Black body

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For the radiation from a black body in thermal equilibrium, see Black-body radiation.

A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The idea was originally introduced by 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. [1]

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

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 of radiation for all wavelengths and for all angles of incidence. Hence the blackbody is a perfect absorber for all incident radiation. [2]

Construction of black bodies from absorbers which are nearly perfect over some frequency range remains a topic of interest.[3] An idealized approximate realization of a black body is a hole in the wall of a large enclosure (see below). Any light entering the hole is reflected indefinitely or absorbed inside and is unlikely to re-emerge, making the hole a nearly perfect absorber. The radiation confined in such an enclosure may or may not be in thermal equilibrium, depending upon the nature of the walls and the other contents of the enclosure.[4]

Black-body radiation is distributed in energy (or frequency) in a manner set by the temperature T.

A black body in thermal equilibrium has two notable properties:[5]

  1. It is an ideal emitter: it emits as much or more energy at every frequency than any other body at the same temperature.
  2. It is a diffuse emitter: the energy is radiated isotropically, independent of direction.

A black body in thermal equilibrium emits black-body radiation with a distribution in energy or spectrum that is independent of the nature of the body and characterized only by its temperature, a distribution according to Planck's law as shown in the figure to the right.

By definition, a black body in thermal equilibrium has an emissivity of e = 1.0. In practice, common applications define sources of infrared radiation with emissivity greater than approximately 0.99 as a black body. A source with lower emissivity is often referred to as a gray body.[6]

Contents

[edit] Theoretical models of a black body or surface

An approximate realization of a black body as a tiny hole in an insulated enclosure. The figure is a cross-section containing the hole.

[edit] Cavity with a hole

A widely used model of a black surface is a cavity with walls that are opaque to radiation apart from a hole.[2] Radiation incident on the hole will pass into the cavity, and is very unlikely to be re-emitted if the cavity is large. The fact that not all radiation incident on the hole will enter into the cavity -- particularly if the wavelength is longer than the diameter of the hole -- makes the hole not quite a perfect black body.

Radiation entering the cavity will be "thermalized" (i.e, its energy is shared with the rest of the radiation in the cavity). As a practical matter, this thermalization occurs by continued absorption and re-emission of radiation by material in the cavity or its walls, although other mechanisms (e.g. photon-photon interactions) would accomplish this as well.

Suppose the cavity is held at a fixed temperature, say 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. Then this escaping radiation will exhibit a distribution in energy characteristic of the temperature T known as black-body radiation. This characteristic, continuous spectrum of thermal radiation depends only on the body's temperature, and not upon its shape, and upon the materials of its walls only in the requirement that they be opaque and not perfectly reflective.[7] See the lower figure for the spectrum as a function of the wavelength of the radiation, which is related to the energy of the radiation by the equation E=hc/λ, with E = energy, h = Planck's constant, c = speed of propagation, and λ = wavelength.

[edit] Opaque poorly reflective bodies

Bodies that are opaque and poorly reflective for thermal radiation that falls on them are valuable in the study of heat radiation. Planck analyzed such bodies with the approximation that they be considered topologically to have an interior and to share an interface. They share the interface with their contiguous medium, which may be rarefied material such as air, or transparent material, through which observations can be made. The interface is not a material body and can neither emit nor absorb. It is a mathematical surface belonging jointly to the two media that touch it. It is the site of refraction of radiation that penetrates it and of reflection of radiation that does not. As such it obeys the Helmholtz reciprocity principle. The opaque body is considered to have a material interior that absorbs all and scatters or transmits none of the radiation that reaches it through refraction at the interface. In this sense the material of the opaque body is black to radiation that reaches it, while the whole phenomenon, including the interior and the interface, does not show perfect blackness. In Planck's model, perfectly black bodies, which he noted do not exist in nature, besides their opaque interior, have interfaces that are perfectly transmitting and non-reflective.[8]

[edit] Kirchhoff's perfect black bodies

Kirchhoff in 1860 introduced the theoretical concept of a perfect black body, but Planck noted that the Kirchhoff's model of perfect black bodies was far from what might occur in physical reality. Kirchhoff's perfect black bodies are theoretical fictions. They absorb all the radiation that falls on them, right in an infinitely thin surface layer, with no reflection and no scattering. They emit radiation diffusely, with spectral radiance the same in every direction, in perfect accord with Lambert's cosine law.[9][8]

[edit] Practical approximations to a black surface

[edit] Cavity with a hole

In 1898, Otto Lummer and Ferdinand Kurlbaum published an account of their cavity radiation source.[10] 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.[11]

[edit] Near-black materials

It has long been known that a lamp-black coating will make a body nearly black. Some other materials are nearly black in particular wavelength bands. Such materials do not survive all the very high temperatures that are of interest.

