Black-body radiation - Knowledge (XXG)

8206: 4742:(which can raise the surface temperature of a body above what it would be if it were a perfect black body in all spectrums). 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 and 0.95 respectively, yielding an estimated temperature of about 1.36 °C. 550:

wavelengths towards the peak at relatively shorter wavelengths. Secondly, though, at shorter wavelengths more energy is needed to reach the threshold level to occupy each mode: the more energy needed to excite the mode, the lower the probability that this mode will be occupied. As the wavelength decreases, the probability of exciting the mode becomes exceedingly small, leading to fewer of these modes being occupied: this accounts for the decrease in spectral radiance at very short wavelengths, left of the peak. Combined, they give the characteristic graph.

160:, black bodies start to emit significant amounts of visible light. Viewed in the dark by the human eye, the first faint glow appears as a "ghostly" grey (the visible light is actually red, but low intensity light activates only the eye's grey-level sensors). With rising temperature, the glow becomes visible even when there is some background surrounding light: first as a dull red, then yellow, and eventually a "dazzling bluish-white" as the temperature rises. When the body appears white, it is emitting a substantial fraction of its energy as 221: 129: 243:, with emissivities greater than 0.95, are good approximations to a black material. Experimentally, blackbody radiation may be established best as the ultimately stable steady state equilibrium radiation in a cavity in a rigid body, at a uniform temperature, that is entirely opaque and is only partly reflective. A closed box with walls of graphite at a constant temperature with a small hole on one side produces a good approximation to ideal blackbody radiation emanating from the opening. 270:, 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 blackbody 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 spectral radiation intensity plotted versus frequency(or wavelength) is called the 8266: 5561:

the same time, and later. Kirchhoff stated later in 1860 that his theoretical proof was better than Balfour Stewart's, and in some respects it was so. 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

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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.

4877:. 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." Stewart's statement assumed a general principle: that there exists a body or surface that has the greatest possible absorbing and radiative power for every wavelength and equilibrium temperature. 8242: 4806: 508: 278: 53: 8218: 5980:(The proof, which shall be given here for the proposition stated , rests on the assumption that bodies are conceivable which in the case of infinitely small thicknesses, completely absorb all rays that fall on them, thus neither reflect nor transmit rays. I will call such bodies "completely black " or more briefly "black ".) See also (Kirchhoff, 1860) ( 8254: 358: 251:) is determined solely by the equilibrium temperature and does not depend upon the shape, material or structure of the body. For a black body (a perfect absorber) there is no reflected radiation, and so the spectral radiance is entirely due to emission. In addition, a black body is a diffuse emitter (its emission is independent of direction). 8230: 5084:

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 absorptivity 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

620:. 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 307:. 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. 4056:. 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 4749:(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, one obtains an effective temperature of about 245 K. Similarly using albedo 0.3 and solar constant of 1372 W m, one obtains an effective temperature of 255 K. 2711: 382:: 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. 520:, attenuating the spectrum at high frequency in agreement with experimental observation and resolving the catastrophe. The modes that had more energy than the thermal energy of the substance itself were not considered, and because of quantization modes having infinitesimally little energy were excluded. 4885:

principle. His research did not consider that properties of rays are dependent on wavelength, and he did not use tools 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

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According to Kondepudi and Prigogine, at very high temperatures (above 10 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 spontaneously and are in

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Wien's displacement law shows how the spectrum of blackbody 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

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are very small. In the shorter wavelengths of the ultraviolet range, however, classical theory predicts the energy emitted tends to infinity, hence the ultraviolet catastrophe. The theory even predicted that all bodies would emit most of their energy in the ultraviolet range, clearly contradicted by

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Blackbody radiation has the unique absolutely stable distribution of radiative intensity that can persist in thermodynamic equilibrium in a cavity. In equilibrium, for each frequency, the intensity of radiation which is emitted and reflected from a body relative to other frequencies (that is, the net

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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. Stewart chose lamp-black surfaces as his reference because of various previous experimental findings,

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is only required if radiation and convection are insufficient to maintain a steady-state temperature (but evaporation from the lungs occurs regardless). Free-convection rates are comparable, albeit somewhat lower, than radiative rates. Thus, radiation accounts for about two-thirds of thermal energy

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A perfectly insulated enclosure which is in thermal equilibrium internally contains blackbody radiation, and will emit it through a hole made in its wall, provided the hole is small enough to have a negligible effect upon the equilibrium. The thermal radiation spontaneously emitted by many ordinary

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Bennett, C.L.; Larson, L.; Weiland, J.L.; Jarosk, N.; Hinshaw, N.; Odegard, N.; Smith, K.M.; Hill, R.S.; Gold, B.; Halpern, M.; Komatsu, E.; Nolta, M.R.; Page, L.; Spergel, D.N.; Wollack, E.; Dunkley, J.; Kogut, A.; Limon, M.; Meyer, S.S.; Tucker, G.S.; Wright, E.L. (December 20, 2012). "Nine-Year

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has been called "Kirchhoff's (emission, universal) function," 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

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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. His theoretical proof was and still is considered by some writers to be invalid. His

2720:(LWIR) light. Some materials are transparent in the infrared, but opaque to visible light, as is the plastic bag in this thermal (LWIR) camera image (bottom). Other materials are transparent to visible light, but opaque or reflective in the infrared, noticeable by the darkness of the man's glasses. 349:

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

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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,

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of the hole's radiation (that is, the amount of light emitted from the hole at each wavelength) will be continuous, and will depend only on the temperature and the fact that the walls are opaque and at least partly absorptive, but not on the particular material of which they are built nor on the

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spectrum, which cannot be perceived by the human eye, but can be sensed by some reptiles. As the object increases in temperature to about 500 °C (773 K; 932 °F), the emission spectrum gets stronger and extends into the human visual range, and the object appears dull red. As its

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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

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Notice that there are two factors responsible for the shape of the graph, which can be seen as working opposite to one another. Firstly, shorter wavelengths have a larger number of modes associated with them. This accounts for the increase in spectral radiance as one moves from the longest

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reported the coincidence of the wavelengths of spectrally resolved lines of absorption and 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.

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of skin and most clothing is near unity, as it is for most nonmetallic surfaces. Skin temperature is about 33 °C, but clothing reduces the surface temperature to about 28 °C when the ambient temperature is 20 °C. Hence, the net radiative heat loss is about

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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 emitted and absorbed by a body in equilibrium, the dimensioned total radiation ratio

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has one and the same value common to all bodies. 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

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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.

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Stewart was concerned with selective thermal radiation, which he investigated using plates which selectively radiated and absorbed different wavelengths. He discussed the experiments in terms of rays which could be reflected and refracted, and which obeyed the

3126: 4393: 7524: 7492: 412:) 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. 3541: 4411:

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.

577:, 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, which is to say that it existed in integer multiples of some quantity. 1621: 405:, 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. 373:

With non-black surfaces, the deviations from ideal blackbody 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

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per unit time is strictly proportional to the blackbody curve. This means that the blackbody curve is the amount of light energy emitted by a black body, which justifies the name. This is the condition for the applicability of

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Mekhrengin, M.V.; Meshkovskii, I.K.; Tashkinov, V.A.; Guryev, V.I.; Sukhinets, A.V.; Smirnov, D.S. (June 2019). "Multispectral pyrometer for high temperature measurements inside combustion chamber of gas turbine engines".

5337:, with the dimensions of power. Kirchhoff considered 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 3002:

for a 40-year-old male is about 35 kcal/(m·h), which is equivalent to 1700 kcal per day, assuming the same 2 m area. However, the mean metabolic rate of sedentary adults is about 50% to 70% greater than their basal rate.

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As the temperature increases, the peak of the emitted blackbody radiation curve moves to higher intensities and shorter wavelengths. The blackbody radiation graph is also compared with the classical model of Rayleigh and

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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

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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, though not full thermodynamic, equilibrium with radiation.

2785: 232:, 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 blackbody radiation. 2133: 318:.) 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 4575: 4793:

lights have a continuous black body spectrum with a cooler colour temperature, around 2,700 K (2,430 °C; 4,400 °F), which also emits considerable energy in the infrared range. Modern-day

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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:

3033: 3767: 4458: 1378: 5784: 4959:. (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 4626: 4307: 4733: 5568:

According to Helge Kragh, "Quantum theory owes its origin to the study of thermal radiation, in particular to the "blackbody" radiation that Robert Kirchhoff had first defined in 1859–1860."

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lights, which are more efficient, do not have a continuous black body emission spectrum, rather emitting directly, or using combinations of phosphors that emit multiple narrow spectrums.

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lava flow can be estimated by observing its color. The result agrees well with other measurements of temperatures of lava flows at about 1,000 to 1,200 °C (1,830 to 2,190 °F).

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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

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As the temperature of a black body decreases, the emitted thermal radiation decreases in intensity and its maximum moves to longer wavelengths. Shown for comparison is the classical

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radiation observed today is the most perfect blackbody radiation ever observed in nature, with a temperature of about 2.7 K. It is a "snapshot" of the radiation at the time of

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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

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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 (

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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

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Color of a black body from 800 K to 12200 K. This range of colors approximates the range of colors of stars of different temperatures, as seen or photographed in the night sky.

4656: 1678: 1127: 5480:, the ratio of emissive power to absorptivity has one universal value, which is characteristic of a perfect black body, and is an emissive power which we here represent by 3591: 3419: 3387: 1749: 1214: 1172: 2893: 6912:, p. 12 mentions that Venus' blackbody temperature would be 330 K "in the zero albedo case", but that due to atmospheric warming, its actual surface temperature is 740 K. 3987: 837: 80:) are neither in thermal equilibrium with their surroundings nor perfect black bodies, blackbody radiation is still a good first approximation for the energy they emit. 3846: 1721: 1129:

with respect to an area normal to the propagation direction. At oblique angles, the solid angle spans involved do get smaller, resulting in lower aggregate intensities.

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Substituting the expressions for solar and planet power in equations 1–6 and simplifying yields the estimated temperature of the planet, ignoring greenhouse effect,

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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

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medium filling it, and refutes this view (never actually held by Newton) by saying that a black body under illumination would increase indefinitely in heat.

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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

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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 (

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thermal equilibrium with electromagnetic radiation. These particles form a part of the black body spectrum, in addition to the electromagnetic radiation.

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with temperature. The Stefan–Boltzmann law also says that the total radiant heat energy emitted from a surface is proportional to the fourth power of its

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of a perfectly black body is by definition exactly 1. Then for a perfectly black body, the wavelength-specific ratio of emissive power to absorptivity

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Kirchhoff then went on to consider some bodies that emit and absorb heat radiation, in an opaque enclosure or cavity, in equilibrium at a temperature

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is approximately 2898 μm/T, with the temperature given in kelvins. At a typical room temperature of 293 K (20 °C), the maximum intensity is at

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of classical physics, there would be an equal amount of energy in each mode. Since there are an infinite number of modes, this would imply infinite

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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

546:) were allowed, supporting the data that the energy emitted is reduced for wavelengths less than the wavelength of the observed peak of emission. 5467: 296: 6666: 303:

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

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are frequently regarded as black bodies, though this is often a poor approximation. An almost perfect blackbody spectrum is exhibited by the

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is the radiance density per unit area of emitting surface as the surface area involved in generating the radiance is increased by a factor

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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

5562: 5265:, at thermal equilibrium, all perfectly black bodies of the same size and shape have the one and the same common value of emissive power 1026:

For a black body surface, the spectral radiance density (defined per unit of area normal to the propagation) is independent of the angle

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This is the temperature of the Earth if it radiated as a perfect black body in the infrared, assuming an unchanging albedo and ignoring

379: 4695: 2255:{\displaystyle \sigma \equiv {\frac {2\pi ^{5}}{15}}{\frac {k^{4}}{c^{2}h^{3}}}=5.670373\times 10^{-8}\mathrm {\frac {W}{m^{2}K^{4}}} } 8301: 5727: 5463:

of the arbitrary non-ideal body (Geometrical factors, taken into detailed account by Kirchhoff, have been ignored in the foregoing).

266:, a small opening in the wall of a large uniformly heated opaque-walled cavity (such as an oven), viewed from outside, looks red; at 8127: 8108: 7950: 7852: 7826: 7796: 7766: 7714: 7689: 7663: 7633: 7468: 7151: 6883: 6843: 6461: 6282: 6186: 3137: 1989:{\displaystyle L={\frac {2\pi ^{5}}{15}}{\frac {k^{4}T^{4}}{c^{2}h^{3}}}{\frac {1}{\pi }}=\sigma T^{4}{\frac {\cos(\theta )}{\pi }}} 439:, as well as a nonphysical spectrum of emitted radiation that grows without bound with increasing frequency, a problem known as the 4521: 1219: 5343:. He argued that the flows of heat radiation must be the same in each case. Thus he argued that at thermal equilibrium the ratio 4221: 6667:"Theoretical Prediction and Measurement of the Fabric Surface Apparent Temperature in a Simulated Man/Fabric/Environment System" 4778:

temperature increases further, it emits more and more orange, yellow, green, and then blue light (and ultimately beyond violet,

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The study of the laws of black bodies and the failure of classical physics to describe them helped establish the foundations of

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of approximately 5800 K, is an approximate black body with an emission spectrum peaked in the central, yellow-green part of the

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Siegel, D.M. (1976). "Balfour Stewart and Gustav Robert Kirchhoff: two independent approaches to "Kirchhoff's radiation law"".

