called Wien's displacement constant, equal to 2.8977729(17)×10−3 m⋅K, or to obtain wavelength in micrometers, b ≈ 2900 μm⋅K. If one is considering the peak of black body emission per unit frequency or per proportional bandwidth, one must use a different proportionality constant. However, the form of the law remains the same: the peak wavelength is inversely proportional to temperature, and the peak frequency is directly proportional to temperature.

Wien's displacement law may be referred to as "Wien's law", a term which is also used for the Wien approximation.

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