Black-body radiation - Knowledge (XXG)

8217: 4753:(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. 561:

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.

171:, 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 232: 140: 254:, 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. 281:, 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 8277: 5572:

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.

4888:. 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. 8253: 4817: 519: 289: 64: 8229: 5991:(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) ( 8265: 369: 262:) 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). 8241: 5095:

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

631:. 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 318:. 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. 4067:. 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 4760:(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. 2722: 393:: 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. 531:, 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. 4896:

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

2731:(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. 360:

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

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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.

588:, 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. 1632: 416:, 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. 384:

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".

5348:, 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 3013:

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.

2796: 243:, 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. 2144: 329:.) 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 4586: 4804:

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:

3044: 3778: 4469: 1389: 5795: 4970:. (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 4637: 4318: 4744: 5579:

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.

4667: 1689: 1138: 5491:, 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 3602: 3430: 3398: 1760: 1225: 1183: 2904: 6923:, 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. 3998: 848: 91:) 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. 3857: 1732: 1140:

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

557:) were allowed, supporting the data that the energy emitted is reduced for wavelengths less than the wavelength of the observed peak of emission. 5478: 307: 6677: 314:

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

5573: 5276:, at thermal equilibrium, all perfectly black bodies of the same size and shape have the one and the same common value of emissive power 1037:

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

390: 4706: 2266:{\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}}} } 8312: 5738: 5474:

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

277:, a small opening in the wall of a large uniformly heated opaque-walled cavity (such as an oven), viewed from outside, looks red; at 8138: 8119: 7961: 7863: 7837: 7807: 7777: 7725: 7700: 7674: 7644: 7479: 7162: 6894: 6854: 6472: 6293: 6197: 3148: 2000:{\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 }}} 450:, as well as a nonphysical spectrum of emitted radiation that grows without bound with increasing frequency, a problem known as the 4532: 1230: 5354:. He argued that the flows of heat radiation must be the same in each case. Thus he argued that at thermal equilibrium the ratio 4232: 6678:"Theoretical Prediction and Measurement of the Fabric Surface Apparent Temperature in a Simulated Man/Fabric/Environment System" 4789:

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"".

2686:{\displaystyle \int \cos \theta \,d\Omega =\int _{0}^{2\pi }\int _{0}^{\pi /2}\cos \theta \sin \theta \,d\theta \,d\phi =\pi .} 2526:

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

3205: 2529: 155:. The spectrum is peaked at a characteristic frequency that shifts to higher frequencies with increasing temperature, and at 8297: 8199: 6605: 4000:

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

7615:(1882) , "Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht", 4429: 2274: 675: 7567: 4592: 8207: 613: 216:. The radiation represents a conversion of a body's internal energy into electromagnetic energy, and is therefore called 5808:

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

427: 148: 7935: 6913: 5866: 5588: 4769: 4485: 4003: 609: 6258: 3132:{\displaystyle \lambda _{\text{peak}}=\mathrm {\frac {2.898\times 10^{-3}~K\cdot m}{305~K}} =\mathrm {9.50~\mu m} .} 7799: 7769: 7717: 7666: 7418: 7142: 6493: 4881: 3038: 1308: 512: 7563:"Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme and Licht" 6912:

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

7565:[On the relation between bodies' emission capacity and absorption capacity for heat and light]. 7544: 7512: 6631: 5291:, with the dimensions of power. His proof noted that the dimensionless wavelength-specific absorptivity 4964:

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

7743: 7636: 7576: 7100: 6942: 6721: 6435: 6421: 6355: 6223: 5841: 4829: 4643: 3010: 636: 596:. These theoretical advances eventually resulted in the superseding of classical electromagnetism by 593: 6933:

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.

1638: 1109: 639:. The law was formulated by Josef Stefan in 1879 and later derived by Ludwig Boltzmann. The formula 8172: 7873: 7599:"On the relation between the radiating and absorbing powers of different bodies for light and heat" 7461: 6585: 6097: 5871: 5846: 4825: 3577: 3547:{\displaystyle P_{\rm {SE}}=P_{\rm {S\ emt}}\left({\frac {\pi R_{\rm {E}}^{2}}{4\pi D^{2}}}\right)} 3405: 3373: 1739: 1188: 1146: 565: 511:

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

8190: 8026: 7910: 7847: 7829: 7624: 7129: 6920: 6652: 6488: 6403: 4876: 4837: 3220: 1766: 985: 925: 861: 851: 589: 7929: 5851: 3609: 692: 573: 152: 8086: 7580: 7104: 6946: 6725: 6586:"Wien's Displacement Law and Other Ways to Characterize the Peak of Blackbody Radiation" 6439: 6359: 6227: 5214:. It required that the bodies be kept in a cavity in thermal equilibrium at temperature 3153:

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

2306: 2283: 60:, which is assumed, for the sake of calculations and theory, to be uniform and constant. 8281: 8221: 8195: 8160: 7989: 7787: 7659: 7628: 6744: 6709: 5710: 4937:

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

4864: 4757: 4221: 3026: 2407: 1847: 1317:

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

1011: 959: 951: 933: 907: 885: 581: 527:

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

6807: 6235: 4863:. He says that Newton imagined particles of light traversing space uninhibited by the 4824:) of blackbody radiation scales inversely with the temperature of the black body; the 2091:{\displaystyle \int _{0}^{\infty }dx\,{\frac {x^{3}}{e^{x}-1}}={\frac {\pi ^{4}}{15}}} 608:. In addition, it led to the development of quantum probability distributions, called 8291: 8056: 7976:

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

7943: 7817: 7761: 7465: 6962: 6375: 6367: 6243: 4897:

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

3201: 447: 213: 8018: 4121:

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

1762:. At a typical room temperature of 293 K (20 °C), the maximum intensity is for 310:: the blackbody curve is characteristic of thermal light, which depends only on the 8276: 8245: 8064: 6336:

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

5981:"Der Beweis, welcher für die ausgesprochene Behauptung hier gegeben werden soll, … 5876: 5836: 5713:. This can be simplified for the special cases of objects moving directly towards ( 4854: 4821: 3226: 3030: 803:{\displaystyle B_{\nu }(T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{h\nu /kT}-1}},} 439: 266: 251: 17: 6609: 6555: 5690:{\displaystyle f'=f{\frac {1-{\frac {v}{c}}\cos \theta }{\sqrt {1-v^{2}/c^{2}}}},} 2994:{\displaystyle P_{\text{net}}=P_{\text{emit}}-P_{\text{absorb}}=\mathrm {100~W} .} 131: 7947: 7684: 7654: 7435: 4806: 4790: 4471:

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

3022: 2871:{\displaystyle P_{\text{net}}=A\sigma \varepsilon \left(T^{4}-T_{0}^{4}\right),} 1029: 855: 311: 57: 7536:

Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin

7504:

Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin

6784: 5261:

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

8154: 8048: 7925: 6417: 3018: 2927: 2907: 605: 569: 458: 413: 357: 330: 240: 203: 53: 45: 8094: 7589: 7533:[On the relation between emission and absorption of light and heat]. 6448: 4922:

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

7791: 7531:"Über den Zusammenhang zwischen Emission und Absorption von Licht und Wärme" 7471: 6314: 5856: 5826: 4816: 3948:{\displaystyle P_{\rm {emt\,bb}}=4\pi R_{\rm {E}}^{2}\sigma T_{\rm {E}}^{4}} 3002: 2721: 1057:

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

1003: 879: 397: 151:

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

8163:

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

6792: 6753: 6424:[On the law of the distribution of energy in the normal spectrum]. 6102:

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

3316:{\displaystyle P_{\rm {S\ emt}}=4\pi R_{\rm {S}}^{2}\sigma T_{\rm {S}}^{4}} 3212:

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

2710: 6734: 4853:(1788–1827) responded to a view he extracted from a French translation of 3859:. If the planet were a perfect black body, it would emit according to the 288: 8010: 7095: 4785: 2739: 2728: 346: 322: 247: 212:) matter emits electromagnetic radiation when it has a temperature above 160: 4193:{\displaystyle P_{\rm {emt}}={\overline {\epsilon }}\,P_{\rm {emt\,bb}}} 7918: 6954: 3006: 1321:

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

617: 518: 225: 168: 143:

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

63: 6054:

Sitzungberichte der Königlich-Preußischen Akademie der Wissenschaften

6007:"How Do Blacksmiths Measure The Temperature Of Their Forge And Steel?" 568:

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

368: 361:

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

4859: 3677: 3183: 1473:{\displaystyle {\frac {hc}{k}}{\frac {1}{5+W_{0}(-5e^{-5})}}\approx } 858:

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

601: 534:

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

209: 7149:

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

6769:"Nonexercise activity thermogenesis (NEAT): environment and biology" 2727:

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

83:

Of particular importance, although planets and stars (including the

8240: 8002: 135:

Blacksmiths judge workpiece temperatures by the colour of the glow.

