Editing Black body (section)

== References ==

=== Citations ===
{{reflist|refs=

<ref name="Adkins">
{{cite book |author=Clement John Adkins |chapter=§4.1 The function of the second law |title=Equilibrium thermodynamics |chapter-url=https://books.google.com/books?id=FW4Oz48TWwQC&pg=PA50 |page=50 |isbn=978-0-521-27456-2 |edition=3rd |publisher=Cambridge University Press |year=1983}}
</ref>

<ref name=Aller>
{{cite book |title=Atoms, stars, and nebulae |url=https://books.google.com/books?id=HupvoeJDCGoC&pg=PA61 |page=61 |author=Lawrence Hugh Aller |publisher=Cambridge University Press |isbn=978-0-521-31040-6 |edition=3rd |year=1991}}
</ref>

<ref name=Batrouni>
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 {{cite book |title=Equilibrium and non-equilibrium statistical thermodynamics |author1=Michel Le Bellac |author2=Fabrice Mortessagne |author3=Ghassan George Batrouni |page=8 |url=https://books.google.com/books?id=LZcdi4uzaWIC&pg=PA8 |isbn= 978-0521821438 |year=2004 |publisher=Cambridge University Press}}
</ref>

<ref name=Bergmann>
{{cite book |title=Optics of waves and particles |author1=Ludwig Bergmann |author2=Clemens Schaefer |author3=Heinz Niedrig |url=https://books.google.com/books?id=sJxv-yCSNEAC&pg=PA595 |page=595 |isbn=978-3-11-014318-8 |year=1999 |publisher=Walter de Gruyter |quote=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.}}
</ref>

<ref name=Bertotti>
{{cite book |author1=B. Bertotti |author2=Paolo Farinella |author3=David Vokrouhlický |title=New Views of the Solar System |chapter=Figure 9.2: The temperature profile in the solar atmosphere |page=248 |chapter-url=https://books.google.com/books?id=i-YvHNPEqAIC&pg=PA248 |isbn=978-1-4020-1428-4 |year=2003 |publisher=Springer}}
</ref>

<ref name=boson>
The fundamental bosons are the [[photon]], the vector bosons of the [[weak interaction]], the [[gluon]], and the [[graviton]]. See {{cite book |title=Bose-Einstein condensation |url=https://books.google.com/books?id=suqJdr2pPIsC&pg=PA4 |page=4 |author1=Allan Griffin |author2=D. W. Snoke |author2-link=David Snoke|author3=S. Stringari |publisher=Cambridge University Press |year=1996 |isbn=978-0-521-58990-1}}
</ref>

<ref name=Brown>
See description of work by Richard Brown and his colleagues at the UK's National Physical Laboratory: {{cite journal
|url= https://www.newscientist.com/article/dn3356-mini-craters-key-to-blackest-ever-black.html
|title=Mini craters key to 'blackest ever black'
|date=6 February 2003
|author=Mick Hamer
|journal=New Scientist
}}</ref>

<ref name=Carr>
{{cite book |title=Beyond Extreme Physics: Cutting-edge science |chapter=Chapter 6: Quantum black holes |author1=Bernard J Carr |author2=Steven B Giddings |name-list-style=amp |chapter-url=https://books.google.com/books?id=N-K-q0_TexAC&pg=PA30 |page=[https://archive.org/details/beyondextremephy0000unse/page/30 30] |publisher=Rosen Publishing Group, Scientific American (COR) |isbn=978-1-4042-1402-6 |year=2008 |url=https://archive.org/details/beyondextremephy0000unse/page/30 }}
</ref>

<ref name=Champion>
{{cite book |title=MEMS and Microstructures in aerospace applications |author1=Robert Osiander |author2=M. Ann Garrison Darrin |author3=John Champion |url=https://books.google.com/books?id=DaqsgZ2HtIwC&pg=PA187 |page=187 |isbn=978-0-8247-2637-9 |year=2006 |publisher=CRC Press}}
</ref>