2675:{\displaystyle \int \cos \theta \,d\Omega =\int _{0}^{2\pi }\int _{0}^{\pi /2}\cos \theta \sin \theta \,d\theta \,d\phi =\pi .} 2515:

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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is the angle between the velocity vector and the observer-source direction measured in the reference frame of the source, and

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of light originating from a source that is moving in relation to the observer, so that the wave is observed to have frequency

3194: 2518: 144:. The spectrum is peaked at a characteristic frequency that shifts to higher frequencies with increasing temperature, and at 8286: 8188: 6594: 3989:

is the temperature of the planet. This temperature, calculated for the case of the planet acting as a black body by setting

7604:(1882) , "Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht", 4418: 2263: 664: 7556: 4581: 8196: 602: 205:. The radiation represents a conversion of a body's internal energy into electromagnetic energy, and is therefore called 5797:

This is an important effect in astronomy, where the velocities of stars and galaxies can reach significant fractions of

416: 137: 7924: 6902: 5855: 5577: 4758: 4474: 3992: 598: 6247: 3121:{\displaystyle \lambda _{\text{peak}}=\mathrm {\frac {2.898\times 10^{-3}~K\cdot m}{305~K}} =\mathrm {9.50~\mu m} .} 7788: 7758: 7706: 7655: 7407: 7131: 6482: 4870: 3027: 1297: 501: 7552:"Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme and Licht" 6901:

by Raymond T. Peirrehumbert, Cambridge University Press (2011), p. 146. From Chapter 3 which is available online

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at thermal equilibrium. His fresh theoretical proof was and still is considered by some writers to be invalid.

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In the laboratory, blackbody radiation is approximated by the radiation from a small hole in a large cavity, a

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For this reason, thermal imaging devices for human subjects are most sensitive in the 7–14 micrometer range.

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Wien, W. (1893). Eine neue Beziehung der Strahlung schwarzer Körper zum zweiten Hauptsatz der Wärmetheorie,

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of emitting power to absorptivity is a dimensioned quantity, with the dimensions of emitting power, because

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built on this idea and proposed the quantization of electromagnetic radiation itself in 1905 to explain the

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The concept of the black body is an idealization, as perfect black bodies do not exist in nature. However,

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The Earth only has an absorbing area equal to a two dimensional disk, rather than the surface of a sphere.

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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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Blackbody radiation becomes a visible glow of light if the temperature of the object is high enough. The

7554:[On the relation between bodies' emission capacity and absorption capacity for heat and light]. 7533: 7501: 6620: 5280:, with the dimensions of power. His proof noted that the dimensionless wavelength-specific absorptivity 4953:

of that body is dimensionless, the ratio of absorbed to incident radiation in the cavity at temperature

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of the Sun's light, and reflects the rest. The power absorbed by the planet and its atmosphere is then:

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For any material at all, radiating and absorbing in thermodynamic equilibrium at any given temperature

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An Advanced Treatise on Physical Chemistry. Volume 1. Fundamental Principles. The Properties of Gases

7732: 7625: 7565: 7089: 6931: 6710: 6424: 6410: 6344: 6212: 5830: 4818: 4632: 2999: 625: 585:. These theoretical advances eventually resulted in the superseding of classical electromagnetism by 582: 6922:

Saari, J. M.; Shorthill, R. W. (1972). "The Sunlit Lunar Surface. I. Albedo Studies and Full Moon".

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of emitting power to absorptivity is a dimensioned quantity, with the dimensions of emitting power.

1627: 1098: 628:. The law was formulated by Josef Stefan in 1879 and later derived by Ludwig Boltzmann. The formula 8161: 7862: 7588:"On the relation between the radiating and absorbing powers of different bodies for light and heat" 7450: 6574: 6086: 5860: 5835: 4814: 3566: 3536:{\displaystyle P_{\rm {SE}}=P_{\rm {S\ emt}}\left({\frac {\pi R_{\rm {E}}^{2}}{4\pi D^{2}}}\right)} 3394: 3362: 1728: 1177: 1135: 554: 500:

the experimental data which showed a different peak wavelength at different temperatures (see also

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Lummer, O., Pringsheim, E. (1899). Die Vertheilung der Energie im Spectrum des schwarzen Körpers,

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light. The net power radiated is the difference between the power emitted and the power absorbed:

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has one and the same value for all bodies. In this report there was no mention of black bodies.

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or reflectance of the planet in the UV-Vis range. In other words, the planet absorbs a fraction

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is dimensionless. Also here the wavelength-specific emitting power of the body at temperature

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A black body at room temperature (23 °C (296 K; 73 °F)) radiates mostly in the

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For the case of a source moving directly towards or away from the observer, this reduces to

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or observed intensity is not a function of direction. Therefore, a black body is a perfect

8179: 8015: 7899: 7836: 7818: 7613: 7118: 6909: 6641: 6477: 6392: 4865: 4826: 3209: 1755: 974: 914: 850: 840: 578: 7918: 5840: 3598: 681: 562: 141: 8075: 7569: 7093: 6935: 6714: 6575:"Wien's Displacement Law and Other Ways to Characterize the Peak of Blackbody Radiation" 6428: 6348: 6216: 5203:. It required that the bodies be kept in a cavity in thermal equilibrium at temperature 3142:

The blackbody law may be used to estimate the temperature of a planet orbiting the Sun.

2295: 2272: 49:, which is assumed, for the sake of calculations and theory, to be uniform and constant. 8270: 8210: 8184: 8149: 7978: 7776: 7648: 7617: 6733: 6698: 5699: 4926:

denotes a dimensioned quantity, the total radiation emitted by a body labeled by index

4853: 4746: 4210: 3015: 2396: 1836: 1306:

A consequence of Wien's displacement law is that the wavelength at which the intensity

1000: 948: 940: 922: 896: 874: 570: 516:

Instead, in the quantum treatment of this problem, the numbers of the energy modes are

6796: 6224: 4852:. He says that Newton imagined particles of light traversing space uninhibited by the 4813:) of blackbody radiation scales inversely with the temperature of the black body; the 2080:{\displaystyle \int _{0}^{\infty }dx\,{\frac {x^{3}}{e^{x}-1}}={\frac {\pi ^{4}}{15}}} 597:. In addition, it led to the development of quantum probability distributions, called 8280: 8045: 7965:

Experimenting theory: the proofs of Kirchhoff's radiation law before and after Planck

7932: 7806: 7750: 7454: 6951: 6364: 6356: 6232: 4886:

bodies in a condition near the thermal equilibrium in which they had been prepared.

3190: 436: 202: 8007: 4110:

is the average emissivity in the IR range. The power emitted by the planet is then:

1751:. At a typical room temperature of 293 K (20 °C), the maximum intensity is for 299:: the blackbody curve is characteristic of thermal light, which depends only on the 8265: 8234: 8053: 6325:

Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results".

5970:"Der Beweis, welcher für die ausgesprochene Behauptung hier gegeben werden soll, … 5865: 5825: 5702:. This can be simplified for the special cases of objects moving directly towards ( 4843: 4810: 3215: 3019: 792:{\displaystyle B_{\nu }(T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{h\nu /kT}-1}},} 428: 255: 240: 6598: 6544: 5679:{\displaystyle f'=f{\frac {1-{\frac {v}{c}}\cos \theta }{\sqrt {1-v^{2}/c^{2}}}},} 2983:{\displaystyle P_{\text{net}}=P_{\text{emit}}-P_{\text{absorb}}=\mathrm {100~W} .} 120: 7936: 7673: 7643: 7424: 4795: 4779: 4460:

comes to the same temperature as a black body no matter how dark or light gray.

3011: 2860:{\displaystyle P_{\text{net}}=A\sigma \varepsilon \left(T^{4}-T_{0}^{4}\right),} 1018: 844: 300: 46: 7525:

Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin

7493:

Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin

6773: 5250:

of the non-ideal body, however partly transparent or partly reflective it was.

8143: 8037: 7914: 6406: 3007: 2916: 2896: 594: 558: 447: 402: 346: 319: 229: 192: 42: 34: 8083: 7578: 7522:[On the relation between emission and absorption of light and heat]. 6437: 4911:

Here is used a notation different from Kirchhoff's. Here, the emitting power

7780: 7520:"Über den Zusammenhang zwischen Emission und Absorption von Licht und Wärme" 7460: 6303: 5845: 5815: 4805: 3937:{\displaystyle P_{\rm {emt\,bb}}=4\pi R_{\rm {E}}^{2}\sigma T_{\rm {E}}^{4}} 2991: 2710: 1046:

of emission with respect to the normal. However, this means that, following

992: 868: 386: 140:

that depends only on the body's temperature, called the Planck spectrum or

8152:

Interactive calculator with Doppler Effect. Includes most systems of units.

6781: 6742: 6413:[On the law of the distribution of energy in the normal spectrum]. 6091:

London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science

3305:{\displaystyle P_{\rm {S\ emt}}=4\pi R_{\rm {S}}^{2}\sigma T_{\rm {S}}^{4}} 3201:

The analysis only considers the Sun's heat for a planet in a Solar System.

2699: 6723: 4842:(1788–1827) responded to a view he extracted from a French translation of 3848:. If the planet were a perfect black body, it would emit according to the 277: 7999: 7084: 4774: 2728: 2717: 335: 311: 236: 201:) matter emits electromagnetic radiation when it has a temperature above 149: 4182:{\displaystyle P_{\rm {emt}}={\overline {\epsilon }}\,P_{\rm {emt\,bb}}} 7907: 6943: 2995: 1310:

of the radiation produced by a black body has a local maximum or peak,

606: 507: 214: 157: 132:

This blacksmith's colourchart stops at the melting temperature of steel

52: 6043:

Sitzungberichte der Königlich-Preußischen Akademie der Wissenschaften

5996:"How Do Blacksmiths Measure The Temperature Of Their Forge And Steel?" 557:

during the late nineteenth century. The problem was solved in 1901 by

357: 350:

wavelength so that the emissivity is a constant. This is known as the

4848: 3666: 3172: 1462:{\displaystyle {\frac {hc}{k}}{\frac {1}{5+W_{0}(-5e^{-5})}}\approx } 847:

and per unit of area normal to the propagation) density of frequency

590: 523:

Thus for shorter wavelengths very few modes (having energy more than

198: 7138:

The Edge of Objectivity: An Essay in the History of Scientific Ideas

6758:"Nonexercise activity thermogenesis (NEAT): environment and biology" 2716:

Much of a person's energy is radiated away in the form of long-wave

72:

Of particular importance, although planets and stars (including the

8229: 7991: 124:

Blacksmiths judge workpiece temperatures by the colour of the glow.

7650:

Quantum Generations: a History of Physics in the Twentieth Century

7622:

Modern Thermodynamics. From Heat Engines to Dissipative Structures

6339: 2383:{\displaystyle dI=\sigma T^{4}{\frac {\cos \theta }{\pi d^{2}}}dA} 610: 569:(not to be confused with Wien's displacement law) consistent with 276: 127: 119: 73: 51: 6520: 5193:

Kirchhoff's proof considered an arbitrary non-ideal body labeled

2780:{\displaystyle P_{\text{net}}=P_{\text{emit}}-P_{\text{absorb}}.} 45:, inversely related to intensity, that depend only on the body's 6552: 3175:

effect causing a fraction of light to be reflected by the planet

390: 362: 282: 6510: 4468:

Substituting the measured values for the Sun and Earth yields:

3815:, it emits in all directions; the spherical surface area being 3145: 642:

is the radiant heat emitted from a unit of area per unit time,

37:(an idealized opaque, non-reflective body). It has a specific, 6456:(3rd Edition Part 1 ed.). Oxford: Butterworth–Heinemann. 4799: 3617: 2390:

when the receiving surface is perpendicular to the radiation.