7661:

Quantum Generations: a History of Physics in the Twentieth Century

7633:

Modern Thermodynamics. From Heat Engines to Dissipative Structures

6350: 2394:{\displaystyle dI=\sigma T^{4}{\frac {\cos \theta }{\pi d^{2}}}dA} 621: 580:(not to be confused with Wien's displacement law) consistent with 287: 138: 130: 84: 62: 6531: 5204:

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

2791:{\displaystyle P_{\text{net}}=P_{\text{emit}}-P_{\text{absorb}}.} 56:, inversely related to intensity, that depend only on the body's 6563: 3186:

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

401: 373: 293: 6521: 4479:

Substituting the measured values for the Sun and Earth yields:

3826:, it emits in all directions; the spherical surface area being 3156: 653:

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

48:(an idealized opaque, non-reflective body). It has a specific, 6467:(3rd Edition Part 1 ed.). Oxford: Butterworth–Heinemann. 4810: 3628: 2401:

when the receiving surface is perpendicular to the radiation.

176: 88: 4581:{\displaystyle R_{\rm {S}}=6.957\times 10^{8}\ \mathrm {m} ,} 3017:

There are other important thermal loss mechanisms, including

269:

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

5701:

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

285:. Different curves are obtained by varying the temperature. 8179:

Descriptions of radiation emitted by many different objects

5530:

Kirchhoff announced that the determination of the function

6422:"Ueber das Gesetz der Energieverteilung im Normalspectrum" 6889:(1st ed.). IOP Publishing. pp. 36–37, 380–382. 6026:"§2.3: Thermodynamic equilibrium and blackbody radiation" 564:

Calculating the blackbody curve was a major challenge in

187:, but with significant power in the ultraviolet as well. 7980:

Münchner Zentrum für Wissenschafts und Technikgeschichte

6071:

Verhandlungen der Deutschen Physikalischen Gessellschaft

3168:

The temperature of a planet depends on several factors:

604:

and the blackbody cavity was thought of as containing a

438:

According to the Classical Theory of Radiation, if each

6560:

The NIST Reference on Constants, Units, and Uncertainty

3796:

Even though the planet only absorbs as a circular area

3773:{\displaystyle P_{\rm {abs}}=(1-\alpha )\,P_{\rm {SE}}} 3041:

to human-body emission results in a peak wavelength of

167:. As the temperature increases past about 500 degrees 6886:

Planetary Science: The Science of Planets Around Stars

6827:

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

5721:= 0) from the observer, and for speeds much less than 4464:{\displaystyle (1-\alpha )={\overline {\varepsilon }}} 3196:

Energy generated internally by a planet itself due to

1384:{\displaystyle \lambda _{\text{peak}}={\frac {b}{T}},} 147:

Black-body radiation has a characteristic, continuous

8205: 8157:

Blackbody radiation by Fu-Kwun Hwang and Loo Kang Wee

7304: 7120:, pp. 227–228; also Section 11.6, pages 294–296. 7012:

Willem Jozef Meine Martens & Jan Rotmans (1999).

5741: 5605: 4709: 4678: 4646: 4595: 4535: 4488: 4432: 4321: 4235: 4132: 4100: 4073: 4006: 3977: 3873: 3832: 3802: 3717: 3686: 3662: 3642: 3612: 3580: 3449: 3408: 3376: 3349: 3242: 3047: 2937: 2892: 2804: 2748: 2578: 2532: 2493: 2473: 2450: 2430: 2410: 2332: 2309: 2286: 2147: 2104: 2013: 1870: 1850: 1799: 1769: 1742: 1700: 1641: 1564: 1530: 1499: 1401: 1395:, known as Wien's displacement constant, is equal to 1354: 1327: 1233: 1191: 1149: 1112: 1067: 1043: 1014: 988: 962: 936: 910: 888: 864: 820: 703: 616:, each applicable to a different class of particles, 540: 490: 467: 7227: 7225: 7223: 4632:{\displaystyle D=1.496\times 10^{11}\ \mathrm {m} ,} 4094:

of the radiation that a black body would emit where

258:

amount of radiation leaving its surface, called the

80:

objects can be approximated as blackbody radiation.

7619:, Leipzig: Johann Ambrosius Barth, pp. 571–598 6849:, second edition, D. Reidel Publishing, Dordrecht, 6653:"Temperature of a Healthy Human (Skin Temperature)" 6390:"Blackbody Radiation – University Physics Volume 3" 6190:

