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| {{See also |Black body|Planck's law|Thermal radiation}}
| | <br><br>Create garden room walls with hedges, fences, or flower beds. If I want entirely separate the room, I could use a tall formal hedge or privacy palisade. To keep the rooms open and more connected I might choose the a different type of floor surface, flower beds, or just containers.<br><br>I remember going your thick hedges from men and women walkway towards beach, it also was like entering a huge other economy. We set up our base of operations, and finally, the moment of truth arrived. I was supremely cognizant of what I used to be about to do, nonetheless took off my swim trunks quickly yet gently. I made it look as I had done it lot of times right before.<br><br>In particular you for you to be keep a vision on pots to payments they don't dry presently there. Hanging baskets need extra special attention so dead head regularly, feed monthly and water frequently to maximise plants growth and florals.<br><br>A stone wall likewise be furthered you house landscape to provide as a seating discipline. You can enclose your outdoor grilling area with a reduced stone wall where guests can sit and mix with people. This will be a perfect location for entertaining guests or for intimate barbecue dinners for that family.<br><br>If your home has wallpaper, and it's dingy and faded, you have to remove this situation. This, however, is quick uncomplicated to engage in. The best method is to use steam for this function. It will make job go fast. If you do not have a steamer, next the is something else that can be affordably rented. Common white vinegar mixed with water a good alternative involving removing wallpaper from your walls. Saturate the walls with drinking water and white vinegar. This is easy to do with a large sponge. After just a while of soaking, you should not have any trouble eliminating the wallpaper. Wash off aged wallpaper glue and permit the wall waterless. The final step is to repaint however with a neutral, light color. This will make the room seem larger and won't clash with any furnishings a new owner perhaps have.<br><br>If anyone could have a bright room, hang new, fully mature plants in the area. This will necessary impression how the room is ideal for growing beautiful seedlings. If you have some rooms which receive little sunlight, brighten them track of a light coloured coat of wallpaper. Finally, one of proper way ways to improve the appearance of any room usually simply raise the wattage with the lightbulbs - the room will linkedin profile show better, it may look massive.<br><br>Clinton told the story of how he was at Australia at Port Douglas on September 11th plus the way his daughter Chelsea is in downtown Texas. He pertaining to every parent in the area when he talked about his feelings when he couldn't contact his daughter for three hours tomorrow.<br><br>In the event you loved this informative article and you would like to receive details concerning [http://www.hedgingplants.com/ www.hedgingplants.com] generously visit the webpage. |
| [[File:Black body.svg|thumb|303px|As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.]]
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| [[Image:PlanckianLocus.png|thumb|303px|The color ([[chromaticity]]) of black-body radiation depends on the temperature of the black body; the [[Locus (mathematics)|locus]] of such colors, shown here in [[CIE 1931 color space|CIE 1931 ''x,y'' space]], is known as the [[Planckian locus]].]]
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| '''Black-body radiation''' is the type of [[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) held at constant, uniform temperature. The radiation has a specific spectrum and intensity that depends only on the temperature of the body.<ref>{{harvnb|Loudon|2000}}, Chapter 1.</ref><ref>{{harvnb|Mandel|Wolf|1995}}, Chapter 13.</ref><ref>{{harvnb|Kondepudi|Prigogine|1998}}, Chapter 11.</ref><ref name=Landsberg>{{cite book |title=Thermodynamics and statistical mechanics |author=Peter Theodore Landsberg |chapter=Chapter 13: Bosons: black-body radiation |url=http://books.google.com/books?id=0gnWL7tmxm0C&pg=PA208 |pages=208 ''ff'' |publisher=Courier Dover Publications |year=1990 |isbn=0-486-66493-7 |edition=Reprint of Oxford University Press 1978}}</ref>
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| The thermal radiation spontaneously emitted by many ordinary objects can be approximated as blackbody 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.
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| 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. At higher temperatures, black bodies glow with increasing intensity and colors that range from dull red to blindingly brilliant blue-white as the temperature increases.
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| 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.<ref name=Morison>
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| {{cite book |title=Introduction to Astronomy and Cosmology |author=Ian Morison |url=http://books.google.com/books?id=yrV8vvJzgWkC&pg=PA48 |page=48 |isbn=0-470-03333-9 |year=2008 |publisher=J Wiley & Sons}}
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| </ref> | |
| [[Black holes]] are near-perfect black bodies, and it is believed that they emit black-body radiation (called [[Hawking radiation]]), with a temperature that depends on the mass of the black hole.<ref name=Fabbri>
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| {{cite book |title=Modeling black hole evaporation |url=http://books.google.com/books?id=gUhZZtb6yA8C&pg=PA1 |chapter=Chapter 1: Introduction |author=Alessandro Fabbri, José Navarro-Salas |isbn=1-86094-527-9 |year=2005 |publisher=Imperial College Press}}
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| </ref>
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| The term ''black body'' was introduced by [[Gustav Kirchhoff]] in 1860. When used as a [[compound adjective]], the term is typically written as hyphenated, for example, ''black-body radiation'', but sometimes also as one word, as in ''blackbody radiation''. Black-body radiation is also called ''complete radiation'' or ''temperature radiation'' or ''thermal radiation''.
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| ==Spectrum==
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| Black-body radiation has a characteristic, continuous [[spectral energy distribution|frequency spectrum]] that depends only on the body's temperature,<ref name=Kogure>
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| {{cite book |url=http://books.google.com/books?id=qt5sueHmtR4C&pg=PA41 |page=41 |chapter=§2.3: Thermodynamic equilibrium and black-body radiation |title=The astrophysics of emission-line stars |author=Tomokazu Kogure, Kam-Ching Leung |isbn=0-387-34500-0 |year=2007 |publisher=Springer}}
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| </ref> called the Planck spectrum or [[Planck's law]]. The spectrum is peaked at a characteristic frequency that shifts to higher frequencies with increasing temperature, and at [[room temperature]] most of the emission is in the [[infrared]] region of the [[electromagnetic spectrum]].<ref>Wien, W. (1893). Eine neue Beziehung der Strahlung schwarzer Körper zum zweiten Hauptsatz der Wärmetheorie, ''Sitzungberichte der Königlich-Preußischen Akademie der Wissenschaften '' (Berlin), 1893, '''1''': 55–62.</ref><ref>Lummer, O., Pringsheim, E. (1899). Die Vertheilung der Energie im Spectrum des schwarzen Körpers, ''Verhandlungen der Deutschen Physikalischen Gessellschaft'' (Leipzig), 1899, '''1''': 23–41.</ref><ref name="Planck 1914">{{harvnb|Planck|1914}}</ref> As the temperature increases past about 500 degrees [[Celsius]], black bodies start to emit significant amounts of visible light. Viewed in the dark, the first faint glow appears as a "ghostly" grey. With rising temperature, the glow becomes visible even when there is some background surrounding light: first as a dull red, then yellow, and eventually a "dazzling bluish-white" as the temperature rises.<ref>[[John William Draper|Draper, J.W.]] (1847). On the production of light by heat, ''London, Edinburgh and Dublin Philosophical Magazine and Journal of Science'', series 3, '''30''': 345–360. [http://www.archive.org/stream/londonedinburghp30lond#page/344/mode/2up]</ref><ref>{{harvnb|Partington|1949|pages = 466–467, 478}}.</ref> When the body appears white, it is emitting a substantial fraction of its energy as [[ultraviolet radiation]]. The Sun, with an [[effective temperature]] of approximately 5800 K,<ref>{{harvnb|Goody|Yung|1989|pages=482, 484}}</ref> is an approximately black body with an emission spectrum peaked in the central, yellow-green part of the [[visible spectrum]], but with significant power in the ultraviolet as well.
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| Black-body radiation provides insight into the [[thermodynamic equilibrium]] state of cavity radiation. If each [[Fourier mode]] of the equilibrium radiation in an otherwise empty cavity with perfectly reflective walls is considered as a degree of freedom capable of exchanging energy, then, according to the [[equipartition theorem]] of classical physics, there would be an equal amount of energy in each mode. Since there are an infinite number of modes this implies infinite [[heat capacity]] (infinite energy at any non-zero temperature), as well as an unphysical spectrum of emitted radiation that grows without bound with increasing frequency, a problem known as the [[ultraviolet catastrophe]]. Instead, in quantum theory the [[quantum field theory|occupation numbers]] of the modes are quantized, cutting off the spectrum at high frequency in agreement with experimental observation and resolving the catastrophe. The study of the laws of black bodies and the failure of classical physics to describe them helped establish the foundations of [[history of quantum mechanics|quantum mechanics]].