165: 77: 4570:{\displaystyle R_{\rm {S}}=6.957\times 10^{8}\ \mathrm {m} ,} 3006:

There are other important thermal loss mechanisms, including

258:

is the temperature at which all solids glow a dim red, about

5690:

is the velocity of the source in the observer's rest frame,

274:. Different curves are obtained by varying the temperature. 8168:

Descriptions of radiation emitted by many different objects

5519:

Kirchhoff announced that the determination of the function

6411:"Ueber das Gesetz der Energieverteilung im Normalspectrum" 6878:(1st ed.). IOP Publishing. pp. 36–37, 380–382. 6015:"§2.3: Thermodynamic equilibrium and blackbody radiation" 553:

Calculating the blackbody curve was a major challenge in

176:, but with significant power in the ultraviolet as well. 7969:

Münchner Zentrum für Wissenschafts und Technikgeschichte

6060:

Verhandlungen der Deutschen Physikalischen Gessellschaft

3157:

The temperature of a planet depends on several factors:

593:

and the blackbody cavity was thought of as containing a

427:

According to the Classical Theory of Radiation, if each

6549:

The NIST Reference on Constants, Units, and Uncertainty

3785:

Even though the planet only absorbs as a circular area

3762:{\displaystyle P_{\rm {abs}}=(1-\alpha )\,P_{\rm {SE}}} 3030:

to human-body emission results in a peak wavelength of

156:. As the temperature increases past about 500 degrees 6875:

Planetary Science: The Science of Planets Around Stars

6816:

Prevost, P. (1791). "Mémoire sur l'équilibre du feu".

5710:= 0) from the observer, and for speeds much less than 4453:{\displaystyle (1-\alpha )={\overline {\varepsilon }}} 3185:

Energy generated internally by a planet itself due to

1373:{\displaystyle \lambda _{\text{peak}}={\frac {b}{T}},} 136:

Black-body radiation has a characteristic, continuous

8194: 8146:

Blackbody radiation by Fu-Kwun Hwang and Loo Kang Wee

7293: 7109:, pp. 227–228; also Section 11.6, pages 294–296. 7001:

Willem Jozef Meine Martens & Jan Rotmans (1999).

5730: 5594: 4698: 4667: 4635: 4584: 4524: 4477: 4421: 4310: 4224: 4121: 4089: 4062: 3995: 3966: 3862: 3821: 3791: 3706: 3675: 3651: 3631: 3601: 3569: 3438: 3397: 3365: 3338: 3231: 3036: 2926: 2881: 2793: 2737: 2567: 2521: 2482: 2462: 2439: 2419: 2399: 2321: 2298: 2275: 2136: 2093: 2002: 1859: 1839: 1788: 1758: 1731: 1689: 1630: 1553: 1519: 1488: 1390: 1384:, known as Wien's displacement constant, is equal to 1343: 1316: 1222: 1180: 1138: 1101: 1056: 1032: 1003: 977: 951: 925: 899: 877: 853: 809: 692: 605:, each applicable to a different class of particles, 529: 479: 456: 7216: 7214: 7212: 4621:{\displaystyle D=1.496\times 10^{11}\ \mathrm {m} ,} 4083:

of the radiation that a black body would emit where

247:

amount of radiation leaving its surface, called the

69:

objects can be approximated as blackbody radiation.

7608:, Leipzig: Johann Ambrosius Barth, pp. 571–598 6838:, second edition, D. Reidel Publishing, Dordrecht, 6642:"Temperature of a Healthy Human (Skin Temperature)" 6379:"Blackbody Radiation – University Physics Volume 3" 6179:

Passive infrared detection: theory and applications

401:is the hypothetical blackbody radiation emitted by 7647: 7230: 7228: 7135: 7106: 5913: 5778: 5678: 4727: 4680: 4650: 4620: 4569: 4509: 4452: 4387: 4266: 4209:with its surroundings, the rate at which it emits 4181: 4102: 4075: 4044: 3981: 3936: 3840: 3807: 3761: 3687: 3657: 3637: 3608: 3585: 3535: 3413: 3381: 3345: 3304: 3132:Temperature relation between a planet and its star 3120: 2982: 2887: 2859: 2779: 2674: 2553: 2496: 2468: 2448: 2425: 2405: 2382: 2307: 2284: 2254: 2122: 2079: 1988: 1845: 1825: 1764: 1743: 1715: 1672: 1615: 1532: 1501: 1461: 1372: 1329: 1281: 1208: 1166: 1121: 1087: 1038: 1009: 983: 957: 931: 905: 883: 859: 831: 791: 538: 491: 465: 7393:The Doppler Effect, T. P. Gill, Logos Press, 1965 6872:Cole, George H. A.; Woolfson, Michael M. (2002). 6133: 6131: 6129: 4728:{\displaystyle T_{\rm {E}}=254.356\ \mathrm {K} } 8060:[Temperature and entropy of radiation]. 8020:"An account of some experiments on radiant heat" 6583:Provides 5 variations of Wien's displacement law 5199:as well as various perfect black bodies labeled 5026:and the wavelength-specific absorption ratio by 2990:The total energy radiated in one day is about 8 7678:Black–Body Theory and the Quantum Discontinuity 7357: 7281: 6496: 6249:Radiation heat transfer: a statistical approach 5779:{\displaystyle T'=T{\sqrt {\frac {c-v}{c+v}}}.} 4510:{\displaystyle T_{\rm {S}}=5772\ \mathrm {K} ,} 4045:{\displaystyle P_{\rm {abs}}=P_{\rm {emt\,bb}}} 2269:On a side note, at a distance d, the intensity 8025:Transactions of the Royal Society of Edinburgh 7369: 7032:. In Pascale Ehrenfreund; et al. (eds.). 6964:Lunar and Planetary Science XXXVII (2006) 2406 4415:Notice that a gray (flat spectrum) ball where 3164:Emitted radiation of the planet (for example, 2315:of radiating surface is the useful expression 1132:The emitted energy flux density or irradiance 179:Blackbody radiation provides insight into the 7729:Statistical Physics: A Probabilistic Approach 7477:Frühgeschichte der Quantentheorie (1899–1913) 7257: 7078:White, M. (1999). "Anisotropies in the CMB". 6699:"A Biometric Study of Human Basal Metabolism" 4213:is equal to the rate at which it absorbs it: 3153:intensity, from clouds, atmosphere and ground 565:of blackbody radiation. By making changes to 8: 7815:The Historical Development of Quantum Theory 7220: 6089:(1847). On the production of light by heat, 5433:is a continuous function, dependent only on 5209:. His proof intended to show that the ratio 3389:is the effective temperature of the Sun, and 2911:The total surface area of an adult is about 1282:{\displaystyle B_{\nu }(T,E)=Eb_{\nu }(T,E)} 91:in 1860. Blackbody radiation is also called 8144:Blackbody radiation JavaScript Interactives 7538:: CS1 maint: numeric names: authors list ( 7506:: CS1 maint: numeric names: authors list ( 7058:Atmospheric Science. An Introductory Survey 6545:"Wien wavelength displacement law constant" 6327:The Astrophysical Journal Supplement Series 5510:, Kirchhoff's original notation was simply 5253:His proof first argued that for wavelength 4267:{\displaystyle P_{\rm {abs}}=P_{\rm {emt}}} 3018:is much greater than unity. Evaporation by 2875:are the body surface area and temperature, 2123:{\displaystyle x\equiv {\frac {h\nu }{kT}}} 8099:Kroemer, Herbert; Kittel, Charles (1980). 7234: 7188: 7177: 6108: 5901: 4681:{\displaystyle {\overline {\varepsilon }}} 1623:In unitless form, the maximum occurs when 675: 7577: 7305: 7200: 7198: 7196: 7083: 6732: 6722: 6436: 6338: 6300:"New 'Baby Picture' of Universe Unveiled" 6120: 6013:Tomokazu Kogure; Kam-Ching Leung (2007). 5925: 5745: 5729: 5664: 5655: 5649: 5618: 5609: 5593: 4720: 4704: 4703: 4697: 4668: 4666: 4634: 4610: 4601: 4583: 4559: 4550: 4530: 4529: 4523: 4499: 4483: 4482: 4476: 4440: 4420: 4348: 4342: 4334: 4328: 4315: 4309: 4251: 4250: 4230: 4229: 4223: 4169: 4159: 4158: 4153: 4143: 4127: 4126: 4120: 4090: 4088: 4063: 4061: 4032: 4022: 4021: 4001: 4000: 3994: 3972: 3971: 3965: 3928: 3922: 3921: 3908: 3902: 3901: 3878: 3868: 3867: 3861: 3832: 3820: 3799: 3790: 3749: 3748: 3743: 3712: 3711: 3705: 3674: 3650: 3630: 3605: 3600: 3582: 3575: 3574: 3568: 3520: 3502: 3496: 3495: 3485: 3462: 3461: 3444: 3443: 3437: 3410: 3403: 3402: 3396: 3378: 3371: 3370: 3364: 3342: 3337: 3296: 3290: 3289: 3276: 3270: 3269: 3237: 3236: 3230: 3101: 3063: 3050: 3041: 3035: 2966: 2957: 2944: 2931: 2925: 2880: 2843: 2838: 2825: 2798: 2792: 2768: 2755: 2742: 2736: 2656: 2649: 2621: 2617: 2612: 2599: 2594: 2580: 2566: 2542: 2526: 2520: 2486: 2481: 2461: 2438: 2418: 2398: 2365: 2344: 2338: 2320: 2297: 2274: 2243: 2233: 2223: 2214: 2192: 2182: 2171: 2165: 2153: 2143: 2135: 2100: 2092: 2066: 2060: 2042: 2031: 2025: 2024: 2012: 2007: 2001: 1962: 1956: 1936: 1927: 1917: 1905: 1895: 1888: 1876: 1866: 1858: 1838: 1793: 1787: 1757: 1730: 1702: 1688: 1653: 1635: 1629: 1605: 1600: 1592: 1583: 1558: 1552: 1524: 1518: 1493: 1487: 1441: 1422: 1406: 1391: 1389: 1357: 1348: 1342: 1337:, is a function only of the temperature: 1321: 1315: 1258: 1227: 1221: 1185: 1179: 1143: 1137: 1105: 1100: 1061: 1055: 1031: 1002: 976: 950: 924: 898: 876: 852: 814: 808: 764: 757: 747: 739: 728: 715: 697: 691: 528: 478: 455: 7702:Thermodynamics and statistical mechanics 7429:Atmospheric Radiation: Theoretical Basis 7004:Climate Change an Integrated Perspective 6980:. Taylor & Francis. pp. 10–11. 6595:"Emissivity Values for Common Materials" 6252:(3rd ed.). Wiley-IEEE. p. 58. 5794:< 0 indicates an approaching source. 5790:> 0 indicates a receding source, and 4804: 3214: 3144: 2554:{\displaystyle j^{\star }=\sigma T^{4},} 1826:{\displaystyle B_{\nu }(T)\cos(\theta )} 1174:, is related to the photon flux density 506: 450:this deviation is not so noticeable, as 356: 219: 8201: 8118:Tipler, Paul; Llewellyn, Ralph (2002). 8103:(2nd ed.). W. H. Freeman Company. 8058:"Temperatur und Entropie der Strahlung" 7865:(1930). "Thermodynamics of the Stars". 7333: 7321: 7166: 7142:. Princeton University Press. pp. 7060:, second edition, Elsevier, Amsterdam, 7030:"The Prebiotic Atmosphere of the Earth" 6856: 6854: 6852: 6697:Harris J, Benedict F; Benedict (1918). 6019:The astrophysics of emission-line stars 5941:Introduction to Astronomy and Cosmology 5882: 4103:{\displaystyle {\overline {\epsilon }}} 4076:{\displaystyle {\overline {\epsilon }}} 1088:{\displaystyle B_{\nu }(T)\cos \theta } 7841:Foundations of Radiation Hydrodynamics 7531: 7499: 7245: 7204: 6515:. Imperial College Press. p. 19. 6452:Landau, L. D.; E. M. Lifshitz (1996). 6160: 6137: 6075: 5889: 5721:) for the frequency in this equation. 1725:The approximate numerical solution is 1533:{\displaystyle \lambda _{\text{peak}}} 1330:{\displaystyle \lambda _{\text{peak}}} 871:at thermal equilibrium at temperature 7381: 7269: 6834:Iribarne, J.V., Godson, W.L. (1981). 6175:"§4.2.2: Calculation of Planck's law" 5803:cosmic microwave background radiation 5565:, which is a form of the second law. 395:cosmic microwave background radiation 367:cosmic microwave background radiation 327:material in the cavity (compare with 7: 7876:Müller-Kirsten, Harald J.W. (2013). 7785:Optical Coherence and Quantum Optics 7345: 6149: 5468:Kirchhoff's law of thermal radiation 4301: 4215: 4112: 3853: 3697: 3429: 3222: 3212:(energy/second) that the Sun emits: 3195:adiabatic contraction due to cooling 297:Kirchhoff's law of thermal radiation 7938:Radiative Processes in Astrophysics 7056:Wallace, J.M., Hobbs, P.V. (2006). 6298:Gannon, Megan (December 21, 2012). 6277:. New York: John Wiley & Sons. 2787:Applying the Stefan–Boltzmann law, 676:Planck's law of blackbody radiation 33:with its environment, emitted by a 8156:Color-to-Temperature demonstration 7488:"Über die Fraunhofer'schen Linien" 6797:"Heat Transfer and the Human Body" 5944:. J Wiley & Sons. p. 48. 4721: 4705: 4611: 4560: 4531: 4500: 4484: 4258: 4255: 4252: 4237: 4234: 4231: 4173: 4170: 4166: 4163: 4160: 4134: 4131: 4128: 4036: 4033: 4029: 4026: 4023: 4008: 4005: 4002: 3973: 3923: 3903: 3882: 3879: 3875: 3872: 3869: 3753: 3750: 3719: 3716: 3713: 3576: 3497: 3475: 3472: 3469: 3463: 3448: 3445: 3404: 3372: 3291: 3271: 3250: 3247: 3244: 3238: 3111: 3092: 3081: 3075: 2973: 2727:The human body radiates energy as 2584: 2420: 2240: 2230: 2225: 2013: 1606: 1596: 1593: 29:within, or surrounding, a body in 14: 8162:Cooling Mechanisms for Human Body 7490:[On Fraunhofer's lines]. 7320:(1896), personal letter cited by 7294:Mihalas & Weibel-Mihalas 1984 7034:Astrobiology: Future Perspectives 6977:Space physics and space astronomy 6225:10.1016/j.measurement.2019.02.084 3138:Planetary equilibrium temperature 3014:. Conduction is negligible – the 995:of the electromagnetic radiation; 646:is the absolute temperature, and 16:Thermal electromagnetic radiation 8264: 8252: 8240: 8228: 8216: 8204: 6621:"Emissivity of Common Materials" 5580:causes a shift in the frequency 5445:, and an increasing function of 3593:is the radius of the planet, and 3161:Incident radiation from its star 2915:, and the mid- and far-infrared 2709: 2698: 1833:over the frequency the radiance 1291: 8150:Calculating Blackbody Radiation 8122:(4th ed.). W. H. Freeman. 7479:, Physik Verlag, Mosbach/Baden. 6974:Michael D. Papagiannis (1972). 6899:Principles of Planetary Climate 4651:{\displaystyle \alpha =0.309\ } 1303:of wavelength or of frequency. 376:local thermodynamic equilibrium 148:most of the emission is in the 8189:Wolfram Demonstrations Project 7107:Kondepudi & Prigogine 1998 7068:, exercise 4.6, pages 119–120. 7036:. Springer. pp. 279–280. 5914:Kondepudi & Prigogine 1998 5244:was independent of the nature 4817:of such colors, shown here in 4464:Effective temperature of Earth 4434: 4422: 4207:radiative exchange equilibrium 3740: 3728: 3182:for planets with an atmosphere 2433:for all azimuthal angle (0 to 1977: 1971: 1820: 1814: 1805: 1799: 1673:{\displaystyle e^{x}(1-x/3)=1} 1661: 1641: 1450: 1428: 1276: 1264: 1245: 1233: 1203: 1191: 1161: 1149: 1122:{\displaystyle 1/\cos \theta } 1073: 1067: 839:is the spectral radiance (the 826: 820: 709: 703: 561:in the formalism now known as 1: 7925:P. Blakiston's Sons & Co. 7878:Basics of Statistical Physics 7839:; Weibel-Mihalas, B. (1984). 