Passive infrared detection: theory and applications

412:is the hypothetical blackbody radiation emitted by 7658: 7241: 7239: 7146: 7117: 5924: 5789: 5689: 4738: 4691: 4661: 4631: 4580: 4520: 4463: 4398: 4277: 4220:with its surroundings, the rate at which it emits 4192: 4113: 4086: 4055: 3992: 3947: 3851: 3818: 3772: 3698: 3668: 3648: 3619: 3596: 3546: 3424: 3392: 3356: 3315: 3143:Temperature relation between a planet and its star 3131: 2993: 2898: 2870: 2790: 2685: 2564: 2507: 2479: 2459: 2436: 2416: 2393: 2318: 2295: 2265: 2133: 2090: 1999: 1856: 1836: 1775: 1754: 1726: 1683: 1626: 1543: 1512: 1472: 1383: 1340: 1292: 1219: 1177: 1132: 1098: 1049: 1020: 994: 968: 942: 916: 894: 870: 842: 802: 549: 502: 476: 7404:The Doppler Effect, T. P. Gill, Logos Press, 1965 6883:Cole, George H. A.; Woolfson, Michael M. (2002). 6144: 6142: 6140: 4739:{\displaystyle T_{\rm {E}}=254.356\ \mathrm {K} } 8071:[Temperature and entropy of radiation]. 8031:"An account of some experiments on radiant heat" 6594:Provides 5 variations of Wien's displacement law 5210:as well as various perfect black bodies labeled 5037:and the wavelength-specific absorption ratio by 3001:The total energy radiated in one day is about 8 7689:Black–Body Theory and the Quantum Discontinuity 7368: 7292: 6507: 6260:Radiation heat transfer: a statistical approach 5790:{\displaystyle T'=T{\sqrt {\frac {c-v}{c+v}}}.} 4521:{\displaystyle T_{\rm {S}}=5772\ \mathrm {K} ,} 4056:{\displaystyle P_{\rm {abs}}=P_{\rm {emt\,bb}}} 2280:On a side note, at a distance d, the intensity 8036:Transactions of the Royal Society of Edinburgh 7380: 7043:. In Pascale Ehrenfreund; et al. (eds.). 6975:Lunar and Planetary Science XXXVII (2006) 2406 4426:Notice that a gray (flat spectrum) ball where 3175:Emitted radiation of the planet (for example, 2326:of radiating surface is the useful expression 1143:The emitted energy flux density or irradiance 190:Blackbody radiation provides insight into the 7740:Statistical Physics: A Probabilistic Approach 7488:Frühgeschichte der Quantentheorie (1899–1913) 7268: 7089:White, M. (1999). "Anisotropies in the CMB". 6710:"A Biometric Study of Human Basal Metabolism" 4224:is equal to the rate at which it absorbs it: 3164:intensity, from clouds, atmosphere and ground 576:of blackbody radiation. By making changes to 8: 7826:The Historical Development of Quantum Theory 7231: 6100:(1847). On the production of light by heat, 5444:is a continuous function, dependent only on 5220:. His proof intended to show that the ratio 3400:is the effective temperature of the Sun, and 2922:The total surface area of an adult is about 1293:{\displaystyle B_{\nu }(T,E)=Eb_{\nu }(T,E)} 102:in 1860. Blackbody radiation is also called 8155:Blackbody radiation JavaScript Interactives 7549:: CS1 maint: numeric names: authors list ( 7517:: CS1 maint: numeric names: authors list ( 7069:Atmospheric Science. An Introductory Survey 6556:"Wien wavelength displacement law constant" 6338:The Astrophysical Journal Supplement Series 5521:, Kirchhoff's original notation was simply 5264:His proof first argued that for wavelength 4278:{\displaystyle P_{\rm {abs}}=P_{\rm {emt}}} 3029:is much greater than unity. Evaporation by 2886:are the body surface area and temperature, 2134:{\displaystyle x\equiv {\frac {h\nu }{kT}}} 8110:Kroemer, Herbert; Kittel, Charles (1980). 7245: 7199: 7188: 6119: 5912: 4692:{\displaystyle {\overline {\varepsilon }}} 1634:In unitless form, the maximum occurs when 686: 7588: 7316: 7211: 7209: 7207: 7094: 6743: 6733: 6447: 6349: 6311:"New 'Baby Picture' of Universe Unveiled" 6131: 6024:Tomokazu Kogure; Kam-Ching Leung (2007). 5936: 5756: 5740: 5675: 5666: 5660: 5629: 5620: 5604: 4731: 4715: 4714: 4708: 4679: 4677: 4645: 4621: 4612: 4594: 4570: 4561: 4541: 4540: 4534: 4510: 4494: 4493: 4487: 4451: 4431: 4359: 4353: 4345: 4339: 4326: 4320: 4262: 4261: 4241: 4240: 4234: 4180: 4170: 4169: 4164: 4154: 4138: 4137: 4131: 4101: 4099: 4074: 4072: 4043: 4033: 4032: 4012: 4011: 4005: 3983: 3982: 3976: 3939: 3933: 3932: 3919: 3913: 3912: 3889: 3879: 3878: 3872: 3843: 3831: 3810: 3801: 3760: 3759: 3754: 3723: 3722: 3716: 3685: 3661: 3641: 3616: 3611: 3593: 3586: 3585: 3579: 3531: 3513: 3507: 3506: 3496: 3473: 3472: 3455: 3454: 3448: 3421: 3414: 3413: 3407: 3389: 3382: 3381: 3375: 3353: 3348: 3307: 3301: 3300: 3287: 3281: 3280: 3248: 3247: 3241: 3112: 3074: 3061: 3052: 3046: 2977: 2968: 2955: 2942: 2936: 2891: 2854: 2849: 2836: 2809: 2803: 2779: 2766: 2753: 2747: 2667: 2660: 2632: 2628: 2623: 2610: 2605: 2591: 2577: 2553: 2537: 2531: 2497: 2492: 2472: 2449: 2429: 2409: 2376: 2355: 2349: 2331: 2308: 2285: 2254: 2244: 2234: 2225: 2203: 2193: 2182: 2176: 2164: 2154: 2146: 2111: 2103: 2077: 2071: 2053: 2042: 2036: 2035: 2023: 2018: 2012: 1973: 1967: 1947: 1938: 1928: 1916: 1906: 1899: 1887: 1877: 1869: 1849: 1804: 1798: 1768: 1741: 1713: 1699: 1664: 1646: 1640: 1616: 1611: 1603: 1594: 1569: 1563: 1535: 1529: 1504: 1498: 1452: 1433: 1417: 1402: 1400: 1368: 1359: 1353: 1348:, is a function only of the temperature: 1332: 1326: 1269: 1238: 1232: 1196: 1190: 1154: 1148: 1116: 1111: 1072: 1066: 1042: 1013: 987: 961: 935: 909: 887: 863: 825: 819: 775: 768: 758: 750: 739: 726: 708: 702: 539: 489: 466: 7713:Thermodynamics and statistical mechanics 7440:Atmospheric Radiation: Theoretical Basis 7015:Climate Change an Integrated Perspective 6991:. Taylor & Francis. pp. 10–11. 6606:"Emissivity Values for Common Materials" 6263:(3rd ed.). Wiley-IEEE. p. 58. 5805:< 0 indicates an approaching source. 5801:> 0 indicates a receding source, and 4815: 3225: 3155: 2565:{\displaystyle j^{\star }=\sigma T^{4},} 1837:{\displaystyle B_{\nu }(T)\cos(\theta )} 1185:, is related to the photon flux density 517: 461:this deviation is not so noticeable, as 367: 230: 8212: 8129:Tipler, Paul; Llewellyn, Ralph (2002). 8114:(2nd ed.). W. H. Freeman Company. 8069:"Temperatur und Entropie der Strahlung" 7876:(1930). "Thermodynamics of the Stars". 7344: 7332: 7177: 7153:. Princeton University Press. pp. 7071:, second edition, Elsevier, Amsterdam, 7041:"The Prebiotic Atmosphere of the Earth" 6867: 6865: 6863: 6708:Harris J, Benedict F; Benedict (1918). 6030:The astrophysics of emission-line stars 5952:Introduction to Astronomy and Cosmology 5893: 4114:{\displaystyle {\overline {\epsilon }}} 4087:{\displaystyle {\overline {\epsilon }}} 1099:{\displaystyle B_{\nu }(T)\cos \theta } 7852:Foundations of Radiation Hydrodynamics 7542: 7510: 7256: 7215: 6526:. Imperial College Press. p. 19. 