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| ==Explanation==
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| [[Image:Blackbody-colours-vertical.svg|right|38px]]
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| All normal ([[baryon]]ic) matter emits electromagnetic radiation when it has a temperature above [[absolute zero]]. The radiation represents a conversion of a body's thermal energy into electromagnetic energy, and is therefore called [[thermal radiation]]. It is a [[spontaneous process]] of radiative distribution of [[entropy]].
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| Conversely all normal matter absorbs electromagnetic radiation to some degree. An object that absorbs all radiation falling on it, at all [[wavelength]]s, is called a black body. When a black body is at a uniform temperature, its emission has a characteristic frequency distribution that depends on the temperature. Its emission is called black-body radiation.
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| The concept of the black body is an idealization, as perfect black bodies do not exist in nature.<ref name="Planck 1914 42">{{harvnb|Planck|1914|page=42}}</ref> [[Graphite]] and [[carbon black|lamp black]], with emissivities greater than 0.95, however, are good approximations to a black material. Experimentally, black-body radiation may be established best as the ultimately stable steady state equilibrium radiation in a cavity in a rigid body, at a uniform temperature, that is entirely opaque and is only partly reflective.<ref name="Planck 1914 42"/> A closed box of graphite walls at a constant temperature with a small hole on one side produces a good approximation to ideal black-body radiation emanating from the opening.<ref>{{harvnb|Wien|1894}}</ref><ref>{{harvnb|Planck|1914|page=43}}</ref>
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| Black-body radiation has the unique absolutely stable distribution of radiative intensity that can persist in thermodynamic equilibrium in a cavity.<ref name="Planck 1914 42"/> In equilibrium, for each frequency the total intensity of radiation that is emitted and reflected from a body (that is, the net amount of radiation leaving its surface, called the ''spectral radiance'') is determined solely by the equilibrium temperature, and does not depend upon the shape, material or structure of the body.<ref name=Caniou>
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| {{cite book |url=http://books.google.com/books?id=X-aFGcf6pOEC&pg=PA107 |page=107 |chapter=§4.2.2: Calculation of Planck's law |title=Passive infrared detection: theory and applications |author=Joseph Caniou |isbn=0-7923-8532-2 |year=1999 |publisher=Springer}}
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| </ref> For a black body (a perfect absorber) there is no reflected radiation, and so the spectral radiance is due entirely to emission. In addition, a black body is a diffuse emitter (its emission is independent of direction). Consequently, black-body radiation may be viewed as the radiation from a black body at thermal equilibrium.
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| Black-body radiation becomes a visible glow of light if the temperature of the object is high enough. The [[Draper point]] is the temperature at which all solids glow a dim red, about 798 K.<ref>{{cite journal
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| |journal = The Academy
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| |title = Science: Draper's Memoirs
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| |volume = XIV
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| |issue = 338
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| |publisher = London: Robert Scott Walker
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| |date = Oct 26, 1878
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| |page = 408
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| |url = http://www.archive.org/details/scientificmemoi00drapgoog}}</ref><ref>{{cite book
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| |title = Radiation heat transfer: a statistical approach
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| |author = J. R. Mahan
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| |edition = 3rd
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| |publisher = Wiley-IEEE
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| |year = 2002
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| |isbn = 978-0-471-21270-6
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| |page = 58
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| |url = http://books.google.com/?id=y9zUEzA7iN0C&pg=PA58&dq=draper-point+red
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| }}</ref> At 1000 K, a small opening in the wall of a large uniformly heated opaque-walled cavity (let us call it an oven), viewed from outside, looks red; at 6000 K, it looks white. No matter how the oven is constructed, or of what material, as long as it is built so that almost all light entering is absorbed by its walls, it will contain a good approximation to black-body radiation. The spectrum, and therefore color, of the light that comes out will be a function of the cavity temperature alone. A graph of the amount of energy inside the oven per unit volume and per unit frequency interval plotted versus frequency, is called the ''black-body curve''. Different curves are obtained by varying the temperature.
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| [[Image:Pahoehoe toe.jpg|thumb|left|250px|The temperature of a [[Lava#Pāhoehoe|Pāhoehoe]] lava flow can be estimated by observing its color. The result agrees well with measured temperatures of lava flows at about {{Convert|1000|to|1200|C|F}}.]]
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| Two bodies that are at the same temperature stay in thermal equilibrium, so a body at temperature ''T'' surrounded by a cloud of light at temperature ''T'' on average will emit as much light into the cloud as it absorbs, following Prevost's exchange principle, which refers to [[radiative equilibrium]]. The principle of [[detailed balance]] says that in thermodynamic equilibrium every elementary process works equally in its forward and backward sense.<ref>de Groot, SR., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam.</ref><ref>{{harvnb|Kondepudi|Prigogine|1998}}, Section 9.4.</ref> Prevost also showed that the emission from a body is logically determined solely by its own internal state. The causal effect of thermodynamic absorption on thermodynamic (spontaneous) emission is not direct, but is only indirect as it affects the internal state of the body. This means that at thermodynamic equilibrium the amount of every wavelength in every direction of thermal radiation emitted by a body at temperature ''T'', black or not, is equal to the corresponding amount that the body absorbs because it is surrounded by light at temperature ''T''.<ref name="Stewart 1858"/>
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| When the body is black, the absorption is obvious: the amount of light absorbed is all the light that hits the surface. For a black body much bigger than the wavelength, the light energy absorbed at any wavelength ''λ'' per unit time is strictly proportional to the black-body curve. This means that the black-body curve is the amount of light energy emitted by a black body, which justifies the name. This is the condition for the applicability of [[Kirchhoff's law of thermal radiation]]: the black-body curve is characteristic of thermal light, which depends only on the [[temperature]] of the walls of the cavity, provided that the walls of the cavity are completely opaque and are not very reflective, and that the cavity is in [[thermodynamic equilibrium]].<ref name="Huang">{{cite book |last=Huang |first=Kerson|title=Statistical Mechanics |year=1967 |publisher=John Wiley & Sons |location=New York |isbn=0-471-81518-7}}</ref> When the black body is small, so that its size is comparable to the wavelength of light, the absorption is modified, because a small object is not an efficient absorber of light of long wavelength, but the principle of strict equality of emission and absorption is always upheld in a condition of thermodynamic equilibrium.
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| In the laboratory, black-body radiation is approximated by the radiation from a small hole in a large cavity, a [[hohlraum]], in an entirely opaque body that is only partly reflective, that is maintained at a constant temperature. (This technique leads to the alternative term ''cavity radiation''.) Any light entering the hole would have to reflect off the walls of the cavity multiple times before it escaped, in which process it is nearly certain to be absorbed. Absorption occurs regardless of the [[wavelength]] of the radiation entering (as long as it is small compared to the hole). The hole, then, is a close approximation of a theoretical black body and, if the cavity is heated, the [[Power spectral density|spectrum]] of the hole's radiation (i.e., the amount of light emitted from the hole at each wavelength) will be continuous, and will depend only on the opacity and partial reflectivity of the walls, but not on the particular material of which they are built nor on the material in the cavity (compare with [[emission spectrum]]).
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| Calculating the black-body curve was a major challenge in [[theoretical physics]] during the late nineteenth century. The problem was solved in 1901 by [[Max Planck]] in the formalism now known as [[Planck's law]] of black-body radiation.<ref>{{cite journal
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| |last = Planck
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| |first = Max
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| |authorlink = Max_Planck
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| |coauthors =
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| |title =On the Law of Distribution of Energy in the Normal Spectrum
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| |journal = [[Annalen der Physik]]
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| |volume = 4
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| |page = 553
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| |year = 1901
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| |url = http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html
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| |doi=10.1002/andp.19013090310
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| |bibcode=1901AnP...309..553P
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| }} {{dead link|date=November 2009}}</ref>
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| By making changes to [[Wien's radiation law]] (not to be confused with [[Wien's displacement law]]) consistent with [[thermodynamics]] and [[electromagnetism]], he found a mathematical expression fitting the experimental data satisfactorily. Planck had to assume that the energy of the oscillators in the cavity was quantized, i.e., it existed in integer multiples of some quantity. [[Albert Einstein|Einstein]] built on this idea and proposed the quantization of electromagnetic radiation itself in 1905 to explain the [[photoelectric effect]]. These theoretical advances eventually resulted in the superseding of classical electromagnetism by [[quantum electrodynamics]]. These quanta were called [[photon]]s and the black-body cavity was thought of as containing a [[photon gas|gas of photons]]. In addition, it led to the development of quantum probability distributions, called [[Fermi–Dirac statistics]] and [[Bose–Einstein statistics]], each applicable to a different class of particles, [[fermion]]s and [[boson]]s.