<ref name=Chun>
{{cite journal |doi=10.1038/nnano.2008.29|title=Blacker than black|year=2008|last1=Chun|first1=Ai Lin|journal=Nature Nanotechnology|doi-access=free}}
</ref>

<ref name=Davies>
{{cite journal |title=Thermodynamics of black holes |author=PCW Davies |journal=Rep Prog Phys |volume=41 |issue=8 |pages=1313–1355 |year=1978 |url=http://cosmos.asu.edu/publications/papers/ThermodynamicTheoryofBlackHoles%2034.pdf |doi=10.1088/0034-4885/41/8/004 |bibcode=1978RPPh...41.1313D |s2cid=250916407 |url-status=dead |archive-url=https://web.archive.org/web/20130510184530/http://cosmos.asu.edu/publications/papers/ThermodynamicTheoryofBlackHoles%2034.pdf |archive-date=2013-05-10 }}
</ref>

<ref name=emissivity>
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 {{cite book |title=Principles of heat transfer |author=Massoud Kaviany |chapter=Figure 4.3(b): Behaviors of a gray (no wavelength dependence), diffuse (no directional dependence) and opaque (no transmission) surface |page=381 |chapter-url=https://books.google.com/books?id=dKI4k-9jK88C&pg=PA381  |isbn=978-0-471-43463-4 |year=2002 |publisher=Wiley-IEEE}} and {{cite book |title=Encyclopedia of optical engineering, Volume 3  |author=Ronald G. Driggers |url=https://books.google.com/books?id=9ExHkgDv2z0C&pg=PA2303 |page=2303 |isbn=978-0-8247-4252-2 |publisher=CRC Press |year=2003}}
</ref>

<ref name=Frolov>
{{cite book |title=Introduction to Black Hole Physics |author1=Valeri P. Frolov |author2=Andrei Zelnikov |chapter-url=https://books.google.com/books?id=r_l5AK9DdXsC&pg=PA321 |page=321 |chapter=Equation 9.7.1 |isbn=978-0-19-969229-3 |year=2011 |publisher=Oxford University Press}}
</ref>

<ref name=Golay>
{{cite book |title=Introduction to astronomical photometry |author=M Golay |chapter-url=https://books.google.com/books?id=OmNuvvt31BkC&pg=PA82 |page=82 |chapter=Table IX: ''U-B'' Indices |isbn=978-90-277-0428-3 |year=1974 |publisher=Springer}}
</ref>

<ref name=Gray>
{{cite journal |author=David F Gray |journal=Publications of the Astronomical Society of the Pacific |volume=107 |pages=120–123 |date=February 1995 |title=Comparing the sun with other stars along the temperature coordinate |doi=10.1086/133525|bibcode = 1995PASP..107..120G |doi-access=free }}
</ref>

<ref name=gray_body>Some authors describe sources of infrared radiation with emissivity greater than approximately 0.99 as a black body. See {{cite web |title=What is a Blackbody and Infrared Radiation? |url=http://www.electro-optical.com/eoi_page.asp?h=What%20is%20a%20Blackbody%20and%20Infrared%20Radiation? |work=Education/Reference tab |publisher=Electro Optical Industries, Inc. |year=2008 |access-date=2019-06-10 |archive-url=https://web.archive.org/web/20160307024120/http://electro-optical.com/eoi_page.asp?h=what%20is%20a%20blackbody%20and%20infrared%20radiation%3F |archive-date=2016-03-07 |url-status=dead }}</ref>

<ref name=Green>
{{cite book |title=An introduction to the sun and stars |author1=Simon F. Green |author2=Mark H. Jones |author3=S. Jocelyn Burnell |url=https://books.google.com/books?id=lb5owLGIQGsC&pg=PA53 |pages=21–22, 53 |quote=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 |isbn=978-0-521-54622-5 |year=2004 |publisher=Cambridge University Press}}
</ref>

<ref name=infinitesimal>
The notion of an infinitely thin layer was dropped by Planck. See {{harvnb|Planck|1914|page=10, footnote 2}}.
</ref>