6463:Landau, L. D.; E. M. Lifshitz (1996). 6171: 6148: 6086: 5900: 5732:) for the frequency in this equation. 1736:The approximate numerical solution is 1544:{\displaystyle \lambda _{\text{peak}}} 1341:{\displaystyle \lambda _{\text{peak}}} 882:at thermal equilibrium at temperature 7392: 7280: 6845:Iribarne, J.V., Godson, W.L. (1981). 6186:"§4.2.2: Calculation of Planck's law" 5814:cosmic microwave background radiation 5576:, which is a form of the second law. 406:cosmic microwave background radiation 378:cosmic microwave background radiation 338:material in the cavity (compare with 7: 7887:Müller-Kirsten, Harald J.W. (2013). 7796:Optical Coherence and Quantum Optics 7356: 6160: 5479:Kirchhoff's law of thermal radiation 4312: 4226: 4123: 3864: 3708: 3440: 3233: 3223:(energy/second) that the Sun emits: 3206:adiabatic contraction due to cooling 308:Kirchhoff's law of thermal radiation 7949:Radiative Processes in Astrophysics 7067:Wallace, J.M., Hobbs, P.V. (2006). 6309:Gannon, Megan (December 21, 2012). 6288:. New York: John Wiley & Sons. 2798:Applying the Stefan–Boltzmann law, 687:Planck's law of blackbody radiation 44:with its environment, emitted by a 8167:Color-to-Temperature demonstration 7499:"Über die Fraunhofer'schen Linien" 6808:"Heat Transfer and the Human Body" 5955:. J Wiley & Sons. p. 48. 4732: 4716: 4622: 4571: 4542: 4511: 4495: 4269: 4266: 4263: 4248: 4245: 4242: 4184: 4181: 4177: 4174: 4171: 4145: 4142: 4139: 4047: 4044: 4040: 4037: 4034: 4019: 4016: 4013: 3984: 3934: 3914: 3893: 3890: 3886: 3883: 3880: 3764: 3761: 3730: 3727: 3724: 3587: 3508: 3486: 3483: 3480: 3474: 3459: 3456: 3415: 3383: 3302: 3282: 3261: 3258: 3255: 3249: 3122: 3103: 3092: 3086: 2984: 2738:The human body radiates energy as 2595: 2431: 2251: 2241: 2236: 2024: 1617: 1607: 1604: 40:within, or surrounding, a body in 25: 8173:Cooling Mechanisms for Human Body 7501:[On Fraunhofer's lines]. 7331:(1896), personal letter cited by 7305:Mihalas & Weibel-Mihalas 1984 7045:Astrobiology: Future Perspectives 6988:Space physics and space astronomy 6236:10.1016/j.measurement.2019.02.084 3149:Planetary equilibrium temperature 3025:. Conduction is negligible – the 1006:of the electromagnetic radiation; 657:is the absolute temperature, and 27:Thermal electromagnetic radiation 8275: 8263: 8251: 8239: 8227: 8215: 6632:"Emissivity of Common Materials" 5591:causes a shift in the frequency 5456:, and an increasing function of 3604:is the radius of the planet, and 3172:Incident radiation from its star 2926:, and the mid- and far-infrared 2720: 2709: 1844:over the frequency the radiance 1302: 8161:Calculating Blackbody Radiation 8133:(4th ed.). W. H. Freeman. 7490:, Physik Verlag, Mosbach/Baden. 6985:Michael D. Papagiannis (1972). 6910:Principles of Planetary Climate 4662:{\displaystyle \alpha =0.309\ } 1314:of wavelength or of frequency. 387:local thermodynamic equilibrium 159:most of the emission is in the 8200:Wolfram Demonstrations Project 7118:Kondepudi & Prigogine 1998 7079:, exercise 4.6, pages 119–120. 7047:. Springer. pp. 279–280. 5925:Kondepudi & Prigogine 1998 5255:was independent of the nature 4828:of such colors, shown here in 4475:Effective temperature of Earth 4445: 4433: 4218:radiative exchange equilibrium 3751: 3739: 3193:for planets with an atmosphere 2444:for all azimuthal angle (0 to 1988: 1982: 1831: 1825: 1816: 1810: 1684:{\displaystyle e^{x}(1-x/3)=1} 1672: 1652: 1461: 1439: 1287: 1275: 1256: 1244: 1214: 1202: 1172: 1160: 1133:{\displaystyle 1/\cos \theta } 1084: 1078: 850:is the spectral radiance (the 837: 831: 720: 714: 572:in the formalism now known as 1: 7936:P. Blakiston's Sons & Co. 7889:Basics of Statistical Physics 7850:; Weibel-Mihalas, B. (1984). 7595:Translated by Guthrie, F. as 7568:Annalen der Physik und Chemie 7467:The Genesis of Quantum Theory 6773:Am J Physiol Endocrinol Metab 5977:Annalen der Physik und Chemie 5812:. An example is found in the 4949:. The total absorption ratio 3597:{\displaystyle R_{\rm {E}}\,} 3425:{\displaystyle R_{\rm {S}}\,} 3393:{\displaystyle T_{\rm {S}}\,} 1755:{\displaystyle x\approx 2.82} 1220:{\displaystyle b_{\nu }(T,E)} 1178:{\displaystyle B_{\nu }(T,E)} 224:of radiative distribution of 7931:The Theory of Heat Radiation 7607:. Series 4, volume 20: 1–21. 7018:. Springer. pp. 52–55. 4684: 4672:With the average emissivity 4456: 4377: 4159: 4106: 4079: 3627:is the distance between the 2919:is the ambient temperature. 2899:{\displaystyle \varepsilon } 2404:By subsequently integrating 7934:. translated by Masius, M. 7766:The Quantum Theory of Light 7369:Mehra & Rechenberg 1982 7293:Rybicki & Lightman 1979 7143:Gillispie, Charles Coulston 6829:Journal de Physique (Paris) 6508:Rybicki & Lightman 1979 6005:Dustin (18 December 2018). 5589:relativistic Doppler effect 5404:, which may now be denoted 4770:cosmic microwave background 3993:{\displaystyle T_{\rm {E}}} 843:{\displaystyle B_{\nu }(T)} 600:. These quanta were called 194:state of cavity radiation. 8329: 7800:Cambridge University Press 7770:Cambridge University Press 7718:Courier Dover Publications 7667:Princeton University Press 6847:Atmospheric Thermodynamics 6785:10.1152/ajpendo.00562.2003 6523:The Physics of Solar Cells 6430:. 4th series (in German). 6368:10.1088/0067-0049/208/2/20 3852:{\displaystyle 4\pi R^{2}} 3146: 1727:{\displaystyle x=h\nu /kT} 1306: 690: 201: 8313:Electromagnetic radiation 8184:Blackbody Emission Applet 8049:10.1017/S0080456800031288 7710:Landsberg, P. T. (1990). 7381:Kirchhoff & 1862/1882 7371:, pp. 26, 28, 31, 39 6192:. Springer. p. 107. 3819:{\displaystyle \pi R^{2}} 3699:{\displaystyle 1-\alpha } 3432:is the radius of the Sun. 3366:Stefan–Boltzmann constant 3357:{\displaystyle \sigma \,} 3160:Earth's longwave thermal 2275:Stefan–Boltzmann constant 697:Planck's law states that 676:Stefan–Boltzmann constant 316:thermodynamic equilibrium 192:thermodynamic equilibrium 42:thermodynamic equilibrium 38:electromagnetic radiation 8095:10.1002/andp.18942880511 7879:Handbuch der Astrophysik 7590:10.1002/andp.18601850205 7470:. Nash, C.W. (transl.). 6651:Farzana, Abanty (2001). 6449:10.1002/andp.19013090310 6032:. Springer. p. 41. 5975:From (Kirchhoff, 1860) ( 614:Bose–Einstein statistics 165:electromagnetic spectrum 7919:Longmans, Green and Co. 7856:Oxford University Press 7828:. Vol. 1, part 1. 