7584:Translated by Guthrie, F. as 7557:Annalen der Physik und Chemie 7456:The Genesis of Quantum Theory 6762:Am J Physiol Endocrinol Metab 5966:Annalen der Physik und Chemie 5801:. An example is found in the 4938:. The total absorption ratio 3586:{\displaystyle R_{\rm {E}}\,} 3414:{\displaystyle R_{\rm {S}}\,} 3382:{\displaystyle T_{\rm {S}}\,} 1744:{\displaystyle x\approx 2.82} 1209:{\displaystyle b_{\nu }(T,E)} 1167:{\displaystyle B_{\nu }(T,E)} 213:of radiative distribution of 7920:The Theory of Heat Radiation 7596:. Series 4, volume 20: 1–21. 7007:. Springer. pp. 52–55. 4673: 4661:With the average emissivity 4445: 4366: 4148: 4095: 4068: 3616:is the distance between the 2908:is the ambient temperature. 2888:{\displaystyle \varepsilon } 2393:By subsequently integrating 7923:. translated by Masius, M. 7755:The Quantum Theory of Light 7358:Mehra & Rechenberg 1982 7282:Rybicki & Lightman 1979 7132:Gillispie, Charles Coulston 6818:Journal de Physique (Paris) 6497:Rybicki & Lightman 1979 5994:Dustin (18 December 2018). 5578:relativistic Doppler effect 5393:, which may now be denoted 4759:cosmic microwave background 3982:{\displaystyle T_{\rm {E}}} 832:{\displaystyle B_{\nu }(T)} 589:. These quanta were called 183:state of cavity radiation. 8318: 7789:Cambridge University Press 7759:Cambridge University Press 7707:Courier Dover Publications 7656:Princeton University Press 6836:Atmospheric Thermodynamics 6774:10.1152/ajpendo.00562.2003 6512:The Physics of Solar Cells 6419:. 4th series (in German). 6357:10.1088/0067-0049/208/2/20 3841:{\displaystyle 4\pi R^{2}} 3135: 1716:{\displaystyle x=h\nu /kT} 1295: 679: 190: 8302:Electromagnetic radiation 8173:Blackbody Emission Applet 8038:10.1017/S0080456800031288 7699:Landsberg, P. T. (1990). 7370:Kirchhoff & 1862/1882 7360:, pp. 26, 28, 31, 39 6181:. Springer. p. 107. 3808:{\displaystyle \pi R^{2}} 3688:{\displaystyle 1-\alpha } 3421:is the radius of the Sun. 3355:Stefan–Boltzmann constant 3346:{\displaystyle \sigma \,} 3149:Earth's longwave thermal 2264:Stefan–Boltzmann constant 686:Planck's law states that 665:Stefan–Boltzmann constant 305:thermodynamic equilibrium 181:thermodynamic equilibrium 31:thermodynamic equilibrium 27:electromagnetic radiation 8084:10.1002/andp.18942880511 7868:Handbuch der Astrophysik 7579:10.1002/andp.18601850205 7459:. Nash, C.W. (transl.). 6640:Farzana, Abanty (2001). 6438:10.1002/andp.19013090310 6021:. Springer. p. 41. 5964:From (Kirchhoff, 1860) ( 603:Bose–Einstein statistics 154:electromagnetic spectrum 7908:Longmans, Green and Co. 7845:Oxford University Press 7817:. Vol. 1, part 1. 7725:Lavenda, Bernard Howard 7682:Oxford University Press 7606:Gessamelte Abhandlungen 7433:Oxford University Press 7416:Oxford University Press 6908:March 28, 2012, at the 6483:Encyclopædia Britannica 6111:, pp. 466–467, 478 5856:Sakuma–Hattori equation 5476:, for every wavelength 4896:Gustav Robert Kirchhoff 3658:{\displaystyle \alpha } 3638:{\displaystyle \alpha } 2469:{\displaystyle \theta } 2426:{\displaystyle \Omega } 1298:Wien's displacement law 1292:Wien's displacement law 1039:{\displaystyle \theta } 587:quantum electrodynamics 441:ultraviolet catastrophe 62:ultraviolet catastrophe 7593:Philosophical Magazine 7586:Kirchhoff, G. (1860). 6703:Proc Natl Acad Sci USA 6478:"Stefan-Boltzmann law" 6273:Huang, Kerson (1967). 6173:Joseph Caniou (1999). 5982:Philosophical Magazine 5902:Mandel & Wolf 1995 5780: 5680: 4830: 4729: 4682: 4652: 4622: 4571: 4511: 4454: 4389: 4268: 4183: 4104: 4077: 4046: 3983: 3938: 3842: 3809: 3763: 3689: 3659: 3639: 3610: 3587: 3537: 3415: 3383: 3347: 3306: 3220: 3154: 3122: 2984: 2889: 2861: 2781: 2676: 2555: 2498: 2497:{\displaystyle \pi /2} 2470: 2450: 2427: 2407: 2384: 2309: 2286: 2256: 2124: 2081: 1990: 1853:(units: power / ) is 1847: 1827: 1766: 1745: 1717: 1674: 1617: 1534: 1503: 1463: 1374: 1331: 1283: 1210: 1168: 1123: 1089: 1040: 1011: 985: 959: 933: 907: 885: 861: 833: 793: 599:Fermi–Dirac statistics 540: 513: 493: 492:{\displaystyle nh\nu } 467: 370: 286: 225: 133: 125: 65: 8287:Astrophysics concepts 7943:John Wiley & Sons 7733:John Wiley & Sons 7626:John Wiley & Sons 7306:Goody & Yung 1989 6724:10.1073/pnas.4.12.370 6509:Jenny Nelson (2002). 6393:"Blackbody Radiation" 6275:Statistical Mechanics 6121:Goody & Yung 1989 5781: 5681: 5439:at fixed temperature 4883:Helmholtz reciprocity 4840:Augustin-Jean Fresnel 4838:In his first memoir, 4808: 4730: 4690:effective temperature 4683: 4653: 4623: 4572: 4512: 4455: 4390: 4269: 4184: 4105: 4078: 4054:effective temperature 4047: 3984: 3939: 3843: 3810: 3764: 3690: 3660: 3645:of this energy where 3640: 3611: 3588: 3538: 3416: 3384: 3348: 3307: 3218: 3166:Earth's infrared glow 3148: 3123: 2994:, or 2000 kcal (food 2985: 2890: 2862: 2782: 2677: 2556: 2499: 2471: 2451: 2449:{\displaystyle 2\pi } 2428: 2413:over the solid angle 2408: 2385: 2310: 2287: 2257: 2125: 2082: 1991: 1848: 1828: 1767: 1746: 1718: 1675: 1618: 1535: 1504: 1502:{\displaystyle W_{0}} 1464: 1375: 1332: 1284: 1211: 1169: 1124: 1090: 1041: 1012: 986: 960: 934: 908: 886: 862: 834: 794: 541: 539:{\displaystyle h\nu } 510: 494: 468: 466:{\displaystyle h\nu } 433:equipartition theorem 360: 281:The temperature of a 280: 223: 170:effective temperature 162:ultraviolet radiation 131: 123: 105:temperature radiation 55: 8185:"Blackbody Spectrum" 7871:. 3, part 1: 63–255. 7705:(Reprint ed.). 6646:The Physics Factbook 6246:J. R. Mahan (2002). 5938:Ian Morison (2008). 5831:Infrared thermometer 5728: 5592: 5451:at fixed wavelength 4869:especially those of 4696: 4665: 4633: 4582: 4522: 4475: 4419: 4308: 4222: 4119: 4087: 4060: 3993: 3964: 3860: 3850:Stefan–Boltzmann law 3819: 3789: 3704: 3673: 3649: 3629: 3599: 3567: 3436: 3395: 3363: 3336: 3229: 3206:Stefan–Boltzmann law 3034: 3000:Basal metabolic rate 2924: 2879: 2791: 2735: 2565: 2519: 2506:Stefan–Boltzmann law 2480: 2460: 2437: 2417: 2397: 2319: 2296: 2273: 2134: 2091: 2000: 1857: 1837: 1786: 1778:Stefan–Boltzmann law 1765:{\displaystyle \nu } 1756: 1729: 1687: 1628: 1551: 1517: 1486: 1388: 1341: 1314: 1220: 1178: 1136: 1099: 1054: 1048:Lambert's cosine law 1030: 1001: 984:{\displaystyle \nu } 975: 949: 923: 897: 875: 860:{\displaystyle \nu } 851: 807: 690: 626:absolute temperature 618:Stefan–Boltzmann law 583:photoelectric effect 567:Wien's radiation law 527: 477: 454: 369:across the universe. 365:image (2012) of the 20:Black-body radiation 8164:– From Hyperphysics 8076:1894AnP...288..132W 7570:1860AnP...185..275K 7094:1999dpf..conf.....W 6936:1972Moon....5..161S 6861:NASA Sun Fact Sheet 6715:1918PNAS....4..370H 6619:Omega Engineering. 6593:Infrared Services. 6454:Statistical Physics 6429:1901AnP...309..553P 6349:2013ApJS..208...20B 6217:2019Meas..139..355M 6123:, pp. 482, 484 5972:vollkommen schwarze 5861:Terahertz radiation 5836:Photon polarization 5259:and at temperature 5045:. Again, the ratio 3933: 3913: 3609:{\displaystyle D\,} 3507: 3301: 3281: 2848: 2690:Human-body emission 2630: 2607: 2504:, we arrive at the 2017: 1380:where the constant 1308:per unit wavelength 891:. Units: power / . 867:radiation per unit 555:theoretical physics 423:Further explanation 211:spontaneous process 39:continuous spectrum 8178:2010-06-09 at the 8063:Annalen der Physik 7757:(third ed.). 7735:. pp. 41–42. 7412:Radiative Transfer 7258:Chandrasekhar 1950 7028:F. Selsis (2004). 6944:10.1007/BF00562111 6756:Levine, J (2004). 6416:Annalen der Physik 5871:Wien approximation 5851:Rayleigh–Jeans law 5776: 5676: 5563:Carnot's principle 5490:(For our notation 4831: 4825:, is known as the 4740:greenhouse effects 4735:or −18.8 °C. 4725: 4688:set to unity, the 4678: 4648: 4618: 4567: 4507: 4450: 4385: 4264: 4179: 4100: 4073: 4052:, is known as the 4042: 3979: 3934: 3917: 3897: 3838: 3805: 3759: 3685: 3655: 3635: 3606: 3583: 3533: 3491: 3411: 3379: 3343: 3302: 3285: 3265: 3221: 3155: 3118: 2980: 2885: 2857: 2834: 2777: 2672: 2608: 2590: 2551: 2494: 2466: 2456:) and polar angle 2446: 2423: 2403: 2380: 2308:{\displaystyle dA} 2305: 2285:{\displaystyle dI} 2282: 2252: 2120: 2077: 2003: 1986: 1843: 1823: 1762: 1741: 1713: 1670: 1613: 1530: 1511:Lambert W function 1499: 1459: 1370: 1327: 1279: 1206: 1164: 1119: 1085: 1036: 1007: 981: 967:Boltzmann constant 955: 929: 903: 881: 857: 829: 789: 536: 514: 489: 463: 389:, objects such as 371: 287: 226: 138:frequency spectrum 134: 126: 101:complete radiation 87:was introduced by 66: 58:Rayleigh–Jeans law 7891:978-981-4449-53-3 7742:978-0-471-54607-8 7475:a translation of 7442:978-0-19-510291-8 7408:Chandrasekhar, S. 7221:Schirrmacher 2001 7066:978-0-12-732951-2 7043:978-1-4020-2587-7 7014:978-0-7923-5996-8 6987:978-0-677-04000-4 6530:978-1-86094-340-9 6259:978-0-471-21270-6 6062:(Leipzig), 1899, 6028:978-0-387-34500-0 5951:978-0-470-03333-3 5821:Color temperature 5771: 5770: 5671: 5670: 5626: 4791:Tungsten filament 4719: 4692:of the Earth is: 4676: 4647: 4609: 4558: 4498: 4448: 4409: 4408: 4383: 4382: 4371: 4370: 4369: 4288: 4287: 4203: 4202: 4151: 4098: 4071: 3958: 3957: 3783: 3782: 3557: 3556: 3527: 3468: 3326: 3325: 3243: 3187:radioactive decay 3180:greenhouse effect 3107: 3096: 3091: 3074: 3044: 2972: 2960: 2947: 2934: 2801: 2771: 2758: 2745: 2406:{\displaystyle L} 2372: 2250: 2199: 2163: 2118: 2075: 2055: 1984: 1944: 1934: 1886: 1846:{\displaystyle L} 1591: 1561: 1527: 1454: 1404: 1365: 1351: 1324: 1010:{\displaystyle T} 958:{\displaystyle k} 932:{\displaystyle c} 906:{\displaystyle h} 884:{\displaystyle T} 784: 745: 417:quantum mechanics 399:Hawking radiation 329:emission spectrum 249:spectral radiance 207:thermal radiation 93:thermal radiation 8309: 8269: 8268: 8257: 8256: 8255: 8245: 8244: 8243: 8233: 8232: 8221: 8220: 8219: 8209: 8208: 8200: 8187:by Jeff Bryant, 8133: 8114: 8087: 8049: 8011: 7972: 7961:Schirrmacher, A. 7956: 7931:Rybicki, G. B.; 7927: 7910: 7900:Partington, J.R. 7895: 7882:World Scientific 7880:(2nd ed.). 