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| The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the [[Stefan–Boltzmann law]]. So, as temperature increases, the glow color changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue. It will never become invisible—indeed, the radiation of visible light increases [[monotonic function|monotonically]] with temperature.<ref name="Landau">{{cite book |last=Landau |first=L. D.|coauthors=E. M. Lifshitz|title=Statistical Physics |edition=3rd Edition Part 1 |year=1996|publisher=Butterworth–Heinemann |location=Oxford |isbn=0-521-65314-2}}</ref>
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| The [[radiance]] or observed intensity is not a function of direction. Therefore a black body is a perfect [[Lambert's cosine law|Lambertian]] radiator.
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| Real objects never behave as full-ideal black bodies, and instead the emitted radiation at a given frequency is a fraction of what the ideal emission would be. The [[emissivity]] of a material specifies how well a real body radiates energy as compared with a black body. This emissivity depends on factors such as temperature, emission angle, and wavelength. However, it is typical in engineering to assume that a surface's spectral emissivity and absorptivity do not depend on wavelength, so that the emissivity is a constant. This is known as the ''gray body'' assumption.
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| [[File:Ilc 9yr moll4096.png|thumb|300px|9-year [[WMAP]] image (2012) of the [[cosmic microwave background radiation]] across the universe.<ref name="Space-20121221">{{cite web |last=Gannon |first=Megan |title=New 'Baby Picture' of Universe Unveiled |url=http://www.space.com/19027-universe-baby-picture-wmap.html|date=December 21, 2012 |publisher=[[Space.com]] |accessdate=December 21, 2012 }}</ref><ref name="arXiv-20121220">{{cite journal |last=Bennett |first=C.L. |last2=Larson |first2=L.|last3=Weiland |first3=J.L. |last4=Jarosk |first4= N. |last5=Hinshaw |first5=N. |last6=Odegard|first6=N. |last7=Smith |first7=K.M. |last8=Hill |first8=R.S. |last9=Gold |first9=B.|last10=Halpern |first10=M. |last11=Komatsu |first11=E. |last12=Nolta |first12=M.R.|last13=Page |first13=L. |last114=Spergel |first14=D.N. |last15=Wollack |first15=E.|last16=Dunkley |first16=J. |last17=Kogut |first17=A. |last18=Limon |first18=M. |last19=Meyer|first19=S.S. |last20=Tucker |first20=G.S. |last21=Wright |first21=E.L. |title=Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results|url=http://arxiv.org/abs/1212.5225 |arxiv=1212.5225 |date=December 20, 2012|accessdate=December 22, 2012 |bibcode = 2012arXiv1212.5225B }}</ref>]]
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| With non-black surfaces, the deviations from ideal black-body behavior are determined by both the surface structure, such as roughness or granularity, and the chemical composition. On a "per wavelength" basis, real objects in states of [[Thermodynamic equilibrium#Local and global equilibrium|local thermodynamic equilibrium]] still follow [[Kirchhoff's law (thermodynamics)|Kirchhoff's Law]]: emissivity equals absorptivity, so that an object that does not absorb all incident light will also emit less radiation than an ideal black body; the incomplete absorption can be due to some of the incident light being transmitted through the body or to some of it being reflected at the surface of the body.
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| In [[astronomy]], objects such as [[star]]s are frequently regarded as black bodies, though this is often a poor approximation. An almost perfect black-body spectrum is exhibited by the [[cosmic microwave background radiation]]. [[Hawking radiation]] is the hypothetical black-body radiation emitted by [[black hole]]s, at a temperature that depends on the mass, charge, and spin of the hole. If this prediction is correct, black holes will very gradually shrink and evaporate over time as they lose mass by the emission of photons and other particles.
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| A black body radiates energy at all frequencies, but its intensity rapidly tends to zero at high frequencies (short wavelengths). For example, a black body at room temperature (300 K) with one square meter of surface area will emit a photon in the visible range (390–750 nm) at an average rate of one photon every 41 seconds, meaning that for most practical purposes, such a black body does not emit in the visible range.<ref>Mathematica:Planck intensity (energy/sec/area/solid angle/wavelength) is:
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| : <math> i_{w,t} = \frac{2hc^2}{w^5 (\exp(hc/wkt) - 1)} </math>
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| i[w_, t_] = 2*h*c^2/(w^5*(Exp[h*c/(w*k*t)] - 1))<br>
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| The number of photons/sec/area is:
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| NIntegrate[2*Pi*i[w, 300]/(h*c/w), {w, 390*10^(-9), 750*10^(-9)}] = 0.0244173...</ref>
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| ==Equations==
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| ===Planck's law of black-body radiation===
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| {{Main|Planck's law}}
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| Planck's law states that<ref name="Rybicki 1979 22">{{harvnb|Rybicki|Lightman|1979|p=22}}</ref>
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| :<math>I(\nu,T) =\frac{ 2 h\nu^{3}}{c^2}\frac{1}{ e^{\frac{h\nu}{kT}}-1}</math>
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| where
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| :''I''(''ν'',''T'') is the [[energy]] per unit [[time]] (or the [[power (physics)|power]]) radiated per unit area of emitting surface in the [[Normal (geometry)|normal]] direction per unit [[solid angle]] per unit [[frequency]] by a black body at temperature ''T'', also known as spectral radiance;
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| :''h'' is the [[Planck constant]];
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| :''c'' is the [[speed of light]] in a vacuum;
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| :''k'' is the [[Boltzmann constant]];
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| :''ν'' is the [[frequency]] of the electromagnetic radiation; and
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| :''T'' is the absolute [[temperature]] of the body.
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| ===Wien's displacement law===
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| [[Wien's displacement law]] shows how the spectrum of black-body radiation at any temperature is related to the spectrum at any other temperature. If we know the shape of the spectrum at one temperature, we can calculate the shape at any other temperature. Spectral intensity can be expressed as a function of wavelength or of frequency.
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| A consequence of Wien's displacement law is that the wavelength at which the intensity ''per unit wavelength'' of the radiation produced by a black body is at a maximum, <math>\lambda_\max</math>, is a function only of the temperature
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| :<math>\lambda_\max = \frac{b}{T}</math>
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| where the constant, ''b'', known as Wien's displacement constant, is equal to {{val|fmt=commas|2.8977721|(26)|e=-3|u=K m}}.<ref>http://physics.nist.gov/cgi-bin/cuu/Value?bwien</ref>
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| Planck's Law was also stated above as a function of frequency. The intensity maximum for this is given by
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| :<math>\nu_\max = T \times 58.8\ \mathrm{GHz}\ \mathrm{K}^{-1}</math>.<ref>
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| {{cite web
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| | last = Nave
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| | first = Dr. Rod
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| | authorlink =
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| | coauthors =
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| | title = Wien's Displacement Law and Other Ways to Characterize the Peak of Blackbody Radiation
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| | work = HyperPhysics
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| | publisher =
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| | date =
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| | url = http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/wien3.html#c1
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| | doi =
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| | accessdate = }}
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| Provides 5 variations of Wien's Displacement Law
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| </ref>
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| ===Stefan–Boltzmann law===
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| The [[Stefan–Boltzmann law]] states that the power emitted per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature:
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| :<math>j^{\star} = \sigma T^4,</math>
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| where ''j''*is the total power radiated per unit area, ''T'' is the [[absolute temperature]] and {{nowrap|''σ'' {{=}} {{val|5.67|e=-8|u=W m<sup>−2</sup> K<sup>−4</sup>}}}} is the [[Stefan–Boltzmann constant]].