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%.[12][13]

In 2009, a team of Japanese scientists created a material 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.[14]

Another example of a nearly perfect black material is super black, produced from a nickel-phosphorus alloy.[15]

[edit] Black bodies in nature

[edit] Stars and planets

For more about the UBV color index, see Photometric system.
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. 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.[16]

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.[17]

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,[18] with the Sun having an index of +0.648 ± 0.006.[19] 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.[20] The two indices for two types of stars are compared in the figure with the effective surface temperature of the stars assuming they are black bodies. It can be seen that there is only a rough correlation. For example, for a given B-V index from the blue-visible region of the spectrum., the curves for both types of star lie below the corresponding black-body U-B index that includes the ultraviolet spectrum, showing that both types 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.[21] For example, the Sun has an effective temperature of 5780 K,[22] which can be compared to the temperature of the photosphere of the Sun (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 approximately 500 km deep.[23]

[edit] Black holes

See also: Hawking radiation

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 (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).[24] Physicists believe that black holes have a non-zero temperature and emit radiation with a nearly perfect black-body spectrum, although this prediction has not been tested either observationally or experimentally.[25]

[edit] References

[edit] Citations

  1. ^ 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 (Taylor & Francis) 20 (130). http://books.google.com/books?id=RVYEAAAAYAAJ&pg=PA1&lpg=PA1. 
  2. ^ a b Siegel, Robert; Howell, John R. (2002). Thermal Radiation Heat Transfer; Volume 1 (4th ed.). Taylor & Francis. p. 7. ISBN 1560328398. http://books.google.com/books?id=O389yQ0-fecC&pg=PA7. 
  3. ^ For some sources describing construction of black bodies, see Pierre-Marie Robitaille (October, 2009). "Kirchhoff's law of thermal emission: 150 years". Progress in Physics 4: 3 ff. http://www.ptep-online.com/index_files/2009/PP-19-01.PDF. 
  4. ^ 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. Thermodynamics and statistical mechanics (Reprint of Oxford University Press 1978 ed.). Courier Dover Publications. p. 209. ISBN 0486664937. http://books.google.com/books?id=0gnWL7tmxm0C&pg=PA209. 
  5. ^ Mahmoud Massoud (2005). "§2.1 Blackbody radiation". Engineering thermofluids: thermodynamics, fluid mechanics, and heat transfer. Springer. p. 568. ISBN 3540222928. http://books.google.com/books?id=9KIp_fmC9A0C&pg=PA568. 
  6. ^ Electro Optical Industries, Inc. (2008)What is a Blackbody and Infrared Radiation? In Education/Reference
  7. ^ Georg Joos (1986). Theoretical Physics (Reprint of Hafner Publishing Company 1958 Third ed.). Courier Dover Publications. p. 621. ISBN 0486652270. http://books.google.com/books?id=vIw5m2XuvpIC&pg=PA621. 
  8. ^ a b Planck 1914
  9. ^ Kirchhoff 1860
  10. ^ Lummer & Kurlbaum 1898
  11. ^ Kangro 1976, p. 159
  12. ^ Ai Lin Chun, "Carbon nanotubes: Blacker than black," Nature Nanotechnology (25 Jan 2008), doi:10.1038/nnano.2008.29.
  13. ^ Z.-P. Yang et al., "Experimental Observation of an Extremely Dark Material Made By a Low-Density Nanotube Array," Nano Letters vol. 8, pp. 446-451 (2008).
  14. ^ K. Mizuno et al. (2009). "A black body absorber from vertically aligned single-walled carbon nanotubes" (free download). Proceedings of the National Academy of Sciences 106 (15): 6044–6077. Bibcode 2009PNAS..106.6044M. doi:10.1073/pnas.0900155106. PMC 2669394. PMID 19339498. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2669394. 
  15. ^ New Scientist (6 February 2003). "Mini craters key to 'blackest ever black'". http://www.newscientist.com/article/dn3356-mini-craters-key-to-blackest-ever-black.html. 
  16. ^ 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 0521546222. http://books.google.com/books?id=lb5owLGIQGsC&pg=PA53. "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" 
  17. ^ 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 0521348692. http://books.google.com/books?id=JWrtilsCycQC&pg=PA26. 
  18. ^ 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 144197623X. http://books.google.com/books?id=ILBuYcGASxcC&pg=PA52. 
  19. ^ 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. http://adsabs.harvard.edu/full/1995PASP..107..120G. Retrieved 2012-01-26. 
  20. ^ M Golay (1974). "Table IX: U-B Indices". Introduction to astronomical photometry. Springer. p. 82. ISBN 9027704287. http://books.google.com/books?id=OmNuvvt31BkC&pg=PA82. 
  21. ^ Lawrence Hugh Aller (1991). Atoms, stars, and nebulae (3rd ed.). Cambridge University Press. p. 61. ISBN 0521310407. http://books.google.com/books?id=HupvoeJDCGoC&pg=PA61. 
  22. ^ Kenneth R. Lang (2006). Astrophysical formulae, Volume 1 (3rd ed.). Birkhäuser. p. 23. ISBN 3540296921. http://books.google.com/books?id=HlGIXqzVEAgC&pg=PA23. 
  23. ^ 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 1402014287. http://books.google.com/books?id=i-YvHNPEqAIC&pg=PA248. 
  24. ^ PCW Davies (1978). "Thermodynamics of black holes". Rep Prog Phys 41 (8): 1313 ff. Bibcode 1978RPPh...41.1313D. doi:10.1088/0034-4885/41/8/004. http://cosmos.asu.edu/publications/papers/ThermodynamicTheoryofBlackHoles%2034.pdf. 
  25. ^ Robert M Wald (2005). "The thermodynamics of black holes". In Andrés Gomberoff, Donald Marolf, eds. Lectures on quantum gravity. Springer. pp. 1 ff. ISBN 0387239952. http://books.google.com/books?id=ZDtxnw-b1xEC&pg=PA1. 

[edit] Bibliography

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