7872: 7858: 7832: 7802: 7772: 7746: 7720: 7695: 7669: 7653: 7639: 7609: 7597: 7583: 7581: 7543: 7537: 7529: 7511: 7505: 7497: 7474: 7446: 7431:(2nd ed.). 7419: 7394: 7391: 7385: 7379: 7373: 7367: 7361: 7355: 7349: 7348:, pp. 8, 29 7343: 7337: 7331: 7325: 7315: 7309: 7308:, pp. 27–28 7303: 7297: 7291: 7285: 7284:, pp. 16–17 7279: 7273: 7267: 7261: 7255: 7249: 7243: 7237: 7232: 7223: 7218: 7207: 7202: 7191: 7186: 7180: 7175: 7169: 7164: 7158: 7157: 7141: 7128: 7122: 7119:Partington, J.R. 7116: 7110: 7104: 7098: 7097: 7087: 7085:astro-ph/9903232 7075: 7069: 7054: 7048: 7047: 7025: 7019: 7018: 6998: 6992: 6991: 6971: 6965: 6962: 6956: 6955: 6930:(1–2): 161–178. 6919: 6913: 6896: 6890: 6889: 6869: 6863: 6858: 6847: 6832: 6826: 6825: 6813: 6807: 6806: 6804: 6803: 6792: 6786: 6785: 6768:(5): E675–E685. 6753: 6747: 6746: 6736: 6726: 6694: 6688: 6687: 6685: 6684: 6678: 6672:. Archived from 6671: 6662: 6656: 6655: 6653: 6652: 6637: 6631: 6630: 6628: 6627: 6616: 6610: 6609: 6607: 6606: 6597:. Archived from 6590: 6584: 6582: 6570: 6564: 6563: 6561: 6559: 6541: 6535: 6534: 6506: 6500: 6494: 6488: 6487: 6474: 6468: 6467: 6449: 6443: 6442: 6440: 6403: 6397: 6396: 6389: 6383: 6382: 6375: 6369: 6368: 6342: 6321: 6315: 6314: 6312: 6310: 6295: 6289: 6288: 6270: 6264: 6263: 6243: 6237: 6236: 6199: 6193: 6192: 6170: 6164: 6158: 6152: 6147: 6141: 6135: 6124: 6118: 6112: 6106: 6100: 6084: 6078: 6073: 6067: 6056: 6050: 6045:(Berlin), 1893, 6039: 6033: 6032: 6010: 6004: 6003: 5991: 5985: 5962: 5956: 5955: 5935: 5929: 5923: 5917: 5911: 5905: 5899: 5893: 5887: 5785: 5783: 5782: 5777: 5772: 5769: 5758: 5747: 5746: 5738: 5685: 5683: 5682: 5677: 5672: 5669: 5668: 5659: 5654: 5653: 5638: 5637: 5627: 5619: 5610: 5602: 5559: 5538: 5515: 5509: 5487: 5479: 5475: 5462: 5456: 5450: 5444: 5438: 5432: 5412: 5392: 5377: 5342: 5336: 5321: 5294: 5279: 5264: 5258: 5249: 5243: 5208: 5202: 5198: 5185: 5149: 5118: 5079: 5044: 5025: 5006: 5000: 4985: 4958: 4952: 4937: 4931: 4925: 4907: 4890:Gustav Kirchhoff 4734: 4732: 4731: 4726: 4724: 4717: 4710: 4709: 4708: 4687: 4685: 4684: 4679: 4677: 4669: 4657: 4655: 4654: 4649: 4645: 4627: 4625: 4624: 4619: 4614: 4607: 4606: 4605: 4576: 4574: 4573: 4568: 4563: 4556: 4555: 4554: 4536: 4535: 4534: 4516: 4514: 4513: 4508: 4503: 4496: 4489: 4488: 4487: 4459: 4457: 4456: 4451: 4449: 4441: 4403: 4394: 4392: 4391: 4386: 4384: 4381: 4373: 4372: 4362: 4361: 4350: 4349: 4347: 4346: 4336: 4335: 4333: 4332: 4320: 4319: 4302: 4298: 4282: 4273: 4271: 4270: 4265: 4263: 4262: 4261: 4242: 4241: 4240: 4216: 4197: 4188: 4186: 4185: 4180: 4178: 4177: 4176: 4152: 4144: 4139: 4138: 4137: 4113: 4109: 4107: 4106: 4101: 4099: 4091: 4082: 4080: 4079: 4074: 4072: 4064: 4051: 4049: 4048: 4043: 4041: 4040: 4039: 4013: 4012: 4011: 3988: 3986: 3985: 3980: 3978: 3977: 3976: 3952: 3943: 3941: 3940: 3935: 3932: 3927: 3926: 3912: 3907: 3906: 3887: 3886: 3885: 3854: 3847: 3845: 3844: 3839: 3837: 3836: 3814: 3812: 3811: 3806: 3804: 3803: 3777: 3768: 3766: 3765: 3760: 3758: 3757: 3756: 3724: 3723: 3722: 3698: 3694: 3692: 3691: 3686: 3664: 3662: 3661: 3656: 3644: 3642: 3641: 3636: 3615: 3613: 3612: 3607: 3592: 3590: 3589: 3584: 3581: 3580: 3579: 3551: 3542: 3540: 3539: 3534: 3532: 3528: 3526: 3525: 3524: 3508: 3506: 3501: 3500: 3486: 3480: 3479: 3478: 3466: 3453: 3452: 3451: 3430: 3420: 3418: 3417: 3412: 3409: 3408: 3407: 3388: 3386: 3385: 3380: 3377: 3376: 3375: 3352: 3350: 3349: 3344: 3320: 3311: 3309: 3308: 3303: 3300: 3295: 3294: 3280: 3275: 3274: 3255: 3254: 3253: 3241: 3223: 3208:gives the total 3127: 3125: 3124: 3119: 3114: 3105: 3097: 3095: 3089: 3084: 3072: 3071: 3070: 3051: 3046: 3045: 3042: 2989: 2987: 2986: 2981: 2976: 2970: 2962: 2961: 2958: 2949: 2948: 2945: 2936: 2935: 2932: 2914: 2907: 2894: 2892: 2891: 2886: 2874: 2870: 2866: 2864: 2863: 2858: 2853: 2849: 2847: 2842: 2830: 2829: 2803: 2802: 2799: 2786: 2784: 2783: 2778: 2773: 2772: 2769: 2760: 2759: 2756: 2747: 2746: 2743: 2713: 2702: 2681: 2679: 2678: 2673: 2629: 2625: 2616: 2606: 2598: 2560: 2558: 2557: 2552: 2547: 2546: 2531: 2530: 2514: 2503: 2501: 2500: 2495: 2490: 2475: 2473: 2472: 2467: 2455: 2453: 2452: 2447: 2432: 2430: 2429: 2424: 2412: 2410: 2409: 2404: 2389: 2387: 2386: 2381: 2373: 2371: 2370: 2369: 2356: 2345: 2343: 2342: 2314: 2312: 2311: 2306: 2291: 2289: 2288: 2283: 2261: 2259: 2258: 2253: 2251: 2249: 2248: 2247: 2238: 2237: 2224: 2222: 2221: 2200: 2198: 2197: 2196: 2187: 2186: 2176: 2175: 2166: 2164: 2159: 2158: 2157: 2144: 2129: 2127: 2126: 2121: 2119: 2117: 2109: 2101: 2086: 2084: 2083: 2078: 2076: 2071: 2070: 2061: 2056: 2054: 2047: 2046: 2036: 2035: 2026: 2016: 2011: 1995: 1993: 1992: 1987: 1985: 1980: 1963: 1961: 1960: 1945: 1937: 1935: 1933: 1932: 1931: 1922: 1921: 1911: 1910: 1909: 1900: 1899: 1889: 1887: 1882: 1881: 1880: 1867: 1852: 1850: 1849: 1844: 1832: 1830: 1829: 1824: 1798: 1797: 1773: 1771: 1769: 1768: 1763: 1750: 1748: 1747: 1742: 1724: 1722: 1720: 1719: 1714: 1706: 1681: 1679: 1677: 1676: 1671: 1657: 1640: 1639: 1622: 1620: 1619: 1614: 1609: 1604: 1599: 1589: 1588: 1587: 1563: 1562: 1559: 1543: 1539: 1537: 1536: 1531: 1529: 1528: 1525: 1508: 1506: 1505: 1500: 1498: 1497: 1481: 1479: 1476: 1473: 1468: 1466: 1465: 1460: 1455: 1453: 1449: 1448: 1427: 1426: 1407: 1405: 1400: 1392: 1379: 1377: 1376: 1371: 1366: 1358: 1353: 1352: 1349: 1336: 1334: 1333: 1328: 1326: 1325: 1322: 1288: 1286: 1285: 1280: 1263: 1262: 1232: 1231: 1215: 1213: 1212: 1207: 1190: 1189: 1173: 1171: 1170: 1165: 1148: 1147: 1128: 1126: 1125: 1120: 1109: 1094: 1092: 1091: 1086: 1066: 1065: 1045: 1043: 1042: 1037: 1017:is the absolute 1016: 1014: 1013: 1008: 990: 988: 987: 982: 964: 962: 961: 956: 938: 936: 935: 930: 912: 910: 909: 904: 890: 888: 887: 882: 866: 864: 863: 858: 838: 836: 835: 830: 819: 818: 798: 796: 795: 790: 785: 783: 776: 775: 768: 748: 746: 744: 743: 734: 733: 732: 716: 702: 701: 662: 661: 659: 656: 638:is given, where 637: 575:electromagnetism 545: 543: 542: 537: 498: 496: 495: 490: 472: 470: 469: 464: 411: 316:cavity radiation 269: 265: 261: 174:visible spectrum 146:room temperature 97:cavity radiation 89:Gustav Kirchhoff 8317: 8316: 8312: 8311: 8310: 8308: 8307: 8306: 8277: 8276: 8275: 8263: 8253: 8251: 8241: 8239: 8227: 8217: 8215: 8203: 8195: 8180:Wayback Machine 8140: 8130: 8117: 8111: 8101:Thermal Physics 8098: 8095: 8093:Further reading 8090: 8052: 8014: 7975: 7959: 7953: 7933:Lightman, A. P. 7930: 7913: 7898: 7892: 7875: 7861: 7855: 7835: 7829: 7819:Springer-Verlag 7805: 7799: 7775: 7769: 7749: 7743: 7723: 7717: 7698: 7692: 7672: 7666: 7642: 7636: 7612: 7600: 7585: 7546: 7530: 7514: 7498: 7482: 7471: 7449: 7443: 7422: 7406: 7402: 7397: 7392: 7388: 7380: 7376: 7368: 7364: 7356: 7352: 7344: 7340: 7332: 7328: 7316: 7312: 7304: 7300: 7292: 7288: 7280: 7276: 7268: 7264: 7256: 7252: 7244: 7240: 7235:Kirchhoff 1860c 7233: 7226: 7219: 7210: 7203: 7194: 7189:Kirchhoff 1860b 7187: 7183: 7178:Kirchhoff 1860a 7176: 7172: 7165: 7161: 7154: 7130: 7129: 7125: 7121:(1949), p. 466. 7117: 7113: 7105: 7101: 7077: 7076: 7072: 7055: 7051: 7044: 7027: 7026: 7022: 7015: 7000: 6999: 6995: 6988: 6973: 6972: 6968: 6963: 6959: 6921: 6920: 6916: 6910:Wayback Machine 6897: 6893: 6886: 6871: 6870: 6866: 6859: 6850: 6833: 6829: 6815: 6814: 6810: 6801: 6799: 6795:DrPhysics.com. 6794: 6793: 6789: 6755: 6754: 6750: 6696: 6695: 6691: 6682: 6680: 6676: 6669: 6664: 6663: 6659: 6650: 6648: 6639: 6638: 6634: 6625: 6623: 6618: 6617: 6613: 6604: 6602: 6592: 6591: 6587: 6573:Nave, Dr. Rod. 6572: 6571: 6567: 6557: 6555: 6543: 6542: 6538: 6531: 6508: 6507: 6503: 6495: 6491: 6476: 6475: 6471: 6464: 6451: 6450: 6446: 6405: 6404: 6400: 6391: 6390: 6386: 6377: 6376: 6372: 6323: 6322: 6318: 6308: 6306: 6297: 6296: 6292: 6285: 6272: 6271: 6267: 6260: 6245: 6244: 6240: 6201: 6200: 6196: 6189: 6172: 6171: 6167: 6159: 6155: 6148: 6144: 6136: 6127: 6119: 6115: 6109:Partington 1949 6107: 6103: 6085: 6081: 6074: 6070: 6057: 6053: 6040: 6036: 6029: 6012: 6011: 6007: 5993: 5992: 5988: 5963: 5959: 5952: 5937: 5936: 5932: 5924: 5920: 5912: 5908: 5900: 5896: 5888: 5884: 5880: 5875: 5811: 5759: 5748: 5731: 5726: 5725: 5660: 5645: 5611: 5595: 5590: 5589: 5574: 5549: 5541: 5528: 5520: 5511: 5499: 5491: 5485: 5481: 5477: 5473: 5470:can be stated: 5458: 5452: 5446: 5440: 5434: 5422: 5414: 5402: 5394: 5379: 5344: 5338: 5323: 5296: 5281: 5266: 5260: 5254: 5245: 5210: 5204: 5200: 5194: 5152: 5124: 5085: 5046: 5027: 5008: 5002: 4987: 4960: 4954: 4939: 4933: 4932:at temperature 4927: 4912: 4903: 4892: 4866:Balfour Stewart 4862: 4860:Balfour Stewart 4836: 4827:Planckian locus 4788: 4755: 4699: 4694: 4693: 4663: 4662: 4631: 4630: 4597: 4580: 4579: 4546: 4525: 4520: 4519: 4478: 4473: 4472: 4466: 4417: 4416: 4401: 4374: 4351: 4338: 4337: 4324: 4311: 4306: 4305: 4297: 4291: 4280: 4246: 4225: 4220: 4219: 4195: 4154: 4122: 4117: 4116: 4085: 4084: 4058: 4057: 4017: 3996: 3991: 3990: 3967: 3962: 3961: 3950: 3863: 3858: 3857: 3828: 3817: 3816: 3795: 3787: 3786: 3775: 3744: 3707: 3702: 3701: 3671: 3670: 3647: 3646: 3627: 3626: 3623: 3620:and the planet. 