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| ==Human body emission==
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| {| class="bordered infobox" style="width:22em"
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| | style="text-align:left;"|[[Image:Human-Visible.jpg|229px]]
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| |-
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| | style="text-align:left;"|[[Image:Human-Infrared.jpg|284px]]
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| |-
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| |Much of a person's energy is radiated away in the form of [[infrared]] light. Some materials are transparent in the infrared, but opaque to visible light, as is the plastic bag in this infrared image (bottom). Other materials are transparent to visible light, but opaque or reflective in the infrared, noticeable by darkness of the man's glasses.
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| |}
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| As all matter, the human body radiates some of a person's energy away as [[infrared]] light.
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| The net power radiated is the difference between the power emitted and the power absorbed:
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| :<math>P_\mathrm{net}=P_\mathrm{emit}-P_\mathrm{absorb}. \, </math>
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| Applying the Stefan–Boltzmann law,
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| :<math>P_{\rm net}=A\sigma \varepsilon \left( T^4 - T_0^4 \right).</math>
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| The total surface area of an adult is about 2 m<sup>2</sup>, and the mid- and far-infrared [[emissivity]] of skin and most clothing is near unity, as it is for most nonmetallic surfaces.<ref>{{cite web
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| | author=Infrared Services
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| | title=Emissivity Values for Common Materials
| |
| | url=http://infrared-thermography.com/material-1.htm
| |
| | accessdate=2007-06-24}}</ref><ref>{{cite web
| |
| | author=Omega Engineering
| |
| | title=Emissivity of Common Materials
| |
| | url=http://www.omega.com/literature/transactions/volume1/emissivityb.html
| |
| | accessdate=2007-06-24}}</ref> Skin temperature is about 33 °C,<ref>{{cite web
| |
| | last= Farzana|first= Abanty
| |
| | title=Temperature of a Healthy Human (Skin Temperature)|year=2001|work=The Physics Factbook
| |
| | url=http://hypertextbook.com/facts/2001/AbantyFarzana.shtml
| |
| | accessdate=2007-06-24}}</ref> but clothing reduces the surface temperature to about 28 °C when the ambient temperature is 20 °C.<ref>{{cite web
| |
| | author=Lee, B.
| |
| | title=Theoretical Prediction and Measurement of the Fabric Surface Apparent Temperature in a Simulated Man/Fabric/Environment System
| |
| | url=http://www.dsto.defence.gov.au/publications/2135/DSTO-TR-0849.pdf
| |
| | accessdate=2007-06-24}}</ref> Hence, the net radiative heat loss is about
| |
| :<math>P_{\rm net} = 100 \ \mathrm{W}.</math>
| |
| The total energy radiated in one day is about 9 MJ ([[megajoule]]s), or 2000 kcal (food [[calorie]]s). [[Basal metabolic rate]] for a 40-year-old male is about 35 kcal/(m<sup>2</sup>·h),<ref name="Harris1918">{{cite journal|author = Harris J, Benedict F|title = A Biometric Study of Human Basal Metabolism.|journal = Proc Natl Acad Sci USA| volume = 4|issue = 12| pages = 370–3|year = 1918|pmid = 16576330|doi = 10.1073/pnas.4.12.370|pmc = 1091498
| |
| |bibcode = 1918PNAS....4..370H }}</ref> which is equivalent to 1700 kcal per day assuming the same 2 m<sup>2</sup> area. However, the mean metabolic rate of sedentary adults is about 50% to 70% greater than their basal rate.<ref>{{cite journal|author=Levine, J|title=Nonexercise activity thermogenesis (NEAT): environment and biology|journal=Am J Physiol Endocrinol Metab|volume=286|year=2004|pages=E675–E685|url=http://ajpendo.physiology.org/cgi/content/full/286/5/E675|doi=10.1152/ajpendo.00562.2003|pmid=15102614|issue=5}}</ref>
| |
| | |
| There are other important thermal loss mechanisms, including [[convection]] and [[evaporation]]. Conduction is negligible – the [[Nusselt number]] is much greater than unity. Evaporation via [[perspiration]] is only required if radiation and convection are insufficient to maintain a steady state temperature (but evaporation from the lungs occurs regardless).{{citation needed|date=July 2012}} Free convection rates are comparable, albeit somewhat lower, than radiative rates.<ref>{{cite web
| |
| | author=DrPhysics.com
| |
| | title=Heat Transfer and the Human Body
| |
| | url=http://www.drphysics.com/convection/convection.html
| |
| | accessdate=2007-06-24}}</ref> Thus, radiation accounts for about two-thirds of thermal energy loss in cool, still air. Given the approximate nature of many of the assumptions, this can only be taken as a crude estimate. Ambient air motion, causing forced convection, or evaporation reduces the relative importance of radiation as a thermal loss mechanism.
| |
| | |
| Application of [[Wien's displacement law|Wien's Law]] to human body emission results in a peak wavelength of
| |
| :<math>\lambda_{\rm peak} = \frac{2.898\times 10^-3 \ \mathrm{K} \cdot \mathrm{nm}}{305 \ \mathrm{K}} = 9.50 \ \mu\mathrm{m}.</math>
| |
| For this reason, thermal imaging devices for human subjects are most sensitive in the 7–14 micron range.
| |
| | |
| ==Temperature relation between a planet and its star==
| |
| | |
| The black-body law may be used to estimate the temperature of a planet orbiting the Sun.
| |
| | |
| [[Image:Erbe.gif|thumb|300px|Earth's longwave thermal [[Earth's energy budget#Outgoing energy|radiation]] intensity, from clouds, atmosphere and ground]]
| |
| The temperature of a planet depends on several factors:
| |
| *Incident radiation from its star
| |
| *Emitted radiation of the planet, e.g., [[Earth's energy budget#Outgoing energy|Earth's infrared glow]]
| |
| *The [[albedo]] effect causing a fraction of light to be reflected by the planet
| |
| *The [[greenhouse effect]] for planets with an atmosphere
| |
| *Energy generated internally by a planet itself due to [[radioactive decay]], [[tidal heating]], and [[Kelvin–Helmholtz mechanism|adiabatic contraction due by cooling]].
| |
| | |
| The analysis only considers the Sun's heat for a planet in a Solar System.
| |
| | |
| The [[Stefan–Boltzmann law]] gives the total [[power (physics)|power]] (energy/second) the Sun is emitting:
| |
| | |
| [[Image:Sun-Earth-Radiation.png|frame|The Earth only has an absorbing area equal to a two dimensional disk, rather than the surface of a sphere.]]
| |
| :<math>P_{\rm S\ emt} = 4 \pi R_{\rm S}^2 \sigma T_{\rm S}^4 \qquad \qquad (1)</math>
| |
| where
| |
| :<math>\sigma \,</math> is the [[Stefan–Boltzmann law|Stefan–Boltzmann constant]],
| |
| :<math>T_{\rm S} \,</math> is the effective temperature of the Sun, and
| |
| :<math>R_{\rm S} \,</math> is the radius of the Sun.
| |
| | |
| The Sun emits that power equally in all directions. Because of this, the planet is hit with only a tiny fraction of it. The power from the Sun that strikes the planet (at the top of the atmosphere) is:
| |
| | |
| :<math>P_{\rm SE} = P_{\rm S\ emt} \left( \frac{\pi R_{\rm E}^2}{4 \pi D^2} \right) \qquad \qquad (2)</math>
| |
| where
| |
| :<math>R_{\rm E} \,</math> is the radius of the planet and
| |
| :<math>D \,</math> is the [[astronomical unit]], the distance between the [[Sun]] and the planet.