<ref name=Kaviany>
{{cite book |title=Principles of heat transfer |author=Massoud Kaviany |chapter=Figure 4.3(b) Radiation properties of an opaque surface |page=381 |chapter-url=https://books.google.com/books?id=dKI4k-9jK88C&pg=PA381 |publisher=Wiley-IEEE |isbn=978-0-471-43463-4 |year=2002}} 
</ref>

<ref name=Kelley>
{{cite book |title=Exploring Ancient Skies: A Survey of Ancient and Cultural Astronomy |author= David H. Kelley |author2= Eugene F. Milone |author3= Anthony F. (FRW) Aveni |url=https://books.google.com/books?id=ILBuYcGASxcC&pg=PA52 |page=52  |isbn=978-1-4419-7623-9 |publisher=Springer |year=2011 |edition=2nd}}
</ref>

<ref name=Kirchhoff>
Translated by F. Guthrie from ''Annalen der Physik'': '''109''', 275-301 (1860): {{cite journal |url=https://books.google.com/books?id=RVYEAAAAYAAJ&pg=PA1 |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |title=On the relation between the radiating and absorbing powers of different bodies for light and heat |author=G. Kirchhoff |volume=20 |issue=130 |date=July 1860}}
</ref>

<ref name=Landsberg>
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 {{cite book |title= Thermodynamics and statistical mechanics |author=Peter Theodore Landsberg |url=https://books.google.com/books?id=0gnWL7tmxm0C&pg=PA209 |page=209 |isbn=978-0-486-66493-4 |publisher=Courier Dover Publications |edition=Reprint of Oxford University Press 1978 |year=1990 }}
</ref>

<ref name=Lang>
{{cite book |title=Astrophysical formulae, Volume 1 |author=Kenneth R. Lang |url=https://books.google.com/books?id=HlGIXqzVEAgC&pg=PA23 |page=23 |isbn=978-3-540-29692-8 |edition=3rd |publisher=Birkhäuser |year=2006}}
</ref>

<ref name=Lewin>
{{cite book |chapter-url=https://books.google.com/books?id=ukItNVRRSp4C&pg=PA250 |pages=[https://archive.org/details/forloveofphysics0000lewi/page/251 251 ''ff''] |author=Walter Lewin |author2=Warren Goldstein |title=For the love of physics |isbn=978-1-4391-0827-7 |year=2011 |publisher=Simon and Schuster |chapter=X-ray bursters! |url=https://archive.org/details/forloveofphysics0000lewi/page/251 }}
</ref>

<ref name=Lewis>{{cite journal |title=Materials keep a low profile |author=CF Lewis |date=June 1988 |journal=Mech. Eng. |pages=37–41 |url=http://www.cewriters.com/CEWritersSample_MaterialsFeature.pdf |archive-url=https://web.archive.org/web/20220119143001/http://www.cewriters.com/CEWritersSample_MaterialsFeature.pdf |url-status=dead |archive-date=19 January 2022 }}</ref>

<ref name=Mason>
{{cite book |title=Astrophysics update, Volume 2 |author=TE Strohmayer |chapter=Neutron star structure and fundamental physics |editor=John W. Mason |chapter-url=https://books.google.com/books?id=SOzEHo1RteMC&pg=PA41 |page=41 |isbn=978-3-540-30312-1 |publisher=Birkhäuser |year=2006}}
</ref>

<ref name=Massoud>
{{cite book |chapter-url=https://books.google.com/books?id=9KIp_fmC9A0C&pg=PA568 |page=568 |author=Mahmoud Massoud |title=Engineering thermofluids: thermodynamics, fluid mechanics, and heat transfer |chapter=§2.1 Blackbody radiation |isbn=978-3-540-22292-7 |publisher=Springer |year=2005}}
</ref>