7736:Lavenda, Bernard Howard 7693:Oxford University Press 7617:Gessamelte Abhandlungen 7444:Oxford University Press 7427:Oxford University Press 6919:March 28, 2012, at the 6494:Encyclopædia Britannica 6122:, pp. 466–467, 478 5867:Sakuma–Hattori equation 5487:, for every wavelength 4907:Gustav Robert Kirchhoff 3669:{\displaystyle \alpha } 3649:{\displaystyle \alpha } 2480:{\displaystyle \theta } 2437:{\displaystyle \Omega } 1309:Wien's displacement law 1303:Wien's displacement law 1050:{\displaystyle \theta } 598:quantum electrodynamics 452:ultraviolet catastrophe 73:ultraviolet catastrophe 7604:Philosophical Magazine 7597:Kirchhoff, G. (1860). 6714:Proc Natl Acad Sci USA 6489:"Stefan-Boltzmann law" 6284:Huang, Kerson (1967). 6184:Joseph Caniou (1999). 5993:Philosophical Magazine 5913:Mandel & Wolf 1995 5791: 5691: 4841: 4740: 4693: 4663: 4633: 4582: 4522: 4465: 4400: 4279: 4194: 4115: 4088: 4057: 3994: 3949: 3853: 3820: 3774: 3700: 3670: 3650: 3621: 3598: 3548: 3426: 3394: 3358: 3317: 3231: 3165: 3133: 2995: 2900: 2872: 2792: 2687: 2566: 2509: 2508:{\displaystyle \pi /2} 2481: 2461: 2438: 2418: 2395: 2320: 2297: 2267: 2135: 2092: 2001: 1864:(units: power / ) is 1858: 1838: 1777: 1756: 1728: 1685: 1628: 1545: 1514: 1474: 1385: 1342: 1294: 1221: 1179: 1134: 1100: 1051: 1022: 996: 970: 944: 918: 896: 872: 844: 804: 610:Fermi–Dirac statistics 551: 524: 504: 503:{\displaystyle nh\nu } 478: 381: 297: 236: 144: 136: 76: 8298:Astrophysics concepts 7954:John Wiley & Sons 7744:John Wiley & Sons 7637:John Wiley & Sons 7317:Goody & Yung 1989 6735:10.1073/pnas.4.12.370 6520:Jenny Nelson (2002). 6404:"Blackbody Radiation" 6286:Statistical Mechanics 6132:Goody & Yung 1989 5792: 5692: 5450:at fixed temperature 4894:Helmholtz reciprocity 4851:Augustin-Jean Fresnel 4849:In his first memoir, 4819: 4741: 4701:effective temperature 4694: 4664: 4634: 4583: 4523: 4466: 4401: 4280: 4195: 4116: 4089: 4065:effective temperature 4058: 3995: 3950: 3854: 3821: 3775: 3701: 3671: 3656:of this energy where 3651: 3622: 3599: 3549: 3427: 3395: 3359: 3318: 3229: 3177:Earth's infrared glow 3159: 3134: 3005:, or 2000 kcal (food 2996: 2901: 2873: 2793: 2688: 2567: 2510: 2482: 2462: 2460:{\displaystyle 2\pi } 2439: 2424:over the solid angle 2419: 2396: 2321: 2298: 2268: 2136: 2093: 2002: 1859: 1839: 1778: 1757: 1729: 1686: 1629: 1546: 1515: 1513:{\displaystyle W_{0}} 1475: 1386: 1343: 1295: 1222: 1180: 1135: 1101: 1052: 1023: 997: 971: 945: 919: 897: 873: 845: 805: 552: 550:{\displaystyle h\nu } 521: 505: 479: 477:{\displaystyle h\nu } 444:equipartition theorem 371: 292:The temperature of a 291: 234: 181:effective temperature 173:ultraviolet radiation 142: 134: 116:temperature radiation 66: 8196:"Blackbody Spectrum" 7882:. 3, part 1: 63–255. 7716:(Reprint ed.). 6657:The Physics Factbook 6257:J. R. Mahan (2002). 5949:Ian Morison (2008). 5842:Infrared thermometer 5739: 5603: 5462:at fixed wavelength 4880:especially those of 4707: 4676: 4644: 4593: 4533: 4486: 4430: 4319: 4233: 4130: 4098: 4071: 4004: 3975: 3871: 3861:Stefan–Boltzmann law 3830: 3800: 3715: 3684: 3660: 3640: 3610: 3578: 3447: 3406: 3374: 3347: 3240: 3217:Stefan–Boltzmann law 3045: 3011:Basal metabolic rate 2935: 2890: 2802: 2746: 2576: 2530: 2517:Stefan–Boltzmann law 2491: 2471: 2448: 2428: 2408: 2330: 2307: 2284: 2145: 2102: 2011: 1868: 1848: 1797: 1789:Stefan–Boltzmann law 1776:{\displaystyle \nu } 1767: 1740: 1698: 1639: 1562: 1528: 1497: 1399: 1352: 1325: 1231: 1189: 1147: 1110: 1065: 1059:Lambert's cosine law 1041: 1012: 995:{\displaystyle \nu } 986: 960: 934: 908: 886: 871:{\displaystyle \nu } 862: 818: 701: 637:absolute temperature 629:Stefan–Boltzmann law 594:photoelectric effect 578:Wien's radiation law 538: 488: 465: 380:across the universe. 376:image (2012) of the 31:Black-body radiation 8175:– From Hyperphysics 8087:1894AnP...288..132W 7581:1860AnP...185..275K 7105:1999dpf..conf.....W 6947:1972Moon....5..161S 6872:NASA Sun Fact Sheet 6726:1918PNAS....4..370H 6630:Omega Engineering. 6604:Infrared Services. 6465:Statistical Physics 6440:1901AnP...309..553P 6360:2013ApJS..208...20B 6228:2019Meas..139..355M 6134:, pp. 482, 484 5983:vollkommen schwarze 5872:Terahertz radiation 5847:Photon polarization 5270:and at temperature 5056:. Again, the ratio 3944: 3924: 3620:{\displaystyle D\,} 3518: 3312: 3292: 2859: 2701:Human-body emission 2641: 2618: 2515:, we arrive at the 2028: 1391:where the constant 1319:per unit wavelength 902:. Units: power / . 878:radiation per unit 566:theoretical physics 434:Further explanation 222:spontaneous process 50:continuous spectrum 18:Blackbody radiation 8189:2010-06-09 at the 8074:Annalen der Physik 7768:(third ed.). 7746:. pp. 41–42. 7423:Radiative Transfer 7269:Chandrasekhar 1950 7039:F. Selsis (2004). 6955:10.1007/BF00562111 6767:Levine, J (2004). 6427:Annalen der Physik 5882:Wien approximation 5862:Rayleigh–Jeans law 5787: 5687: 5574:Carnot's principle 5501:(For our notation 4842: 4836:, is known as the 4751:greenhouse effects 4746:or −18.8 °C. 4736: 4699:set to unity, the 4689: 4659: 4629: 4578: 4518: 4461: 4396: 4275: 4190: 4111: 4084: 4063:, is known as the 4053: 3990: 3945: 3928: 3908: 3849: 3816: 3770: 3696: 3666: 3646: 3617: 3594: 3544: 3502: 3422: 3390: 3354: 3313: 3296: 3276: 3232: 3166: 3129: 2991: 2896: 2868: 2845: 2788: 2683: 2619: 2601: 2562: 2505: 2477: 2467:) and polar angle 2457: 2434: 2414: 2391: 2319:{\displaystyle dA} 2316: 2296:{\displaystyle dI} 2293: 2263: 2131: 2088: 2014: 1997: 1854: 1834: 1773: 1752: 1724: 1681: 1624: 1541: 1522:Lambert W function 1510: 1470: 1381: 1338: 1290: 1217: 1175: 1130: 1096: 1047: 1018: 992: 978:Boltzmann constant 966: 940: 914: 892: 868: 840: 800: 547: 525: 500: 474: 400:, objects such as 382: 298: 237: 149:frequency spectrum 145: 137: 112:complete radiation 98:was introduced by 77: 69:Rayleigh–Jeans law 7902:978-981-4449-53-3 7753:978-0-471-54607-8 7486:a translation of 7453:978-0-19-510291-8 7419:Chandrasekhar, S. 7232:Schirrmacher 2001 7077:978-0-12-732951-2 7054:978-1-4020-2587-7 7025:978-0-7923-5996-8 6998:978-0-677-04000-4 6541:978-1-86094-340-9 6270:978-0-471-21270-6 6073:(Leipzig), 1899, 6039:978-0-387-34500-0 5962:978-0-470-03333-3 5832:Color temperature 5782: 5781: 5682: 5681: 5637: 4802:Tungsten filament 4730: 4703:of the Earth is: 4687: 4658: 4620: 4569: 4509: 4459: 4420: 4419: 4394: 4393: 4382: 4381: 4380: 4299: 4298: 4214: 4213: 4162: 4109: 4082: 3969: 3968: 3794: 3793: 3568: 3567: 3538: 3479: 3337: 3336: 3254: 3198:radioactive decay 3191:greenhouse effect 3118: 3107: 3102: 3085: 3055: 2983: 2971: 2958: 2945: 2812: 2782: 2769: 2756: 2417:{\displaystyle L} 2383: 2261: 2210: 2174: 2129: 2086: 2066: 1995: 1955: 1945: 1897: 1857:{\displaystyle L} 1602: 1572: 1538: 1465: 1415: 1376: 1362: 1335: 1021:{\displaystyle T} 969:{\displaystyle k} 943:{\displaystyle c} 917:{\displaystyle h} 895:{\displaystyle T} 795: 756: 428:quantum mechanics 410:Hawking radiation 340:emission spectrum 260:spectral radiance 218:thermal radiation 104:thermal radiation 16:(Redirected from 8320: 8280: 8279: 8268: 8267: 8266: 8256: 8255: 8254: 8244: 8243: 8232: 8231: 8230: 8220: 8219: 8211: 8198:by Jeff Bryant, 8144: 8125: 8098: 8060: 8022: 7983: 7972:Schirrmacher, A. 7967: 7942:Rybicki, G. B.; 7938: 7921: 7911:Partington, J.R. 7906: 7893:World Scientific 7891:(2nd ed.). 