| |
| | |
| Because of its high temperature, the Sun emits to a large extent in the ultraviolet and visible (UV-Vis) frequency range. In this frequency range, the planet reflects a fraction <math>\alpha</math> of this energy where <math>\alpha</math> is the [[albedo]] or reflectance of the planet in the UV-Vis range. In other words, the planet absorbs a fraction <math>1-\alpha</math> of the Sun's light, and reflects the rest. The power absorbed by the planet and its atmosphere is then:
| |
| | |
| :<math>P_{\rm abs} = (1-\alpha)\,P_{\rm SE} \qquad \qquad (3)</math>
| |
| | |
| Even though the planet only absorbs as a circular area <math>\pi R^2</math>, it emits equally in all directions as a sphere. If the planet were a perfect black body, it would emit according to the [[Stefan–Boltzmann law]]
| |
| | |
| :<math>P_{\rm emt\,bb} = 4 \pi R_{\rm E}^2 \sigma T_{\rm E}^4 \qquad \qquad (4)</math>
| |
| | |
| where <math>T_{\rm E} </math> is the temperature of the planet. This temperature, calculated for the case of the planet acting as a black body by setting <math>P_{\rm abs} = P_{\rm emt\,bb}</math>, is known as the [[effective temperature]]. The actual temperature of the planet will likely be different, depending on its surface and atmospheric properties. Ignoring the atmosphere and greenhouse effect, the planet, since it is at a much lower temperature than the Sun, emits mostly in the infrared (IR) portion of the spectrum. In this frequency range, it emits <math>\overline{\epsilon}</math> of the radiation that a black body would emit where <math>\overline{\epsilon}</math> is the average emissivity in the IR range. The power emitted by the planet is then:
| |
| | |
| :<math>P_{\rm emt} = \overline{\epsilon}\,P_{\rm emt\,bb} \qquad \qquad (5)</math>
| |
| | |
| For a body in [[Radiative equilibrium#Definitions of radiative equilbrium#radiative exchange equilibrium|radiative exchange equilibrium]] with its surroundings, the rate at which it emits radiant energy is equal to the rate at which it absorbs it:<ref name="Prevost 1791">Prevost, P. (1791). Mémoire sur l'equilibre du feu. ''Journal de Physique'' (Paris), vol 38 pp. 314-322.</ref><ref>Iribarne, J.V., Godson, W.L. (1981). ''Atmospheric Thermodynamics'', second edition, D. Reidel Publishing, Dordrecht, ISBN 90-277-1296-4, page 227.</ref>
| |
| | |
| :<math>P_{\rm abs}=P_{\rm emt} \qquad \qquad (6)</math>
| |
| | |
| Substituting the expressions for solar and planet power in equations 1–6 and simplifying yields the estimated temperature of the planet, ignoring greenhouse effect, ''T''<sub>P</sub>:
| |
| | |
| :<math>T_P = T_S\sqrt{\frac{R_S\sqrt{\frac{1-\alpha}{\overline{\varepsilon}}}}{2D}}</math>
| |
| | |
| In other words, given the assumptions made, the temperature of a planet depends only on the surface temperature of the Sun, the radius of the Sun, the distance between the planet and the Sun, the albedo and the IR emissivity of the planet.
| |
| | |
| ===Temperature of Earth===
| |
| | |
| Substituting the measured values for the Sun and Earth yields:
| |
| :<math>T_{\rm S} = 5778 \ \mathrm{K},</math><ref name="NASA">[http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html NASA Sun Fact Sheet]</ref>
| |
| :<math>R_{\rm S} = 6.96 \times 10^8 \ \mathrm{m},</math><ref name="NASA"/>
| |
| :<math>D = 1.496 \times 10^{11} \ \mathrm{m},</math><ref name="NASA"/>
| |
| :<math>\alpha = 0.306 \ </math><ref name="Cole">{{cite book|author=Cole, George H. A.; Woolfson, Michael M.
| |
| |title=Planetary Science: The Science of Planets Around Stars (1st ed.)
| |
| |publisher=Institute of Physics Publishing|year=2002|isbn=0-7503-0815-X|pages = 36–37, 380–382|url = http://books.google.com/?id=Bgsy66mJ5mYC&pg=RA3-PA382&dq=black-body+emissivity+greenhouse+intitle:Planetary-Science+inauthor:cole}}</ref>
| |
| | |
| With the average emissivity set to unity, the [[effective temperature]] of the Earth is:
| |
| :<math>T_{\rm E} = 254.356\ \mathrm{K}</math>
| |
| | |
| or −18.8 °C.
| |
| | |
| This is the temperature of the Earth if it radiated as a perfect black body in the infrared, ignoring greenhouse effects (which can raise the surface temperature of a body above what it would be if it were a perfect black body in all spectrums<ref>''Principles of Planetary Climate'' by Raymond T. Peirrehumbert, Cambridge University Press (2011), p. 146. From Chapter 3 which is available online [http://www-das.uwyo.edu/~deshler/Atsc4400_5400_Climate/PierreHumbert_Climate_Ch3.pdf here], p. 12 mentions that Venus' black-body temperature would be 330 K "in the zero albedo case", but that due to atmospheric warming, its actual surface temperature is 740 K.</ref>), and assuming an unchanging albedo. The Earth in fact radiates not quite as a perfect black body in the infrared which will raise the estimated temperature a few degrees above the effective temperature. If we wish to estimate what the temperature of the Earth would be if it had no atmosphere, then we could take the albedo and emissivity of the Moon as a good estimate. The albedo and emissivity of the Moon are about 0.1054<ref name="Saari">{{cite journal |last1=Saari |first1=J. M. |last2=Shorthill |first2= R. W.|year=1972 |title=The Sunlit Lunar Surface. I. Albedo Studies and Full Moon |journal=The Moon |volume=5 |issue=1-2 |pages=161–178 |bibcode=1972Moon....5..161S |doi=10.1007/BF00562111 }}</ref> and 0.95<ref>Lunar and Planetary Science XXXVII (2006) 2406</ref> respectively, yielding an estimated temperature of about 1.36 °C.
| |
| | |
| Estimates of the Earth's average albedo vary in the range 0.3–0.4, resulting in different estimated effective temperatures. Estimates are often based on the [[solar constant]] (total insolation power density) rather than the temperature, size, and distance of the Sun. For example, using 0.4 for albedo, and an insolation of 1400 W m<sup>−2</sup>, one obtains an effective temperature of about 245 K.<ref>{{cite book
| |
| |title = Space physics and space astronomy
| |
| |author = Michael D. Papagiannis
| |
| |publisher = Taylor & Francis
| |
| |year = 1972
| |
| |isbn = 978-0-677-04000-4
| |
| |pages = 10–11
| |
| |url = http://books.google.com/?id=SpgOAAAAQAAJ&pg=PA10}}</ref>
| |
| Similarly using albedo 0.3 and solar constant of 1372 W m<sup>−2</sup>, one obtains an effective temperature of 255 K.<ref>{{cite book
| |
| |title = Climate Change an Integrated Perspective
| |
| |author = Willem Jozef Meine Martens and Jan Rotmans
| |
| |publisher = Springer
| |
| |year = 1999
| |
| |isbn = 978-0-7923-5996-8
| |
| |pages = 52–55
| |
| |url = http://books.google.com/?id=o1SELkgK6PcC&pg=RA1-PA53&dq=Earth+effective-temperature+albedo+black-body+0.3
| |
| }}</ref><ref>{{cite book
| |
| |title = Astrobiology: Future Perspectives
| |
| |chapter = The Prebiotic Atmosphere of the Earth
| |
| |author = F. Selsis
| |
| |editor = Pascale Ehrenfreund et al.
| |
| |publisher = Springer
| |
| |year = 2004
| |
| |isbn = 978-1-4020-2587-7
| |
| |pages = 279–280
| |
| |url = http://books.google.com/?id=bA_uR3iwzQUC&pg=PA279&dq=Earth+effective-temperature+albedo+black-body+0.3
| |
| }}</ref><ref>Wallace, J.M., Hobbs, P.V. (2006). ''Atmospheric Science. An Introductory Survey'', second edition, Elsevier, Amsterdam, ISBN 978-0-12-732951-2, exercise 4.6, pages 119-120.</ref>
| |
| | |
| ==Cosmology==
| |
| | |
| The [[cosmic microwave background]] radiation observed today is the most perfect black-body radiation ever observed in nature, with a temperature of about 2.7K.<ref name=White>White, M. (1999). "Anisotropies in the CMB". Proceedings of the Los Angeles Meeting, DPF 99. UCLA. http://arxiv.org/pdf/1106.2188v2.pdf.</ref> It is a "snapshot" of the radiation at the time of [[Decoupling (cosmology)|decoupling]] between matter and radiation in the early universe. Prior to this time, most matter in the universe was in the form of an ionized plasma in thermal equilibrium with radiation.