<ref name=Mizuno>
{{cite journal
|author=K. Mizuno
|title=A black body absorber from vertically aligned single-walled carbon nanotubes
|journal=[[Proceedings of the National Academy of Sciences]]
|volume=106 |pages=6044–6077
|year=2009
|doi=10.1073/pnas.0900155106
|pmid=19339498
|issue=15
|pmc=2669394
|bibcode = 2009PNAS..106.6044M |display-authors=etal|doi-access=free
}}
</ref>

<ref name=Pearson>
A simple example is provided by {{cite book |title=The Person Guide to Objective Physics for the IIT-JEE |author=Srivastava M. K. |chapter=Cooling by radiation |chapter-url=https://books.google.com/books?id=FTpK4a4FTLQC&pg=PA610 |page=610 |publisher=Pearson Education India |year=2011 |isbn=978-81-317-5513-6}}
</ref>

<ref name=Quinn>
{{cite book |title=Textile Futures |author=Bradley Quinn |year=2010 |isbn=978-1-84520-807-3 |publisher=Berg |url=https://books.google.com/books?id=e_wnynE954MC&pg=PA68 |page=68}}
</ref>

<ref name=Rechenberg>
An extensive historical discussion is found in {{cite book |title=The historical development of quantum theory |first1=Jagdish |last1=Mehra |author-link1=Jagdish Mehra |first2=Helmut |last2=Rechenberg |author-link2=Helmut Rechenberg |url=https://books.google.com/books?id=W5kyppVPyesC&pg=PA39 |pages=39 ''ff'' |isbn=978-0-387-95174-4 |year=2000 |publisher=Springer}}
</ref>

<ref name=Schutz>
{{cite book
 | title = Gravity From the Group Up: An Introductory Guide to Gravity and General Relativity 
 | isbn =  978-0-521-45506-0
 | page = 304
 | last1 = Schutz	 | first1 =  Bernard
 | publisher=Cambridge University Press
 | edition=1st
 | year=2004
}}</ref>

<ref name=Shifman>
{{cite book |chapter= 6.2 Coling by Neutrino Emissions (pp. 2135-2136) &ndash; The Condensed Matter Physics of QCD |author1=Krishna Rajagopal |author2=Frank Wilczek |author-link2=Frank Wilczek |pages=2061–2151 |isbn=978-981-02-4969-4 |year=2001 |publisher=[[World Scientific]] |location=Singapore |editor=Mikhail A. Shifman |editor-link=Mikhail Shifman |title=At The Frontier of Particle Physics: Handbook of QCD (On the occasion of the 75th birthday of Professor Boris Ioffe) |volume=3 |quote=For the first 10<sup>5&ndash;6</sup> 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 ''C<sub>V</sub>'' and the neutrino emission rate ''L<sub>&nu;</sub>'' are dominated by physics within ''T'' of the Fermi surface. ... The star will cool rapidly until its interior temperature is ''T''&nbsp;<&nbsp;''T<sub>c</sub>&nbsp;~&nbsp;∆'', 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. |arxiv=hep-ph/0011333v2 |doi=10.1142/9789812810458_0043|citeseerx=10.1.1.344.2269 |s2cid=13606600 }}
</ref>

<ref name=Siegel>
{{cite book
 | title = Thermal Radiation Heat Transfer; Volume 1
 | url = https://books.google.com/books?id=O389yQ0-fecC&pg=PA7
 | isbn = 978-1-56032-839-1
 | page = 7
 | last1 = Siegel	 | first1 =  Robert
 | last2 =  Howell	 | first2 =  John R.
 | publisher=Taylor & Francis
 | edition=4th
 | year=2002
}}</ref>

<ref name=Tipler>
{{cite book |title=Physics for Scientists and Engineers, Parts 1-35; Part 39 |chapter-url=https://books.google.com/books?id=Gp2tzUhbqjMC&pg=PA1044 |page=1044 |chapter=Relative intensity of reflected and transmitted light |isbn=978-0-7167-3821-3 |year=1999 |edition=4th |publisher=Macmillan |author=Paul A. Tipler}}
</ref>