7883: 7869: 7843: 7813: 7783: 7757: 7731: 7706: 7680: 7664: 7650: 7620: 7608: 7594: 7592: 7554: 7548: 7540: 7522: 7516: 7508: 7485: 7457: 7442:(2nd ed.). 7430: 7405: 7402: 7396: 7390: 7384: 7378: 7372: 7366: 7360: 7359:, pp. 8, 29 7354: 7348: 7342: 7336: 7326: 7320: 7319:, pp. 27–28 7314: 7308: 7302: 7296: 7295:, pp. 16–17 7290: 7284: 7278: 7272: 7266: 7260: 7254: 7248: 7243: 7234: 7229: 7218: 7213: 7202: 7197: 7191: 7186: 7180: 7175: 7169: 7168: 7152: 7139: 7133: 7130:Partington, J.R. 7127: 7121: 7115: 7109: 7108: 7098: 7096:astro-ph/9903232 7086: 7080: 7065: 7059: 7058: 7036: 7030: 7029: 7009: 7003: 7002: 6982: 6976: 6973: 6967: 6966: 6941:(1–2): 161–178. 6930: 6924: 6907: 6901: 6900: 6880: 6874: 6869: 6858: 6843: 6837: 6836: 6824: 6818: 6817: 6815: 6814: 6803: 6797: 6796: 6779:(5): E675–E685. 6764: 6758: 6757: 6747: 6737: 6705: 6699: 6698: 6696: 6695: 6689: 6683:. Archived from 6682: 6673: 6667: 6666: 6664: 6663: 6648: 6642: 6641: 6639: 6638: 6627: 6621: 6620: 6618: 6617: 6608:. Archived from 6601: 6595: 6593: 6581: 6575: 6574: 6572: 6570: 6552: 6546: 6545: 6517: 6511: 6505: 6499: 6498: 6485: 6479: 6478: 6460: 6454: 6453: 6451: 6414: 6408: 6407: 6400: 6394: 6393: 6386: 6380: 6379: 6353: 6332: 6326: 6325: 6323: 6321: 6306: 6300: 6299: 6281: 6275: 6274: 6254: 6248: 6247: 6210: 6204: 6203: 6181: 6175: 6169: 6163: 6158: 6152: 6146: 6135: 6129: 6123: 6117: 6111: 6095: 6089: 6084: 6078: 6067: 6061: 6056:(Berlin), 1893, 6050: 6044: 6043: 6021: 6015: 6014: 6002: 5996: 5973: 5967: 5966: 5946: 5940: 5934: 5928: 5922: 5916: 5910: 5904: 5898: 5796: 5794: 5793: 5788: 5783: 5780: 5769: 5758: 5757: 5749: 5696: 5694: 5693: 5688: 5683: 5680: 5679: 5670: 5665: 5664: 5649: 5648: 5638: 5630: 5621: 5613: 5570: 5549: 5526: 5520: 5498: 5490: 5486: 5473: 5467: 5461: 5455: 5449: 5443: 5423: 5403: 5388: 5353: 5347: 5332: 5305: 5290: 5275: 5269: 5260: 5254: 5219: 5213: 5209: 5196: 5160: 5129: 5090: 5055: 5036: 5017: 5011: 4996: 4969: 4963: 4948: 4942: 4936: 4918: 4901:Gustav Kirchhoff 4745: 4743: 4742: 4737: 4735: 4728: 4721: 4720: 4719: 4698: 4696: 4695: 4690: 4688: 4680: 4668: 4666: 4665: 4660: 4656: 4638: 4636: 4635: 4630: 4625: 4618: 4617: 4616: 4587: 4585: 4584: 4579: 4574: 4567: 4566: 4565: 4547: 4546: 4545: 4527: 4525: 4524: 4519: 4514: 4507: 4500: 4499: 4498: 4470: 4468: 4467: 4462: 4460: 4452: 4414: 4405: 4403: 4402: 4397: 4395: 4392: 4384: 4383: 4373: 4372: 4361: 4360: 4358: 4357: 4347: 4346: 4344: 4343: 4331: 4330: 4313: 4309: 4293: 4284: 4282: 4281: 4276: 4274: 4273: 4272: 4253: 4252: 4251: 4227: 4208: 4199: 4197: 4196: 4191: 4189: 4188: 4187: 4163: 4155: 4150: 4149: 4148: 4124: 4120: 4118: 4117: 4112: 4110: 4102: 4093: 4091: 4090: 4085: 4083: 4075: 4062: 4060: 4059: 4054: 4052: 4051: 4050: 4024: 4023: 4022: 3999: 3997: 3996: 3991: 3989: 3988: 3987: 3963: 3954: 3952: 3951: 3946: 3943: 3938: 3937: 3923: 3918: 3917: 3898: 3897: 3896: 3865: 3858: 3856: 3855: 3850: 3848: 3847: 3825: 3823: 3822: 3817: 3815: 3814: 3788: 3779: 3777: 3776: 3771: 3769: 3768: 3767: 3735: 3734: 3733: 3709: 3705: 3703: 3702: 3697: 3675: 3673: 3672: 3667: 3655: 3653: 3652: 3647: 3626: 3624: 3623: 3618: 3603: 3601: 3600: 3595: 3592: 3591: 3590: 3562: 3553: 3551: 3550: 3545: 3543: 3539: 3537: 3536: 3535: 3519: 3517: 3512: 3511: 3497: 3491: 3490: 3489: 3477: 3464: 3463: 3462: 3441: 3431: 3429: 3428: 3423: 3420: 3419: 3418: 3399: 3397: 3396: 3391: 3388: 3387: 3386: 3363: 3361: 3360: 3355: 3331: 3322: 3320: 3319: 3314: 3311: 3306: 3305: 3291: 3286: 3285: 3266: 3265: 3264: 3252: 3234: 3219:gives the total 3138: 3136: 3135: 3130: 3125: 3116: 3108: 3106: 3100: 3095: 3083: 3082: 3081: 3062: 3057: 3056: 3053: 3000: 2998: 2997: 2992: 2987: 2981: 2973: 2972: 2969: 2960: 2959: 2956: 2947: 2946: 2943: 2925: 2918: 2905: 2903: 2902: 2897: 2885: 2881: 2877: 2875: 2874: 2869: 2864: 2860: 2858: 2853: 2841: 2840: 2814: 2813: 2810: 2797: 2795: 2794: 2789: 2784: 2783: 2780: 2771: 2770: 2767: 2758: 2757: 2754: 2724: 2713: 2692: 2690: 2689: 2684: 2640: 2636: 2627: 2617: 2609: 2571: 2569: 2568: 2563: 2558: 2557: 2542: 2541: 2525: 2514: 2512: 2511: 2506: 2501: 2486: 2484: 2483: 2478: 2466: 2464: 2463: 2458: 2443: 2441: 2440: 2435: 2423: 2421: 2420: 2415: 2400: 2398: 2397: 2392: 2384: 2382: 2381: 2380: 2367: 2356: 2354: 2353: 2325: 2323: 2322: 2317: 2302: 2300: 2299: 2294: 2272: 2270: 2269: 2264: 2262: 2260: 2259: 2258: 2249: 2248: 2235: 2233: 2232: 2211: 2209: 2208: 2207: 2198: 2197: 2187: 2186: 2177: 2175: 2170: 2169: 2168: 2155: 2140: 2138: 2137: 2132: 2130: 2128: 2120: 2112: 2097: 2095: 2094: 2089: 2087: 2082: 2081: 2072: 2067: 2065: 2058: 2057: 2047: 2046: 2037: 2027: 2022: 2006: 2004: 2003: 1998: 1996: 1991: 1974: 1972: 1971: 1956: 1948: 1946: 1944: 1943: 1942: 1933: 1932: 1922: 1921: 1920: 1911: 1910: 1900: 1898: 1893: 1892: 1891: 1878: 1863: 1861: 1860: 1855: 1843: 1841: 1840: 1835: 1809: 1808: 1784: 1782: 1780: 1779: 1774: 1761: 1759: 1758: 1753: 1735: 1733: 1731: 1730: 1725: 1717: 1692: 1690: 1688: 1687: 1682: 1668: 1651: 1650: 1633: 1631: 1630: 1625: 1620: 1615: 1610: 1600: 1599: 1598: 1574: 1573: 1570: 1554: 1550: 1548: 1547: 1542: 1540: 1539: 1536: 1519: 1517: 1516: 1511: 1509: 1508: 1492: 1490: 1487: 1484: 1479: 1477: 1476: 1471: 1466: 1464: 1460: 1459: 1438: 1437: 1418: 1416: 1411: 1403: 1390: 1388: 1387: 1382: 1377: 1369: 1364: 1363: 1360: 1347: 1345: 1344: 1339: 1337: 1336: 1333: 1299: 1297: 1296: 1291: 1274: 1273: 1243: 1242: 1226: 1224: 1223: 1218: 1201: 1200: 1184: 1182: 1181: 1176: 1159: 1158: 1139: 1137: 1136: 1131: 1120: 1105: 1103: 1102: 1097: 1077: 1076: 1056: 1054: 1053: 1048: 1028:is the absolute 1027: 1025: 1024: 1019: 1001: 999: 998: 993: 975: 973: 972: 967: 949: 947: 946: 941: 923: 921: 920: 915: 901: 899: 898: 893: 877: 875: 874: 869: 849: 847: 846: 841: 830: 829: 809: 807: 806: 801: 796: 794: 787: 786: 779: 759: 757: 755: 754: 745: 744: 743: 727: 713: 712: 673: 672: 670: 667: 