| |
| | |
| According to Kondepudi and Prigogine, at very high temperatures (above 10<SUP>10</sup>K; such temperatures existed in the very early universe), where the thermal motion separates protons and neutrons in spite of the strong nuclear forces, electron-positron pairs appear and disappear spontanteously and are in thermal equilibrium with electromagnetic radiation. These particles form a part of the black body spectrum, in addition to the electromagnetic radiation.<ref>{{harvnb|Kondepudi|Prigogine|1998|pages = 227–228}}; also Section 11.6, pages 294–296.</ref>
| |
| | |
| ==Doppler effect for a moving black body==
| |
| | |
| The [[relativistic Doppler effect]] causes a shift in the frequency ''f'' of light originating from a source that is moving in relation to the observer, so that the wave is observed to have frequency ''f''':
| |
| :<math>f' = f \frac{1 - \frac{v}{c} \cos \theta}{\sqrt{1-v^2/c^2}}, </math>
| |
| where ''v'' is the velocity of the source in the observer's rest frame, ''θ'' is the angle between the velocity vector and the observer-source direction measured in the reference frame of the source, and ''c'' is the [[speed of light]].<ref>The Doppler Effect, T. P. Gill, Logos Press, 1965</ref> This can be simplified for the special cases of objects moving directly towards (''θ'' = π) or away (''θ'' = 0) from the observer, and for speeds much less than ''c''.
| |
| | |
| Through Planck's law the temperature spectrum of a black body is proportionally related to the frequency of light and one may substitute the temperature (''T'') for the frequency in this equation.
| |
| | |
| For the case of a source moving directly towards or away from the observer, this reduces to
| |
| :<math>T' = T \sqrt{\frac{c-v}{c+v}}.</math>
| |
| Here ''v'' > 0 indicates a receding source, and ''v'' < 0 indicates an approaching source.
| |
| | |
| This is an important effect in astronomy, where the velocities of stars and galaxies can reach significant fractions of ''c''. An example is found in the [[cosmic microwave background radiation]], which exhibits a dipole anisotropy from the Earth's motion relative to this black-body radiation field.
| |
| | |
| ==History==
| |
| | |
| ===Balfour Stewart===
| |
| | |
| In 1858, Balfour Stewart described his experiments on the thermal radiative emissive and absorptive powers of polished plates of various substances, compared with the powers of lamp-black surfaces, at the same temperature.<ref name="Stewart 1858">{{harvnb|Stewart|1858}}</ref> Stewart chose lamp-black surfaces as his reference because of various previous experimental findings, especially those of [[Pierre Prevost]] and of [[John Leslie (physicist)|John Leslie]]. He wrote "Lamp-black, which absorbs all the rays that fall upon it, and therefore possesses the greatest possible absorbing power, will possess also the greatest possible radiating power." More an experimenter than a logician, Stewart failed to point out that his statement presupposed an abstract general principle, that there exist either ideally in theory or really in nature bodies or surfaces that respectively have one and the same unique universal greatest possible absorbing power, likewise for radiating power, for every wavelength and equilibrium temperature.
| |
| | |
| Stewart measured radiated power with a thermo-pile and sensitive galvanometer read with a microscope. He was concerned with selective thermal radiation, which he investigated with plates of substances that radiated and absorbed selectively for different qualities of radiation rather than maximally for all qualities of radiation. He discussed the experiments in terms of rays which could be reflected and refracted, and which obeyed the Stokes-[[Helmholtz reciprocity]] principle (though he did not use an eponym for it). He did not in this paper mention that the qualities of the rays might be described by their wavelengths, nor did he use spectrally resolving apparatus such as prisms or diffraction gratings. His work was quantitative within these constraints. He made his measurements in a room temperature environment, and quickly so as to catch his bodies in a condition near the thermal equilibrium in which they had been prepared by heating to equilibrium with boiling water. His measurements confirmed that substances that emit and absorb selectively respect the principle of selective equality of emission and absorption at thermal equilibrium.
| |
| | |
| Stewart offered a theoretical proof that this should be the case separately for every selected quality of thermal radiation, but his mathematics was not rigorously valid.<ref name="Siegel">{{harvnb|Siegel|1976}}</ref> He made no mention of thermodynamics in this paper, though he did refer to conservation of ''[[vis viva]]''. He proposed that his measurements implied that radiation was both absorbed and emitted by particles of matter throughout depths of the media in which it propagated. He applied the Helmholtz reciprocity principle to account for the material interface processes as distinct from the processes in the interior material. He did not postulate unrealizable perfectly black surfaces. He concluded that his experiments showed that in a cavity in thermal equilibrium, the heat radiated from any part of the interior bounding surface, no matter of what material it might be composed, was the same as would have been emitted from a surface of the same shape and position that would have been composed of lamp-black. He did not state explicitly that the lamp-black-coated bodies that he used as reference must have had a unique common spectral emittance function that depended on temperature in a unique way.
| |
| | |
| ===Gustav Kirchhoff===
| |
| | |
| In 1859, not knowing of Stewart's work, [[Gustav Kirchhoff|Gustav Robert Kirchhoff]] reported the coincidence of the wavelengths of spectrally resolved lines of absorption and of emission of visible light. Importantly for thermal physics, he also observed that bright lines or dark lines were apparent depending on the temperature difference between emitter and absorber.<ref>{{harvnb|Kirchhoff|1860a}}</ref>
| |
| | |
| Kirchhoff then went on to consider bodies that emit and absorb heat radiation, in an opaque enclosure or cavity, in equilibrium at temperature {{math|''T''}}.
| |
| | |
| Here is used a notation different from Kirchhoff's. Here, the emitting power {{math|''E''(''T'', ''i'')}} denotes a dimensioned quantity, the total radiation emitted by a body labeled by index {{math|''i''}} at temperature {{math|''T''}}. The total absorption ratio {{math|''a''(''T'', ''i'')}} of that body is dimensionless, the ratio of absorbed to incident radiation in the cavity at temperature {{math|''T''}} . (In contrast with Balfour Stewart's, Kirchhoff's definition of his absorption ratio did not refer in particular to a lamp-black surface as the source of the incident radiation.) Thus the ratio {{math|''E''(''T'', ''i'') / ''a''(''T'', ''i'')}} of emitting power to absorption ratio is a dimensioned quantity, with the dimensions of emitting power, because {{math|''a''(''T'', ''i'')}} is dimensionless. Also here the wavelength-specific emitting power of the body at temperature {{math|''T''}} is denoted by {{math|''E''(''λ'', ''T'', ''i'')}} and the wavelength-specific absorption ratio by {{math|''a''(''λ'', ''T'', ''i'')}} . Again, the ratio {{math|''E''(''λ'', ''T'', ''i'') / ''a''(''λ'', ''T'', ''i'')}} of emitting power to absorption ratio is a dimensioned quantity, with the dimensions of emitting power.
| |
| | |
| In a second report made in 1859, Kirchhoff announced a new general principle or law for which he offered a theoretical and mathematical proof, though he did not offer quantitative measurements of radiation powers.<ref>{{harvnb|Kirchhoff|1860b}}</ref> His theoretical proof was and still is considered by some writers to be invalid.<ref name="Siegel"/><ref name="Schirrmacher 2001">{{harvnb|Schirrmacher|2001}}</ref> His principle, however, has endured: it was that for heat rays of the same wavelength, in equilibrium at a given temperature, the wavelength-specific ratio of emitting power to absorption ratio has one and the same common value for all bodies that emit and absorb at that wavelength. In symbols, the law stated that the wavelength-specific ratio {{math|''E''(''λ'', ''T'', ''i'') / ''a''(''λ'', ''T'', ''i'')}} has one and the same value for all bodies, that is for all values of index {{math|''i''}} . In this report there was no mention of black bodies.