<ref name=Tolman>
{{cite book |author=Richard Chace Tolman |author-link=Richard Chace Tolman |chapter=§103: Change of ''H'' with time as a result of collisions |title= The principles of statistical mechanics |pages= 455 ''ff'' |chapter-url=https://books.google.com/books?id=4TqQZo962s0C |isbn=978-0-486-63896-6 |edition=Reprint of 1938 Oxford University Press |publisher=Dover Publications |year=2010 |quote=...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)}}
</ref>

<ref name=UBV>
Figure modeled after {{cite book |title=Introduction to Stellar Astrophysics: Basic stellar observations and data |author=E. Böhm-Vitense |chapter-url=https://books.google.com/books?id=JWrtilsCycQC&pg=PA26 |page=26 |chapter=Figure 4.9 |publisher=Cambridge University Press |isbn=978-0-521-34869-0 |year=1989}}
</ref>

<ref name=Venkanna>
{{cite book |title=Fundamentals of heat and mass transfer |author=BA Venkanna |chapter-url=https://books.google.com/books?id=IIIVHRirRgEC&pg=PA386 |pages=385–386 |chapter=§10.3.4 Absorptivity, reflectivity, and transmissivity |isbn=978-81-203-4031-2 |year=2010 |publisher=PHI Learning Pvt. Ltd.}}
</ref>

<ref name=Vollmer>
{{cite book |title=Infrared Thermal Imaging: Fundamentals, Research and Applications |chapter=Figure 1.38: Some examples for temperature dependence of emissivity for different materials |chapter-url=https://books.google.com/books?id=nAIZb8-05IwC&pg=PA45 |page=45  |author1=M Vollmer |author2=K-P Mõllmann |isbn=978-3-527-63087-5 |year=2011 |publisher=John Wiley & Sons}}
</ref>

<ref name=Wald>
{{cite book |chapter=The thermodynamics of black holes |author=Robert M Wald |chapter-url=https://books.google.com/books?id=ZDtxnw-b1xEC&pg=PA1 |pages=1–38 |editor1=Andrés Gomberoff |editor2=Donald Marolf |title=Lectures on quantum gravity |isbn=978-0-387-23995-8 |year=2005 |publisher=[[Springer Science & Business Media]]}}
</ref>

<ref name=Wald2>
{{cite book |editor1=Andrés Gomberoff |editor2=Donald Marolf |author=Robert M Wald |chapter-url=https://books.google.com/books?id=ZDtxnw-b1xEC&pg=PA28 |chapter=The thermodynamics of black holes (pp. 1&ndash;38) |title=Lectures on Quantum Gravity |quote=... no results on black hole thermodynamics have been subject to any experimental or observational tests ... |year=2005 |isbn=978-0-387-23995-8 |page=28 |publisher=[[Springer Science & Business Media]]}}
</ref>

<ref name=White>
{{cite journal|author=White, M. |year=1999 |title=Anisotropies in the CMB |journal= Proceedings of the Los Angeles Meeting, DPF 99. UCLA. |url=http://www.dpf99.library.ucla.edu/session9/white0910.pdf}} See also [https://arxiv.org/abs/astro-ph/9903232v1 arXive.org].
</ref>

<ref name=Yang>
{{cite journal |author=Zu-Po Yang |s2cid= 7412160 |title= Experimental observation of an extremely dark material made by a low-density nanotube array  |journal=Nano Letters  |volume=8 |issue=2|pages= 446–451 |year=2008 |doi=10.1021/nl072369t |bibcode = 2008NanoL...8..446Y |pmid=18181658|display-authors=etal}}
</ref>

<ref name=Zee>
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 {{cite book |title=Cavity-enhanced spectroscopies |url=https://books.google.com/books?id=OuLILePVdJQC&pg=PA202 |page=202 |author1=Roger Dale Van Zee |author2=J. Patrick Looney |isbn=978-0-12-475987-9 |year=2002 |publisher=Academic Press}}
</ref>
}}

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}}
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{{refend}}