649:is given, where 648: 586:electromagnetism 556: 554: 553: 548: 509: 507: 506: 501: 483: 481: 480: 475: 422: 327:cavity radiation 280: 276: 272: 185:visible spectrum 157:room temperature 108:cavity radiation 100:Gustav Kirchhoff 21: 8328: 8327: 8323: 8322: 8321: 8319: 8318: 8317: 8288: 8287: 8286: 8274: 8264: 8262: 8252: 8250: 8238: 8228: 8226: 8214: 8206: 8191:Wayback Machine 8151: 8141: 8128: 8122: 8112:Thermal Physics 8109: 8106: 8104:Further reading 8101: 8063: 8025: 7986: 7970: 7964: 7944:Lightman, A. P. 7941: 7924: 7909: 7903: 7886: 7872: 7866: 7846: 7840: 7830:Springer-Verlag 7816: 7810: 7786: 7780: 7760: 7754: 7734: 7728: 7709: 7703: 7683: 7677: 7653: 7647: 7623: 7611: 7596: 7557: 7541: 7525: 7509: 7493: 7482: 7460: 7454: 7433: 7417: 7413: 7408: 7403: 7399: 7391: 7387: 7379: 7375: 7367: 7363: 7355: 7351: 7343: 7339: 7327: 7323: 7315: 7311: 7303: 7299: 7291: 7287: 7279: 7275: 7267: 7263: 7255: 7251: 7246:Kirchhoff 1860c 7244: 7237: 7230: 7221: 7214: 7205: 7200:Kirchhoff 1860b 7198: 7194: 7189:Kirchhoff 1860a 7187: 7183: 7176: 7172: 7165: 7141: 7140: 7136: 7132:(1949), p. 466. 7128: 7124: 7116: 7112: 7088: 7087: 7083: 7066: 7062: 7055: 7038: 7037: 7033: 7026: 7011: 7010: 7006: 6999: 6984: 6983: 6979: 6974: 6970: 6932: 6931: 6927: 6921:Wayback Machine 6908: 6904: 6897: 6882: 6881: 6877: 6870: 6861: 6844: 6840: 6826: 6825: 6821: 6812: 6810: 6806:DrPhysics.com. 6805: 6804: 6800: 6766: 6765: 6761: 6707: 6706: 6702: 6693: 6691: 6687: 6680: 6675: 6674: 6670: 6661: 6659: 6650: 6649: 6645: 6636: 6634: 6629: 6628: 6624: 6615: 6613: 6603: 6602: 6598: 6584:Nave, Dr. Rod. 6583: 6582: 6578: 6568: 6566: 6554: 6553: 6549: 6542: 6519: 6518: 6514: 6506: 6502: 6487: 6486: 6482: 6475: 6462: 6461: 6457: 6416: 6415: 6411: 6402: 6401: 6397: 6388: 6387: 6383: 6334: 6333: 6329: 6319: 6317: 6308: 6307: 6303: 6296: 6283: 6282: 6278: 6271: 6256: 6255: 6251: 6212: 6211: 6207: 6200: 6183: 6182: 6178: 6170: 6166: 6159: 6155: 6147: 6138: 6130: 6126: 6120:Partington 1949 6118: 6114: 6096: 6092: 6085: 6081: 6068: 6064: 6051: 6047: 6040: 6023: 6022: 6018: 6004: 6003: 5999: 5974: 5970: 5963: 5948: 5947: 5943: 5935: 5931: 5923: 5919: 5911: 5907: 5899: 5895: 5891: 5886: 5822: 5770: 5759: 5742: 5737: 5736: 5671: 5656: 5622: 5606: 5601: 5600: 5585: 5560: 5552: 5539: 5531: 5522: 5510: 5502: 5496: 5492: 5488: 5484: 5481:can be stated: 5469: 5463: 5457: 5451: 5445: 5433: 5425: 5413: 5405: 5390: 5355: 5349: 5334: 5307: 5292: 5277: 5271: 5265: 5256: 5221: 5215: 5211: 5205: 5163: 5135: 5096: 5057: 5038: 5019: 5013: 4998: 4971: 4965: 4950: 4944: 4943:at temperature 4938: 4923: 4914: 4903: 4877:Balfour Stewart 4873: 4871:Balfour Stewart 4847: 4838:Planckian locus 4799: 4766: 4710: 4705: 4704: 4674: 4673: 4642: 4641: 4608: 4591: 4590: 4557: 4536: 4531: 4530: 4489: 4484: 4483: 4477: 4428: 4427: 4412: 4385: 4362: 4349: 4348: 4335: 4322: 4317: 4316: 4308: 4302: 4291: 4257: 4236: 4231: 4230: 4206: 4165: 4133: 4128: 4127: 4096: 4095: 4069: 4068: 4028: 4007: 4002: 4001: 3978: 3973: 3972: 3961: 3874: 3869: 3868: 3839: 3828: 3827: 3806: 3798: 3797: 3786: 3755: 3718: 3713: 3712: 3682: 3681: 3658: 3657: 3638: 3637: 3634: 3631:and the planet. 3608: 3607: 3581: 3576: 3575: 3560: 3527: 3520: 3498: 3492: 3468: 3450: 3445: 3444: 3435: 3409: 3404: 3403: 3377: 3372: 3371: 3345: 3344: 3329: 3243: 3238: 3237: 3151: 3145: 3096: 3070: 3063: 3048: 3043: 3042: 3037:Application of 2964: 2951: 2938: 2933: 2932: 2923: 2917: 2911: 2888: 2887: 2883: 2879: 2832: 2831: 2827: 2805: 2800: 2799: 2775: 2762: 2749: 2744: 2743: 2736: 2735: 2734: 2733: 2732: 2725: 2716: 2715: 2714: 2703: 2698: 2574: 2573: 2549: 2533: 2528: 2527: 2520: 2489: 2488: 2469: 2468: 2446: 2445: 2426: 2425: 2406: 2405: 2372: 2368: 2357: 2345: 2328: 2327: 2305: 2304: 2282: 2281: 2250: 2240: 2239: 2221: 2199: 2189: 2188: 2178: 2160: 2156: 2143: 2142: 2121: 2113: 2100: 2099: 2073: 2049: 2048: 2038: 2009: 2008: 1975: 1963: 1934: 1924: 1923: 1912: 1902: 1901: 1883: 1879: 1866: 1865: 1846: 1845: 1800: 1795: 1794: 1793:By integrating 1791: 1765: 1764: 1763: 1738: 1737: 1696: 1695: 1694: 1642: 1637: 1636: 1635: 1590: 1565: 1560: 1559: 1552: 1531: 1526: 1525: 1500: 1495: 1494: 1488: 1485: 1482: 1480: 1448: 1429: 1422: 1404: 1397: 1396: 1355: 1350: 1349: 1328: 1323: 1322: 1311: 1305: 1265: 1234: 1229: 1228: 1192: 1187: 1186: 1150: 1145: 1144: 1108: 1107: 1068: 1063: 1062: 1039: 1038: 1035: 1010: 1009: 984: 983: 958: 957: 932: 931: 926:Planck constant 906: 905: 884: 883: 860: 859: 821: 816: 815: 764: 763: 746: 735: 728: 704: 699: 698: 695: 689: 684: 668: 665: 663: 658: 640: 536: 535: 486: 485: 463: 462: 436: 420: 391:Kirchhoff's Law 283:blackbody curve 278: 274: 270: 206: 200: 129: 124: 28: 23: 22: 15: 12: 11: 5: 8326: 8324: 8316: 8315: 8310: 8305: 8300: 8290: 8289: 8285: 8284: 8272: 8260: 8248: 8236: 8224: 8204: 8203: 8193: 8181: 8176: 8170: 8169:at Academo.org 8164: 8158: 8150: 8149:External links 8147: 8146: 8145: 8139: 8131:Modern Physics 8126: 8120: 8105: 8102: 8100: 8099: 8081:(5): 132–165. 8061: 8023: 8003:10.1086/351669 7997:(4): 565–600. 7984: 7968: 7962: 7939: 7922: 7907: 7901: 7884: 7870: 7864: 7844: 7838: 7822:Rechenberg, H. 7814: 7808: 7784: 7778: 7758: 7752: 7732: 7726: 7707: 7701: 7681: 7675: 7651: 7645: 7621: 7609: 7575:(2): 275–301. 7555: 7523: 7491: 7480: 7458: 7452: 7434:Goody, R. M.; 7431: 7414: 7412: 7409: 7407: 7406: 7397: 7385: 7373: 7361: 7349: 7337: 7321: 7309: 7297: 7285: 7273: 7261: 7249: 7235: 7219: 7203: 7192: 7181: 7170: 7163: 7134: 7122: 7110: 7081: 7060: 7053: 7031: 7024: 7004: 6997: 6977: 6968: 6925: 6902: 6895: 6875: 6859: 6838: 6819: 6798: 6759: 6700: 6668: 6643: 6622: 6596: 6576: 6547: 6540: 6512: 6500: 6480: 6473: 6455: 6434:(3): 553–563. 