3597: 3596: 3570: 3565: 3564: 3549: 3516: 3509: 3487: 3481: 3457: 3439: 3434: 3433: 3424: 3398: 3393: 3392: 3366: 3361: 3360: 3334: 3333: 3318: 3232: 3227: 3226: 3140: 3134: 3085: 3059: 3052: 3037: 3032: 3031: 3026:Application of 2953: 2940: 2927: 2922: 2921: 2912: 2906: 2900: 2877: 2876: 2872: 2868: 2821: 2820: 2816: 2794: 2789: 2788: 2764: 2751: 2738: 2733: 2732: 2725: 2724: 2723: 2722: 2721: 2714: 2705: 2704: 2703: 2692: 2687: 2563: 2562: 2538: 2522: 2517: 2516: 2509: 2478: 2477: 2458: 2457: 2435: 2434: 2415: 2414: 2395: 2394: 2361: 2357: 2346: 2334: 2317: 2316: 2294: 2293: 2271: 2270: 2239: 2229: 2228: 2210: 2188: 2178: 2177: 2167: 2149: 2145: 2132: 2131: 2110: 2102: 2089: 2088: 2062: 2038: 2037: 2027: 1998: 1997: 1964: 1952: 1923: 1913: 1912: 1901: 1891: 1890: 1872: 1868: 1855: 1854: 1835: 1834: 1789: 1784: 1783: 1782:By integrating 1780: 1754: 1753: 1752: 1727: 1726: 1685: 1684: 1683: 1631: 1626: 1625: 1624: 1579: 1554: 1549: 1548: 1541: 1520: 1515: 1514: 1489: 1484: 1483: 1477: 1474: 1471: 1469: 1437: 1418: 1411: 1393: 1386: 1385: 1344: 1339: 1338: 1317: 1312: 1311: 1300: 1294: 1254: 1223: 1218: 1217: 1181: 1176: 1175: 1139: 1134: 1133: 1097: 1096: 1057: 1052: 1051: 1028: 1027: 1024: 999: 998: 973: 972: 947: 946: 921: 920: 915:Planck constant 895: 894: 873: 872: 849: 848: 810: 805: 804: 753: 752: 735: 724: 717: 693: 688: 687: 684: 678: 673: 657: 654: 652: 647: 629: 525: 524: 475: 474: 452: 451: 425: 409: 380:Kirchhoff's Law 272:blackbody curve 267: 263: 259: 195: 189: 118: 113: 17: 12: 11: 5: 8315: 8313: 8305: 8304: 8299: 8294: 8289: 8279: 8278: 8274: 8273: 8261: 8249: 8237: 8225: 8213: 8193: 8192: 8182: 8170: 8165: 8159: 8158:at Academo.org 8153: 8147: 8139: 8138:External links 8136: 8135: 8134: 8128: 8120:Modern Physics 8115: 8109: 8094: 8091: 8089: 8088: 8070:(5): 132–165. 8050: 8012: 7992:10.1086/351669 7986:(4): 565–600. 7973: 7957: 7951: 7928: 7911: 7896: 7890: 7873: 7859: 7853: 7833: 7827: 7811:Rechenberg, H. 7803: 7797: 7773: 7767: 7747: 7741: 7721: 7715: 7696: 7690: 7670: 7664: 7640: 7634: 7610: 7598: 7564:(2): 275–301. 7544: 7512: 7480: 7469: 7447: 7441: 7423:Goody, R. M.; 7420: 7403: 7401: 7398: 7396: 7395: 7386: 7374: 7362: 7350: 7338: 7326: 7310: 7298: 7286: 7274: 7262: 7250: 7238: 7224: 7208: 7192: 7181: 7170: 7159: 7152: 7123: 7111: 7099: 7070: 7049: 7042: 7020: 7013: 6993: 6986: 6966: 6957: 6914: 6891: 6884: 6864: 6848: 6827: 6808: 6787: 6748: 6689: 6657: 6632: 6611: 6585: 6565: 6536: 6529: 6501: 6489: 6469: 6462: 6444: 6423:(3): 553–563. 6398: 6384: 6370: 6316: 6290: 6283: 6265: 6258: 6238: 6194: 6187: 6165: 6153: 6142: 6125: 6113: 6101: 6079: 6068: 6051: 6034: 6027: 6005: 5986: 5974:, oder kürzer 5957: 5950: 5930: 5926:Landsberg 1990 5918: 5906: 5894: 5881: 5879: 5876: 5874: 5873: 5868: 5863: 5858: 5853: 5848: 5843: 5838: 5833: 5828: 5823: 5818: 5812: 5810: 5807: 5775: 5768: 5765: 5762: 5757: 5754: 5751: 5744: 5741: 5737: 5734: 5706:= π) or away ( 5700:speed of light 5675: 5667: 5663: 5658: 5652: 5648: 5644: 5641: 5636: 5633: 5630: 5625: 5622: 5617: 5614: 5608: 5605: 5601: 5598: 5573: 5572:Doppler effect 5570: 5545: 5524: 5495: 5483: 5418: 5398: 5322:is again just 5007:is denoted by 4891: 4888: 4871:Pierre Prevost 4861: 4858: 4835: 4832: 4787: 4784: 4754: 4751: 4747:solar constant 4723: 4716: 4713: 4707: 4702: 4675: 4672: 4659: 4658: 4644: 4641: 4638: 4628: 4617: 4613: 4604: 4600: 4596: 4593: 4590: 4587: 4577: 4566: 4562: 4553: 4549: 4545: 4542: 4539: 4533: 4528: 4517: 4506: 4502: 4495: 4492: 4486: 4481: 4465: 4462: 4447: 4444: 4439: 4436: 4433: 4430: 4427: 4424: 4407: 4406: 4397: 4395: 4380: 4377: 4368: 4365: 4360: 4357: 4354: 4345: 4341: 4331: 4327: 4323: 4318: 4314: 4295: 4286: 4285: 4276: 4274: 4260: 4257: 4254: 4249: 4245: 4239: 4236: 4233: 4228: 4211:radiant energy 4205:For a body in 4201: 4200: 4191: 4189: 4175: 4172: 4168: 4165: 4162: 4157: 4150: 4147: 4142: 4136: 4133: 4130: 4125: 4097: 4094: 4070: 4067: 4038: 4035: 4031: 4028: 4025: 4020: 4016: 4010: 4007: 4004: 3999: 3975: 3970: 3956: 3955: 3946: 3944: 3931: 3925: 3920: 3916: 3911: 3905: 3900: 3896: 3893: 3890: 3884: 3881: 3877: 3874: 3871: 3866: 3835: 3831: 3827: 3824: 3802: 3798: 3794: 3781: 3780: 3771: 3769: 3755: 3752: 3747: 3742: 3739: 3736: 3733: 3730: 3727: 3721: 3718: 3715: 3710: 3684: 3681: 3678: 3654: 3634: 3622: 3621: 3604: 3594: 3578: 3573: 3561: 3555: 3554: 3545: 3543: 3531: 3523: 3519: 3515: 3512: 3505: 3499: 3494: 3490: 3484: 3477: 3474: 3471: 3465: 3460: 3456: 3450: 3447: 3442: 3423: 3422: 3406: 3401: 3390: 3374: 3369: 3358: 3341: 3330: 3324: 3323: 3314: 3312: 3299: 3293: 3288: 3284: 3279: 3273: 3268: 3264: 3261: 3258: 3252: 3249: 3246: 3240: 3235: 3199: 3198: 3183: 3176: 3169: 3162: 3136:Main article: 3133: 3130: 3117: 3113: 3110: 3104: 3100: 3094: 3088: 3083: 3080: 3077: 3069: 3066: 3062: 3058: 3055: 3049: 3040: 3016:Nusselt number 2979: 2975: 2969: 2965: 2956: 2952: 2943: 2939: 2930: 2904: 2884: 2856: 2852: 2846: 2841: 2837: 2833: 2828: 2824: 2819: 2815: 2812: 2809: 2806: 2797: 2776: 2767: 2763: 2754: 2750: 2741: 2715: 2708: 2707: 2706: 2697: 2696: 2695: 2694: 2693: 2691: 2688: 2686: 2683: 2671: 2668: 2665: 2662: 2659: 2655: 2652: 2648: 2645: 2642: 2639: 2636: 2633: 2628: 2624: 2620: 2615: 2611: 2605: 2602: 2597: 2593: 2589: 2586: 2583: 2579: 2576: 2573: 2570: 2550: 2545: 2541: 2537: 2534: 2529: 2525: 2493: 2489: 2485: 2465: 2445: 2442: 2422: 2402: 2379: 2376: 2368: 2364: 2360: 2355: 2352: 2349: 2341: 2337: 2333: 2330: 2327: 2324: 2304: 2301: 2281: 2278: 2246: 2242: 2236: 2232: 2227: 2220: 2217: 2213: 2209: 2206: 2203: 2195: 2191: 2185: 2181: 2174: 2170: 2162: 2156: 2152: 2148: 2142: 2139: 2116: 2113: 2108: 2105: 2099: 2096: 2074: 2069: 2065: 2059: 2053: 2050: 2045: 2041: 2034: 2030: 2023: 2020: 2015: 2010: 2006: 1983: 1979: 1976: 1973: 1970: 1967: 1959: 1955: 1951: 1948: 1943: 1940: 1930: 1926: 1920: 1916: 1908: 1904: 1898: 1894: 1885: 1879: 1875: 1871: 1865: 1862: 1842: 1822: 1819: 1816: 1813: 1810: 1807: 1804: 1801: 1796: 1792: 1779: 1776: 1761: 1740: 1737: 1734: 1712: 1709: 1705: 1701: 1698: 1695: 1692: 1669: 1666: 1663: 1660: 1656: 1652: 1649: 1646: 1643: 1638: 1634: 1612: 1608: 1603: 1598: 1595: 1586: 1582: 1578: 1575: 1572: 1569: 1566: 1557: 1523: 1496: 1492: 1458: 1452: 1447: 1444: 1440: 1436: 1433: 1430: 1425: 1421: 1417: 1414: 1410: 1403: 1399: 1396: 1369: 1364: 1361: 1356: 1347: 1320: 1296:Main article: 1293: 1290: 1278: 1275: 1272: 1269: 1266: 1261: 1257: 1253: 1250: 1247: 1244: 1241: 1238: 1235: 1230: 1226: 1205: 1202: 1199: 1196: 1193: 1188: 1184: 1163: 1160: 1157: 1154: 1151: 1146: 1142: 1118: 1115: 1112: 1108: 1104: 1084: 1081: 1078: 1075: 1072: 1069: 1064: 1060: 1035: 1023: 1022: 1006: 996: 980: 970: 954: 944: 941:speed of light 928: 918: 902: 892: 880: 856: 828: 825: 822: 817: 813: 801: 788: 782: 779: 774: 771: 767: 763: 760: 756: 751: 742: 738: 731: 727: 723: 720: 714: 711: 708: 705: 700: 696: 680:Main article: 677: 674: 672: 669: 595:gas of photons 571:thermodynamics 535: 532: 488: 485: 482: 462: 459: 446:In the longer 424: 421: 191:Main article: 188: 185: 152:region of the 117: 114: 112: 109: 15: 13: 10: 9: 6: 4: 3: 2: 8314: 8303: 8300: 8298: 8297:Heat transfer 8295: 8293: 8290: 8288: 8285: 8284: 8282: 8272: 8267: 8262: 8260: 8250: 8248: 8238: 8236: 8231: 8226: 8224: 8214: 8212: 8207: 8202: 8198: 8190: 8186: 8183: 8181: 8177: 8174: 8171: 8169: 8166: 8163: 8160: 8157: 8154: 8151: 8148: 8145: 8142: 8141: 8137: 8131: 8129:0-7167-4345-0 8125: 8121: 8116: 8112: 8110:0-7167-1088-9 8106: 8102: 8097: 8096: 8092: 8085: 8081: 8077: 8073: 8069: 8065: 8064: 8059: 8055: 8051: 8047: 8043: 8039: 8035: 8031: 8027: 8026: 8021: 8017: 8013: 8009: 8005: 8001: 7997: 7993: 7989: 7985: 7981: 7980: 7974: 7970: 7966: 7962: 7958: 7954: 7952:0-471-82759-2 7948: 7944: 7940: 7939: 7934: 7929: 7926: 7922: 7921: 7916: 7912: 7909: 7905: 7901: 7897: 7893: 7887: 7883: 7879: 7874: 7870: 7869: 7864: 7860: 7856: 7854:0-19-503437-6 7850: 7846: 7842: 7838: 7834: 7830: 7828:0-387-90642-8 7824: 7820: 7816: 7812: 7808: 7804: 7800: 7798:0-521-41711-2 7794: 7790: 7786: 7782: 7778: 7774: 7770: 7768:0-19-850177-3 7764: 7760: 7756: 7752: 7748: 7744: 7738: 7734: 7730: 7726: 7722: 7718: 7716:0-486-66493-7 7712: 7708: 7704: 7703: 7697: 7693: 7691:0-19-502383-8 7687: 7683: 7679: 7675: 7671: 7667: 7665:0-691-01206-7 7661: 7657: 7652: 7651: 7645: 7641: 7637: 7635:0-471-97393-9 7631: 7627: 7623: 7619: 7618:Prigogine, I. 7615: 7614:Kondepudi, D. 7611: 7607: 7603: 7602:Kirchhoff, G. 7599: 7595: 7594: 7589: 7580: 7575: 7571: 7567: 7563: 7559: 7558: 7553: 7549: 7548:Kirchhoff, G. 7545: 7541: 7535: 7527: 7526: 7521: 7517: 7516:Kirchhoff, G. 7513: 7509: 7503: 7495: 7494: 7489: 7485: 7484:Kirchhoff, G. 7481: 7478: 7472: 7470:0-262-08047-8 7466: 7462: 7458: 7457: 7452: 7448: 7444: 7438: 7434: 7430: 7426: 7421: 7417: 7413: 7409: 7405: 7404: 7399: 7390: 7387: 7383: 7378: 7375: 7372:, p. 573 7371: 7366: 7363: 7359: 7354: 7351: 7347: 7342: 7339: 7335: 7330: 7327: 7323: 7319: 7314: 7311: 7307: 7302: 7299: 7296:, p. 328 7295: 7290: 7287: 7283: 7278: 7275: 7271: 7266: 7263: 7259: 7254: 7251: 7247: 7242: 7239: 7236: 7231: 7229: 7225: 7222: 7217: 7215: 7213: 7209: 7206: 7201: 7199: 7197: 7193: 7190: 7185: 7182: 7179: 7174: 7171: 7168: 7163: 7160: 7155: 7153:0-691-02350-6 7149: 7145: 7140: 7139: 7133: 7127: 7124: 7120: 7115: 7112: 7108: 7103: 7100: 7095: 7091: 7086: 7081: 7074: 7071: 7067: 7063: 7059: 7053: 7050: 7045: 7039: 7035: 7031: 7024: 7021: 7016: 7010: 7006: 7005: 6997: 6994: 6989: 6983: 6979: 6978: 6970: 6967: 6961: 6958: 6953: 6949: 6945: 6941: 6937: 6933: 6929: 6925: 6918: 6915: 6911: 6907: 6904: 6900: 6895: 6892: 6887: 6885:0-7503-0815-X 6881: 6877: 6876: 6868: 6865: 6862: 6857: 6855: 6853: 6849: 6845: 6844:90-277-1296-4 6841: 6837: 6831: 6828: 6823: 6819: 6812: 6809: 6798: 6791: 6788: 6783: 6779: 6775: 6771: 6767: 6763: 6759: 6752: 6749: 6744: 6740: 6735: 6730: 6725: 6720: 6716: 6712: 6709:(12): 370–3. 6708: 6704: 6700: 6693: 6690: 6679:on 2006-09-02 6675: 6668: 6661: 6658: 6647: 6643: 6636: 6633: 6622: 6615: 6612: 6601:on 2007-06-25 6600: 6596: 6589: 6586: 6580: 6576: 6569: 6566: 6554: 6550: 6546: 6540: 6537: 6532: 6526: 6522: 6518: 6514: 6513: 6505: 6502: 6498: 6493: 6490: 6485: 6484: 6479: 6473: 6470: 6465: 6463:0-521-65314-2 6459: 6455: 6448: 6445: 6439: 6434: 6430: 6426: 6422: 6418: 6417: 6412: 6408: 6402: 6399: 6394: 6388: 6385: 6380: 6374: 6371: 6366: 6362: 6358: 6354: 6350: 6346: 6341: 6336: 6332: 6328: 6320: 6317: 6305: 6301: 6294: 6291: 6286: 6284:0-471-81518-7 6280: 6276: 6269: 6266: 6261: 6255: 6251: 6250: 6242: 6239: 6234: 6230: 6226: 6222: 6218: 6214: 6210: 6206: 6198: 6195: 6190: 6188:0-7923-8532-2 6184: 6180: 6176: 6169: 6166: 6162: 6157: 6154: 6151: 6146: 6143: 6139: 6134: 6132: 6130: 6126: 6122: 6117: 6114: 6110: 6105: 6102: 6099: 6096: 6092: 6088: 6083: 6080: 6077: 6072: 6069: 6065: 6061: 6055: 6052: 6048: 6044: 6038: 6035: 6030: 6024: 6020: 6016: 6009: 6006: 6001: 5997: 5990: 5987: 5983: 5979: 5975: 5971: 5967: 5961: 5958: 5953: 5947: 5943: 5942: 5934: 5931: 5928:, Chapter 13. 