| |
| | |
| In 1860, still not knowing of Stewart's measurements for selected qualities of radiation, Kirchhoff pointed out that it was long established experimentally that for total heat radiation, of unselected quality, emitted and absorbed by a body in equilibrium, the dimensioned total radiation ratio {{math|''E''(''T'', ''i'') / ''a''(''T'', ''i'')}}, has one and the same value common to all bodies, that is, for every value of the material index {{math|''i''}}.<ref name="Kirchhoff 1860c">{{harvnb|Kirchhoff|1860c}}</ref> Again without measurements of radiative powers or other new experimental data, Kirchhoff then offered a fresh theoretical proof of his new principle of the universality of the value of the wavelength-specific ratio {{math|''E''(''λ'', ''T'', ''i'') / ''a''(''λ'', ''T'', ''i'')}} at thermal equilibrium. His fresh theoretical proof was and still is considered by some writers to be invalid.<ref name="Siegel"/><ref name="Schirrmacher 2001"/>
| |
| | |
| But more importantly, it relied on a new theoretical postulate of "perfectly black bodies," which is the reason why one speaks of Kirchhoff's law. Such black bodies showed complete absorption in their infinitely thin most superficial surface. They correspond to Balfour Stewart's reference bodies, with internal radiation, coated with lamp-black. They were not the more realistic perfectly black bodies later considered by Planck. Planck's black bodies radiated and absorbed only by the material in their interiors; their interfaces with contiguous media were only mathematical surfaces, capable neither of absorption nor emission, but only of reflecting and transmitting with refraction.<ref>{{harvnb|Planck|1914|page=11}}</ref>
| |
| | |
| Kirchhoff's proof considered an arbitrary non-ideal body labeled {{math|''i''}} as well as various perfect black bodies labeled {{math|BB}} . It required that the bodies be kept in a cavity in thermal equilibrium at temperature {{math|''T''}} . His proof intended to show that the ratio {{math|''E''(''λ'', ''T'', ''i'') / ''a''(''λ'', ''T'', ''i'')}} was independent of the nature {{math|''i''}} of the non-ideal body, however partly transparent or partly reflective it was.
| |
| | |
| His proof first argued that for wavelength {{math|''λ''}} and at temperature {{math|''T''}}, at thermal equilibrium, all perfectly black bodies of the same size and shape have the one and the same common value of emissive power {{math|''E''(''λ'', ''T'', BB)}}, with the dimensions of power. His proof noted that the dimensionless wavelength-specific absorption ratio {{math|''a''(''λ'', ''T'', BB)}} of a perfectly black body is by definition exactly 1. Then for a perfectly black body, the wavelength-specific ratio of emissive power to absorption ratio {{math|''E''(''λ'', ''T'', BB) / ''a''(''λ'', ''T'', BB)}} is again just {{math|''E''(''λ'', ''T'', BB)}}, with the dimensions of power. Kirchhoff considered, successively, thermal equilibrium with the arbitrary non-ideal body, and with a perfectly black body of the same size and shape, in place in his cavity in equilibrium at temperature {{math|''T''}} . He argued that the flows of heat radiation must be the same in each case. Thus he argued that at thermal equilibrium the ratio {{math|''E''(''λ'', ''T'', ''i'') / ''a''(''λ'', ''T'', ''i'')}} was equal to {{math|''E''(''λ'', ''T'', BB)}}, which may now be denoted {{math|''B''<sub>''λ''</sub> (''λ'', ''T'')}}, a continuous function, dependent only on {{math|''λ''}} at fixed temperature {{math|''T''}}, and an increasing function of {{math|''T''}} at fixed wavelength {{math|''λ''}}, at low temperatures vanishing for visible but not for longer wavelengths, with positive values for visible wavelengths at higher temperatures, which does not depend on the nature {{math|''i''}} of the arbitrary non-ideal body. (Geometrical factors, taken into detailed account by Kirchhoff, have been ignored in the foregoing.)
| |
| | |
| Thus [[Kirchhoff's law of thermal radiation]] can be stated: ''For any material at all, radiating and absorbing in thermodynamic equilibrium at any given temperature {{math|T}}, for every wavelength {{math|λ}}, the ratio of emissive power to absorptive ratio has one universal value, which is characteristic of a perfect black body, and is an emissive power which we here represent by {{math|B<sub>λ</sub> (λ, T)}} .'' (For our notation {{math|''B''<sub>''λ''</sub> (''λ'', ''T'')}}, Kirchhoff's original notation was simply {{math|''e''}}.)<ref name="Kirchhoff 1860c"/><ref>{{harvnb|Chandrasekhar|1950|p=8}}</ref><ref>{{harvnb|Milne|1930|page=80}}</ref><ref>{{harvnb|Rybicki|Lightman|1979|pages=16–17}}</ref><ref>{{harvnb|Mihalas|Weibel-Mihalas|1984|page=328}}</ref><ref>{{harvnb|Goody|Yung|1989|pages=27–28}}</ref>
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| Kirchhoff announced that the determination of the function {{math|''B''<sub>''λ''</sub> (''λ'', ''T'')}} was a problem of the highest importance, though he recognized that there would be experimental difficulties to be overcome. He supposed that like other functions that do not depend on the properties of individual bodies, it would be a simple function. Occasionally by historians that function {{math|''B''<sub>''λ''</sub> (''λ'', ''T'')}} has been called "Kirchhoff's (emission, universal) function,"<ref>[[Friedrich Paschen|Paschen, F.]] (1896), personal letter cited by {{harvnb|Hermann|1971|page=6}}</ref><ref>{{harvnb|Hermann|1971|page=7}}</ref><ref>{{harvnb|Kuhn|1978|pages=8, 29}}</ref><ref>{{harvnb|Mehra and Rechenberg|1982|pages=26, 28, 31, 39}}</ref> though its precise mathematical form would not be known for another forty years, till it was discovered by Planck in 1900. The theoretical proof for Kirchhoff's universality principle was worked on and debated by various physicists over the same time, and later.<ref name="Schirrmacher 2001"/> Kirchhoff stated later in 1860 that his theoretical proof was better than Balfour Stewart's, and in some respects it was so.<ref name="Siegel"/> Kirchhoff's 1860 paper did not mention the second law of thermodynamics, and of course did not mention the concept of entropy which had not at that time been established. In a more considered account in a book in 1862, Kirchhoff mentioned the connection of his law with [[Carnot's principle]], which is a form of the second law.<ref>{{harvnb|Kirchhoff|1862/1882|page=573}}</ref>
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| According to Helge Kragh, "Quantum theory owes its origin to the study of thermal radiation, in particular to the "black-body" radiation that Robert Kirchhoff had first defined in 1859–1860."<ref>{{harvnb|Kragh|1999|page=58}}</ref>
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| ==See also==
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| {{colbegin|3}}
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| * [[Bolometer]]
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| * [[Color temperature]]
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| * [[Infrared thermometer]]
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| * [[Photon polarization]]
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| * [[Planck's law]]
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| * [[Pyrometry]]
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| * [[Rayleigh–Jeans law]]
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| * [[Thermography]]
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| * [[Sakuma–Hattori equation]]
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| {{colend}}
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| ==References==
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| {{Reflist|2}}
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| | |
| === Bibliography ===
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| {{refbegin}}
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| *{{cite book
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| |last1=Chandrasekhar |first1=S.
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| |author1-link=Subrahmanyan Chandrasekhar
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| |year=1950
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| |title=Radiative Transfer
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| |publisher=[[Oxford University Press]]
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| |ref=harv
| |
| }}
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| *{{cite book
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| |last1=Goody |first1=R. M.
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| |last2=Yung |first2=Y. L.
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| |author2-link=Yuk L. Yung
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| |year=1989
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| |title=Atmospheric Radiation: Theoretical Basis
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| |edition=2nd
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| |publisher=[[Oxford University Press]]
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| |isbn=978-0-19-510291-8
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| |ref=harv
| |
| }}
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| *{{Cite book
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| |last1=Hermann |first1=A.
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| |author1-link=Armin Hermann
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| |others=Nash, C.W. (transl.)
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| |year=1971
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| |title=The Genesis of Quantum Theory
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| |publisher=[[MIT Press]]
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| |isbn=0-262-08047-8
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| |ref=harv
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| }} a translation of ''Frühgeschichte der Quantentheorie (1899–1913)'', Physik Verlag, Mosbach/Baden.
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| *{{cite journal
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| |last1=Kirchhoff |first1=G.
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| |author1-link=Gustav Kirchhoff
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| |last2=[27 October 1859]
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| |year=1860a
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| |title=Über die Fraunhofer'schen Linien
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| |journal=[[Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin]]
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| |pages=662–665
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| |doi=
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| |ref=harv
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| }}
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| *{{cite journal
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| |last1=Kirchhoff |first1=G.
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| |author1-link=Gustav Kirchhoff
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| |last2=[11 December 1859]
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| |date= 1860b
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| |title=Über den Zusammenhang zwischen Emission und Absorption von Licht und Wärme
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| |journal=[[Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin]]
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| |pages=783–787
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| |doi=
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| |ref=harv
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| }}
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| *{{cite journal
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| |last1=Kirchhoff |first1=G.