5927: 5922: 5919: 5916:, Chapter 11. 5915: 5910: 5907: 5904:, Chapter 13. 5903: 5898: 5895: 5891: 5886: 5883: 5877: 5872: 5869: 5867: 5864: 5862: 5859: 5857: 5854: 5852: 5849: 5847: 5844: 5842: 5839: 5837: 5834: 5832: 5829: 5827: 5824: 5822: 5819: 5817: 5814: 5813: 5808: 5806: 5804: 5800: 5795: 5793: 5789: 5773: 5766: 5763: 5760: 5755: 5752: 5749: 5742: 5739: 5735: 5732: 5722: 5720: 5715: 5713: 5709: 5705: 5701: 5697: 5693: 5689: 5673: 5665: 5661: 5656: 5650: 5646: 5642: 5639: 5634: 5631: 5628: 5623: 5620: 5615: 5612: 5606: 5603: 5599: 5596: 5587: 5583: 5579: 5571: 5569: 5566: 5564: 5557: 5553: 5548: 5544: 5536: 5532: 5527: 5523: 5517: 5514: 5507: 5503: 5498: 5494: 5489: 5469: 5464: 5461: 5455: 5449: 5443: 5437: 5430: 5426: 5421: 5417: 5410: 5406: 5401: 5397: 5390: 5386: 5382: 5378:was equal to 5375: 5371: 5367: 5363: 5359: 5355: 5351: 5347: 5341: 5334: 5330: 5326: 5319: 5315: 5311: 5307: 5303: 5299: 5292: 5288: 5284: 5277: 5273: 5269: 5263: 5257: 5251: 5248: 5241: 5237: 5233: 5229: 5225: 5221: 5217: 5213: 5207: 5197: 5191: 5187: 5183: 5179: 5175: 5171: 5167: 5163: 5159: 5155: 5147: 5143: 5139: 5135: 5131: 5127: 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483: 480: 460: 457: 449: 444: 442: 438: 437:heat capacity 434: 430: 422: 420: 418: 413: 406: 404: 400: 396: 392: 388: 383: 381: 378:still follow 377: 368: 364: 359: 355: 353: 348: 343: 341: 337: 332: 330: 325: 321: 317: 313: 308: 306: 302: 298: 293: 284: 279: 275: 273: 257: 252: 250: 244: 242: 238: 233: 231: 222: 218: 216: 212: 208: 204: 203:absolute zero 200: 194: 186: 184: 182: 177: 175: 171: 167: 163: 159: 155: 151: 147: 143: 139: 130: 122: 115: 110: 108: 106: 102: 98: 94: 90: 86: 81: 79: 75: 70: 63: 59: 54: 50: 48: 44: 40: 36: 32: 28: 25: 21: 8119: 8100: 8067: 8061: 8029: 8023: 7983: 7977: 7964: 7937: 7919: 7903: 7877: 7866: 7840: 7814: 7784: 7754: 7728: 7701: 7677: 7649: 7621: 7605: 7591: 7561: 7555: 7534:cite journal 7523: 7518:; (1860b). 7502:cite journal 7491: 7486:; (1860a). 7476: 7455: 7428: 7411: 7400:Bibliography 7389: 7384:, p. 58 7377: 7365: 7353: 7341: 7334:Hermann 1971 7329: 7322:Hermann 1971 7313: 7301: 7289: 7277: 7272:, p. 80 7265: 7253: 7248:, p. 11 7241: 7184: 7173: 7167:Stewart 1858 7162: 7137: 7126: 7114: 7102: 7073: 7057: 7052: 7033: 7023: 7003: 6996: 6976: 6969: 6960: 6927: 6923: 6917: 6898: 6894: 6874: 6867: 6835: 6830: 6821: 6817: 6811: 6800:. Retrieved 6790: 6765: 6761: 6751: 6706: 6702: 6692: 6681:. Retrieved 6674:the original 6660: 6649:. Retrieved 6645: 6635: 6624:. Retrieved 6614: 6603:. Retrieved 6599:the original 6588: 6579:HyperPhysics 6578: 6568: 6556:. Retrieved 6548: 6539: 6521:10.1142/p276 6511: 6504: 6499:, p. 22 6492: 6481: 6472: 6453: 6447: 6420: 6414: 6401: 6387: 6373: 6330: 6326: 6319: 6309:December 21, 6307:. Retrieved 6293: 6274: 6268: 6248: 6241: 6208: 6204: 6197: 6178: 6168: 6163:, p. 43 6156: 6145: 6140:, p. 42 6116: 6104: 6094: 6093:, series 3, 6090: 6087:Draper, J.W. 6082: 6071: 6063: 6059: 6054: 6046: 6042: 6037: 6018: 6008: 6000:Blacksmith U 5999: 5989: 5981: 5977: 5973: 5969: 5968:), p. 277: 5965: 5960: 5940: 5933: 5921: 5909: 5897: 5892:, Chapter 1. 5885: 5866:Thermography 5841:Planck's law 5826:Draper point 5798: 5796: 5791: 5787: 5723: 5718: 5716: 5711: 5707: 5703: 5695: 5691: 5687: 5585: 5581: 5575: 5567: 5555: 5551: 5546: 5542: 5534: 5530: 5525: 5521: 5518: 5512: 5505: 5501: 5496: 5492: 5471: 5465: 5459: 5453: 5447: 5441: 5435: 5428: 5424: 5419: 5415: 5408: 5404: 5399: 5395: 5388: 5384: 5380: 5373: 5369: 5365: 5361: 5357: 5353: 5349: 5345: 5339: 5332: 5328: 5324: 5317: 5313: 5309: 5305: 5301: 5297: 5290: 5286: 5282: 5275: 5271: 5267: 5261: 5255: 5252: 5246: 5239: 5235: 5231: 5227: 5223: 5219: 5215: 5211: 5205: 5195: 5192: 5188: 5181: 5177: 5173: 5169: 5165: 5161: 5157: 5153: 5145: 5141: 5137: 5133: 5129: 5125: 5121: 5114: 5110: 5106: 5102: 5098: 5094: 5090: 5086: 5082: 5075: 5071: 5067: 5063: 5059: 5055: 5051: 5047: 5040: 5036: 5032: 5028: 5021: 5017: 5013: 5009: 5003: 4996: 4992: 4988: 4981: 4977: 4973: 4969: 4965: 4961: 4955: 4948: 4944: 4940: 4934: 4928: 4921: 4917: 4913: 4910: 4904: 4901: 4893: 4879: 4863: 4847: 4844:Isaac Newton 4837: 4820: 4811:chromaticity 4789: 4772: 4768: 4756: 4744: 4737: 4660: 4467: 4414: 4410: 4399: 4292: 4289: 4278: 4204: 4193: 3959: 3948: 3784: 3773: 3624: 3558: 3547: 3425: 3327: 3316: 3203: 3200: 3156: 3141: 3025: 3020:perspiration 3005: 2910: 2901: 2726: 2685:Applications 2510: 2508:: the power 2392: 2268: 1781: 1546: 1381: 1307: 1305: 1301: 1131: 1025: 1021:of the body. 685: 682:Planck's law 648: 643: 639: 634: 630: 615: 563:Planck's law 552: 548: 522: 515: 445: 429:Fourier mode 426: 414: 407: 384: 372: 354:assumption. 351: 344: 333: 315: 309: 291: 288: 271: 256:Draper point 253: 248: 245: 234: 227: 197:All normal ( 196: 178: 142:Planck's law 135: 104: 100: 96: 84: 82: 71: 67: 19: 18: 8259:Outer space 8247:Spaceflight 8016:Stewart, B. 7863:Milne, E.A. 7837:Mihalas, D. 7674:Kuhn, T. S. 7451:Hermann, A. 7425:Yung, Y. L. 7336:, p. 7 7324:, p. 6 7318:Paschen, F. 7260:, p. 8 7246:Planck 1914 7205:Siegel 1976 6846:, page 227. 6407:Planck, Max 6333:(2): 5225. 6211:: 355–360. 6205:Measurement 6161:Planck 1914 6138:Planck 1914 6097:: 345–360. 6076:Planck 1914 5890:Loudon 2000 4875:John Leslie 4809:The color ( 4796:fluorescent 4780:ultraviolet 3012:evaporation 1542:9.9 μm 1480:10 m K 1019:temperature 845:solid angle 448:wavelengths 403:black holes 301:temperature 268:6000 K 264:1000 K 230:wavelengths 47:temperature 43:wavelengths 8281:Categories 7915:Planck, M. 7777:Mandel, L. 7751:Loudon, R. 7528:: 783–787. 7496:: 662–665. 7382:Kragh 1999 7270:Milne 1930 6824:: 314–322. 6802:2007-06-24 6683:2007-06-24 6651:2007-06-24 6626:2007-06-24 6605:2007-06-24 5978:, nennen." 5878:References 4786:Light bulb 4763:decoupling 3028:Wien's law 3008:convection 2917:emissivity 2897:emissivity 2476:from 0 to 2262:being the 943:in vacuum; 559:Max Planck 502:Wien's law 410:300 K 361:Nine-year 347:emissivity 342:radiator. 340:Lambertian 320:wavelength 260:798 K 241:lamp black 209:. It is a 193:Black body 187:Black body 168:, with an 85:black body 35:black body 8223:Astronomy 8046:122316368 7917:(1914) . 7807:Mehra, J. 7753:(2000) . 7644:Kragh, H. 7550:(1860c). 7461:MIT Press 7346:Kuhn 1978 6952:119892155 6365:119271232 6340:1212.5225 6304:Space.com 6233:116260472 6150:Wien 1894 5846:Pyrometer 5816:Bolometer 5753:− 5643:− 5635:θ 5632:⁡ 5616:− 4894:In 1859, 4864:In 1858, 4819:CIE 1931 4753:Cosmology 4674:¯ 4671:ε 4637:α 4595:× 4544:× 4446:¯ 4443:ε 4432:α 4429:− 4367:¯ 4364:ε 4359:α 4356:− 4149:¯ 4146:ϵ 4096:¯ 4093:ϵ 4069:¯ 4066:ϵ 3915:σ 3895:π 3826:π 3793:π 3738:α 3735:− 3683:α 3680:− 3653:α 3633:α 3514:π 3489:π 3340:σ 3283:σ 3263:π 3151:radiation 3109:μ 3079:⋅ 3065:− 3057:× 3039:λ 2951:− 2883:ε 2832:− 2814:ε 2811:σ 2762:− 2667:π 2661:ϕ 2654:θ 2647:θ 2644:⁡ 2638:θ 2635:⁡ 2619:π 2610:∫ 2604:π 2592:∫ 2585:Ω 2578:θ 2575:⁡ 2569:∫ 2536:σ 2528:⋆ 2484:π 2464:θ 2444:π 2421:Ω 2359:π 2354:θ 2351:⁡ 2332:σ 2292:per area 2216:− 2208:× 2151:π 2141:≡ 2138:σ 2130:and with 2107:ν 2098:≡ 2064:π 2049:− 2014:∞ 2005:∫ 1996:by using 1982:π 1975:θ 1969:⁡ 1950:σ 1942:π 1874:π 1818:θ 1812:⁡ 1795:ν 1760:ν 1736:≈ 1700:ν 1648:− 1577:× 1571:× 1556:ν 1522:λ 1457:≈ 1443:− 1432:− 1346:λ 1319:λ 1260:ν 1229:ν 1187:ν 1145:ν 1117:θ 1114:⁡ 1083:θ 1080:⁡ 1063:ν 1034:θ 993:frequency 979:ν 869:frequency 855:ν 843:per unit 816:ν 778:− 762:ν 726:ν 699:ν 671:Equations 534:ν 518:quantized 487:ν 461:ν 387:astronomy 352:gray body 83:The term 8292:Infrared 8176:Archived 8056:(1894). 8054:Wien, W. 8032:: 1–20. 8018:(1858). 8008:37368520 7963:(2001). 7935:(1979). 7902:(1949). 7813:(1982). 7783:(1995). 7781:Wolf, E. 7727:(1991). 7676:(1978). 7646:(1999). 7620:(1998). 7453:(1971). 7427:(1989). 7410:(1950). 7134:(1960). 6924:The Moon 6906:Archived 6782:15102614 6743:16576330 6665:Lee, B. 6409:(1901). 6066:: 23–41. 6049:: 55–62. 5984:), p. 2. 5976:schwarze 5809:See also 5736:′ 5600:′ 5308:, BB) / 4775:infrared 2996:calories 2913:2 m 2729:infrared 2718:infrared 2561:We used 2205:5.670373 1772:= 17 THz 1574:5.879... 1216:through 607:fermions 579:Einstein 336:radiance 324:spectrum 312:hohlraum 283:Pāhoehoe 237:graphite 199:baryonic 150:infrared 116:Spectrum 60:and its 8271:Science 8211:Physics 8197:Portals 8191:, 2007. 8072:Bibcode 7566:Bibcode 7090:Bibcode 6932:Bibcode 6734:1091498 6711:Bibcode 6558:July 8, 6486:. 2019. 6425:Bibcode 6345:Bibcode 6213:Bibcode 5698:is the 4881:Stokes- 4873:and of 4854:caloric 4834:History 4715:254.356 3665:is the 3353:is the 2895:is the 1509:is the 991:is the 965:is the 939:is the 913:is the 663:is the 591:photons 215:entropy 158:Celsius 24:thermal 22:is the 8126: 8107: 8044: 8006: 8000:794025 7998: 7949: 7888: 7851: 7825: 7795: 7765: 7739: 7713: 7688: 7662: 7632: 7467: 7439: 7150: 7064: 7040: 7011: 6984: 6950: 6882: 6842: 6780: 6741: 6731: 6527: 6460: 6363: 6281: 6256: 6231: 6185: 6025: 5948: 5686:where 5486:(λ, T) 4849:Optics 4718: 4646: 4608: 4557: 4497: 3960:where 3667:albedo 3559:where 3467: 3328:where 3242: 3193:, and 3173:albedo 3106: 3090: 3073: 2971: 2959:absorb 2899:, and 2867:where 2770:absorb 1682:where 1590: 799:where 611:bosons 512:Jeans. 164:. The 111:Theory 8235:Stars 8042:S2CID 8004:S2CID 7144:408–9 7080:arXiv 6948:S2CID 6677:(PDF) 6670:(PDF) 6361:S2CID 6335:arXiv 6229:S2CID 5786:Here 5466:Thus 5391:, BB) 5335:, BB) 5320:, BB) 5293:, BB) 5278:, BB) 4823:space 4815:locus 4643:0.309 4592:1.496 4541:6.957 3210:power 3054:2.898 2087:with 1513:. So 1470:2.897 841:power 653:5.670 391:stars 262:. 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