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| |author1-link=Gustav Kirchhoff
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| |year=1860c
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| |title=Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme and Licht
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| |journal=[[Annalen der Physik und Chemie]]
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| |volume=109
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| |pages=275–301
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| |doi=
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| |ref=harv
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| }} Translated by Guthrie, F. as {{cite journal
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| |last1=Kirchhoff |first1=G.
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| |year=1860
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| |title=On the relation between the radiating and absorbing powers of different bodies for light and heat
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| |journal=[[Philosophical Magazine]]
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| |volume=Series 4, volume 20 |pages=1–21
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| }}
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| *{{Citation
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| | last = Kirchhoff
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| | first = G.
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| | author-link = Gustav Kirchhoff
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| | title = Gessamelte Abhandlungen
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| | place = Leipzig
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| | publisher = Johann Ambrosius Barth
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| | series =
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| | volume =
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| | origyear = 1862
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| | year = 1882
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| | month=
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| | edition =
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| | chapter = Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht
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| | chapterurl =
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| | page =
| |
| | pages = 571–598
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| | ref = harv
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| }}
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| *{{cite book
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| |last1=Kondepudi |first1=D.
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| |author1-link=Dilip Kondepudi
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| |last2=Prigogine |first2=I.
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| |author2-link=Ilya Prigogine
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| |year=1998
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| |title=Modern Thermodynamics. From Heat Engines to Dissipative Structures
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| |publisher=[[John Wiley & Sons]]
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| |isbn=0-471-97393-9
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| |ref=harv
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| }}
| |
| *{{cite book
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| |last1=Kragh |first1=H.
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| |author1-link=Helge Kragh
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| |year=1999
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| |title=Quantum Generations: a History of Physics in the Twentieth Century
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| |publisher=[[Princeton University Press]]
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| |isbn=0-691-01206-7
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| |ref=harv
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| }}
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| *{{cite book
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| |last1=Kuhn |first1=T. S.
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| |author1-link=Thomas Kuhn
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| |year=1978
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| |title=Black–Body Theory and the Quantum Discontinuity
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| |publisher=[[Oxford University Press]]
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| |isbn=0-19-502383-8
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| |ref=harv
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| }}
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| *{{cite book
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| |last1=Loudon |first1=R.
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| |author1-link=Rodney Loudon
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| |year=2000
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| |origyear=1973
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| |title=The Quantum Theory of Light
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| |publisher=[[Cambridge University Press]]
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| |edition=third
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| |isbn=0-19-850177-3
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| |ref=harv
| |
| }}
| |
| *{{cite book
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| |last1=Mandel |first1=L.
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| |author1-link=Leonard Mandel
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| |last2=Wolf |first2=E.
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| |author2-link=Emil Wolf
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| |year=1995
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| |title=Optical Coherence and Quantum Optics
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| |publisher=[[Cambridge University Press]]
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| |isbn=0-521-41711-2
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| |ref=harv
| |
| }}
| |
| *{{cite book
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| |last1=Mehra |first1=J.
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| |author1-link=Jagdish Mehra
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| |last2=Rechenberg |first2=H.
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| |author2-link=Hlemut Rechenberg
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| |year=1982
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| |title=The Historical Development of Quantum Theory
| |
| |volume=volume 1, part 1
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| |publisher=[[Springer-Verlag]]
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| |isbn=0-387-90642-8
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| |ref=harv
| |
| }}
| |
| *{{cite book
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| |last1=Mihalas |first1=D.
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| |author1-link=Dimitri Mihalas
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| |last2=Weibel-Mihalas |first2=B.
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| |year=1984
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| |title=Foundations of Radiation Hydrodynamics
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| |publisher=[[Oxford University Press]]
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| |isbn=0-19-503437-6
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| |ref=harv
| |
| }}
| |
| *{{cite journal
| |
| |last1=Milne |first1=E.A.
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| |author1-link=Edward Arthur Milne
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| |year=1930
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| |title=Thermodynamics of the Stars
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| |journal=[[Handbuch der Astrophysik]]
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| |volume=3, part 1
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| |pages=63–255
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| |doi=
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| |ref=harv
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| }}
| |
| *{{cite book
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| |last1=Partington |first1=J.R.
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| |author1-link=J.R. Partington
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| |year=1949
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| |title=An Advanced Treatise on Physical Chemistry. Volume 1. Fundamental Principles. The Properties of Gases
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| |publisher=[[Longman|Longmans, Green and Co.]]
| |
| |ref=harv
| |
| }}
| |
| *{{cite book
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| |last1=Planck |first1=M.
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| |author1-link=Max Planck
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| |others=translated by Masius, M.
| |
| |origyear= 1912
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| |year=1914
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| |title=The Theory of Heat Radiation
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| |publisher=[[P. Blakiston's Sons & Co.]]
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| |ref=harv
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| }}
| |
| *{{Cite book
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| |last1=Rybicki |first1=G. B.
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| |last2=Lightman |first2=A. P.
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| |author2-link=Alan Lightman
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| |year=1979
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| |title=Radiative Processes in Astrophysics
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| |url=http://books.google.com/books?id=LtdEjNABMlsC&printsec=frontcover
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| |publisher=[[John Wiley & Sons]]
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| |isbn=0-471-82759-2
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| |ref=harv
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| }}
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| *{{cite book
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| |last1=Schirrmacher |first1=A.
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| |author1-link=Arne Schirrmacher
| |
| |year=2001
| |
| |title=Experimenting theory: the proofs of Kirchhoff's radiation law before and after Planck
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| |publisher=[[Münchner Zentrum für Wissenschafts und Technikgeschichte]]
| |
| |ref=harv
| |
| }}
| |
| *{{cite journal
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| |last1=Siegel |first1=D.M.
| |
| |year=1976
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| |title=Balfour Stewart and Gustav Robert Kirchhoff: two independent approaches to "Kirchhoff's radiation law"
| |
| |journal=[[Isis]]
| |
| |volume=67 |pages=565–600
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| |doi=
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| |ref=harv
| |
| }}
| |
| *{{cite journal
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| |last1=Stewart |first1=B.
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| |author1-link=Balfour Stewart
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| |year=1858
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| |title=An account of some experiments on radiant heat
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| |journal=[[Transactions of the Royal Society of Edinburgh]]
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| |volume=22 |pages=1–20
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| |doi=
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| |ref=harv
| |
| }}
| |
| *{{cite journal
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| |last1=Wien |first1=W.
| |
| |author1-link=Wilhelm Wien
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| |year=1894
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| |title=Temperatur und Entropie der Strahlung
| |
| |journal=[[Annalen der Physik]]
| |
| |volume=288 |pages=132–165
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| |doi= 10.1002/andp.18942880511
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| |ref=harv
| |
| |bibcode = 1894AnP...288..132W }}
| |
| {{refend}}
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| | |
| ==Further reading==
| |
| | |
| *{{cite book|author=Kroemer, Herbert; Kittel, Charles
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| |title=Thermal Physics |edition=2nd|publisher=W. H. Freeman Company|year=1980
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| |isbn=0-7167-1088-9}}
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| *{{cite book|author=Tipler, Paul; Llewellyn, Ralph
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| |title=Modern Physics |edition=4th|publisher=W. H. Freeman|year=2002|isbn=0-7167-4345-0}}
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| ==External links==
| |
| *[http://www.spectralcalc.com/blackbody/blackbody.html Calculating Black-body Radiation] Interactive calculator with Doppler Effect. Includes most systems of units.
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| *[http://academo.org/demos/colour-temperature-relationship/ Color-to-Temperature demonstration] at Academo.org
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| *[http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/coobod.html#c1 Cooling Mechanisms for Human Body] – From Hyperphysics
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| *[http://www.x20.org/library/thermal/blackbody.htm Descriptions of radiation emitted by many different objects]
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| *[http://webphysics.davidson.edu/Applets/java11_Archive.html Black-Body Emission Applet]
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| *[http://demonstrations.wolfram.com/BlackbodySpectrum/ "Blackbody Spectrum"] by Jeff Bryant, [[Wolfram Demonstrations Project]], 2007.
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| {{DEFAULTSORT:Black Body}}
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| [[Category:Infrared]]
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| [[Category:Heat transfer]]
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| [[Category:Electromagnetic radiation]]
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| [[Category:Astrophysics]]
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