6409: 6395: 6381: 6327: 6301: 6294: 6276: 6269: 6249: 6205: 6198: 6176: 6164: 6153: 6136: 6124: 6112: 6090: 6079: 6062: 6045: 6038: 6016: 5997: 5985:, oder kürzer 5968: 5961: 5941: 5937:Landsberg 1990 5929: 5917: 5905: 5892: 5890: 5887: 5885: 5884: 5879: 5874: 5869: 5864: 5859: 5854: 5849: 5844: 5839: 5834: 5829: 5823: 5821: 5818: 5786: 5779: 5776: 5773: 5768: 5765: 5762: 5755: 5752: 5748: 5745: 5717:= π) or away ( 5711:speed of light 5686: 5678: 5674: 5669: 5663: 5659: 5655: 5652: 5647: 5644: 5641: 5636: 5633: 5628: 5625: 5619: 5616: 5612: 5609: 5584: 5583:Doppler effect 5581: 5556: 5535: 5506: 5494: 5429: 5409: 5333:is again just 5018:is denoted by 4902: 4899: 4882:Pierre Prevost 4872: 4869: 4846: 4843: 4798: 4795: 4765: 4762: 4758:solar constant 4734: 4727: 4724: 4718: 4713: 4686: 4683: 4670: 4669: 4655: 4652: 4649: 4639: 4628: 4624: 4615: 4611: 4607: 4604: 4601: 4598: 4588: 4577: 4573: 4564: 4560: 4556: 4553: 4550: 4544: 4539: 4528: 4517: 4513: 4506: 4503: 4497: 4492: 4476: 4473: 4458: 4455: 4450: 4447: 4444: 4441: 4438: 4435: 4418: 4417: 4408: 4406: 4391: 4388: 4379: 4376: 4371: 4368: 4365: 4356: 4352: 4342: 4338: 4334: 4329: 4325: 4306: 4297: 4296: 4287: 4285: 4271: 4268: 4265: 4260: 4256: 4250: 4247: 4244: 4239: 4222:radiant energy 4216:For a body in 4212: 4211: 4202: 4200: 4186: 4183: 4179: 4176: 4173: 4168: 4161: 4158: 4153: 4147: 4144: 4141: 4136: 4108: 4105: 4081: 4078: 4049: 4046: 4042: 4039: 4036: 4031: 4027: 4021: 4018: 4015: 4010: 3986: 3981: 3967: 3966: 3957: 3955: 3942: 3936: 3931: 3927: 3922: 3916: 3911: 3907: 3904: 3901: 3895: 3892: 3888: 3885: 3882: 3877: 3846: 3842: 3838: 3835: 3813: 3809: 3805: 3792: 3791: 3782: 3780: 3766: 3763: 3758: 3753: 3750: 3747: 3744: 3741: 3738: 3732: 3729: 3726: 3721: 3695: 3692: 3689: 3665: 3645: 3633: 3632: 3615: 3605: 3589: 3584: 3572: 3566: 3565: 3556: 3554: 3542: 3534: 3530: 3526: 3523: 3516: 3510: 3505: 3501: 3495: 3488: 3485: 3482: 3476: 3471: 3467: 3461: 3458: 3453: 3434: 3433: 3417: 3412: 3401: 3385: 3380: 3369: 3352: 3341: 3335: 3334: 3325: 3323: 3310: 3304: 3299: 3295: 3290: 3284: 3279: 3275: 3272: 3269: 3263: 3260: 3257: 3251: 3246: 3210: 3209: 3194: 3187: 3180: 3173: 3147:Main article: 3144: 3141: 3128: 3124: 3121: 3115: 3111: 3105: 3099: 3094: 3091: 3088: 3080: 3077: 3073: 3069: 3066: 3060: 3051: 3027:Nusselt number 2990: 2986: 2980: 2976: 2967: 2963: 2954: 2950: 2941: 2915: 2895: 2867: 2863: 2857: 2852: 2848: 2844: 2839: 2835: 2830: 2826: 2823: 2820: 2817: 2808: 2787: 2778: 2774: 2765: 2761: 2752: 2726: 2719: 2718: 2717: 2708: 2707: 2706: 2705: 2704: 2702: 2699: 2697: 2694: 2682: 2679: 2676: 2673: 2670: 2666: 2663: 2659: 2656: 2653: 2650: 2647: 2644: 2639: 2635: 2631: 2626: 2622: 2616: 2613: 2608: 2604: 2600: 2597: 2594: 2590: 2587: 2584: 2581: 2561: 2556: 2552: 2548: 2545: 2540: 2536: 2504: 2500: 2496: 2476: 2456: 2453: 2433: 2413: 2390: 2387: 2379: 2375: 2371: 2366: 2363: 2360: 2352: 2348: 2344: 2341: 2338: 2335: 2315: 2312: 2292: 2289: 2257: 2253: 2247: 2243: 2238: 2231: 2228: 2224: 2220: 2217: 2214: 2206: 2202: 2196: 2192: 2185: 2181: 2173: 2167: 2163: 2159: 2153: 2150: 2127: 2124: 2119: 2116: 2110: 2107: 2085: 2080: 2076: 2070: 2064: 2061: 2056: 2052: 2045: 2041: 2034: 2031: 2026: 2021: 2017: 1994: 1990: 1987: 1984: 1981: 1978: 1970: 1966: 1962: 1959: 1954: 1951: 1941: 1937: 1931: 1927: 1919: 1915: 1909: 1905: 1896: 1890: 1886: 1882: 1876: 1873: 1853: 1833: 1830: 1827: 1824: 1821: 1818: 1815: 1812: 1807: 1803: 1790: 1787: 1772: 1751: 1748: 1745: 1723: 1720: 1716: 1712: 1709: 1706: 1703: 1680: 1677: 1674: 1671: 1667: 1663: 1660: 1657: 1654: 1649: 1645: 1623: 1619: 1614: 1609: 1606: 1597: 1593: 1589: 1586: 1583: 1580: 1577: 1568: 1534: 1507: 1503: 1469: 1463: 1458: 1455: 1451: 1447: 1444: 1441: 1436: 1432: 1428: 1425: 1421: 1414: 1410: 1407: 1380: 1375: 1372: 1367: 1358: 1331: 1307:Main article: 1304: 1301: 1289: 1286: 1283: 1280: 1277: 1272: 1268: 1264: 1261: 1258: 1255: 1252: 1249: 1246: 1241: 1237: 1216: 1213: 1210: 1207: 1204: 1199: 1195: 1174: 1171: 1168: 1165: 1162: 1157: 1153: 1129: 1126: 1123: 1119: 1115: 1095: 1092: 1089: 1086: 1083: 1080: 1075: 1071: 1046: 1034: 1033: 1017: 1007: 991: 981: 965: 955: 952:speed of light 939: 929: 913: 903: 891: 867: 839: 836: 833: 828: 824: 812: 799: 793: 790: 785: 782: 778: 774: 771: 767: 762: 753: 749: 742: 738: 734: 731: 725: 722: 719: 716: 711: 707: 691:Main article: 688: 685: 683: 680: 606:gas of photons 582:thermodynamics 546: 543: 499: 496: 493: 473: 470: 457:In the longer 435: 432: 202:Main article: 199: 196: 163:region of the 128: 125: 123: 120: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 8325: 8314: 8311: 8309: 8308:Heat transfer 8306: 8304: 8301: 8299: 8296: 8295: 8293: 8283: 8278: 8273: 8271: 8261: 8259: 8249: 8247: 8242: 8237: 8235: 8225: 8223: 8218: 8213: 8209: 8201: 8197: 8194: 8192: 8188: 8185: 8182: 8180: 8177: 8174: 8171: 8168: 8165: 8162: 8159: 8156: 8153: 8152: 8148: 8142: 8140:0-7167-4345-0 8136: 8132: 8127: 8123: 8121:0-7167-1088-9 8117: 8113: 8108: 8107: 8103: 8096: 8092: 8088: 8084: 8080: 8076: 8075: 8070: 8066: 8062: 8058: 8054: 8050: 8046: 8042: 8038: 8037: 8032: 8028: 8024: 8020: 8016: 8012: 8008: 8004: 8000: 7996: 7992: 7991: 7985: 7981: 7977: 7973: 7969: 7965: 7963:0-471-82759-2 7959: 7955: 7951: 7950: 7945: 7940: 7937: 7933: 7932: 7927: 7923: 7920: 7916: 7912: 7908: 7904: 7898: 7894: 7890: 7885: 7881: 7880: 7875: 7871: 7867: 7865:0-19-503437-6 7861: 7857: 7853: 7849: 7845: 7841: 7839:0-387-90642-8 7835: 7831: 7827: 7823: 7819: 7815: 7811: 7809:0-521-41711-2 7805: 7801: 7797: 7793: 7789: 7785: 7781: 7779:0-19-850177-3 7775: 7771: 7767: 7763: 7759: 7755: 7749: 7745: 7741: 7737: 7733: 7729: 7727:0-486-66493-7 7723: 7719: 7715: 7714: 7708: 7704: 7702:0-19-502383-8 7698: 7694: 7690: 7686: 7682: 7678: 7676:0-691-01206-7 7672: 7668: 7663: 7662: 7656: 7652: 7648: 7646:0-471-97393-9 7642: 7638: 7634: 7630: 7629:Prigogine, I. 7626: 7625:Kondepudi, D. 7622: 7618: 7614: 7613:Kirchhoff, G. 7610: 7606: 7605: 7600: 7591: 7586: 7582: 7578: 7574: 7570: 7569: 7564: 7560: 7559:Kirchhoff, G. 7556: 7552: 7546: 7538: 7537: 7532: 7528: 7527:Kirchhoff, G. 7524: 7520: 7514: 7506: 7505: 7500: 7496: 7495:Kirchhoff, G. 7492: 7489: 7483: 7481:0-262-08047-8 7477: 7473: 7469: 7468: 7463: 7459: 7455: 7449: 7445: 7441: 7437: 7432: 7428: 7424: 7420: 7416: 7415: 7410: 7401: 7398: 7394: 7389: 7386: 7383:, p. 573 7382: 7377: 7374: 7370: 7365: 7362: 7358: 7353: 7350: 7346: 7341: 7338: 7334: 7330: 7325: 7322: 7318: 7313: 7310: 7307:, p. 328 7306: 7301: 7298: 7294: 7289: 7286: 7282: 7277: 7274: 7270: 7265: 7262: 7258: 7253: 7250: 7247: 7242: 7240: 7236: 7233: 7228: 7226: 7224: 7220: 7217: 7212: 7210: 7208: 7204: 7201: 7196: 7193: 7190: 7185: 7182: 7179: 7174: 7171: 7166: 7164:0-691-02350-6 7160: 7156: 7151: 7150: 7144: 7138: 7135: 7131: 7126: 7123: 7119: 7114: 7111: 7106: 7102: 7097: 7092: 7085: 7082: 7078: 7074: 7070: 7064: 7061: 7056: 7050: 7046: 7042: 7035: 7032: 7027: 7021: 7017: 7016: 7008: 7005: 7000: 6994: 6990: 6989: 6981: 6978: 6972: 6969: 6964: 6960: 6956: 6952: 6948: 6944: 6940: 6936: 6929: 6926: 6922: 6918: 6915: 6911: 6906: 6903: 6898: 6896:0-7503-0815-X 6892: 6888: 6887: 6879: 6876: 6873: 6868: 6866: 6864: 6860: 6856: 6855:90-277-1296-4 6852: 6848: 6842: 6839: 6834: 6830: 6823: 6820: 6809: 6802: 6799: 6794: 6790: 6786: 6782: 6778: 6774: 6770: 6763: 6760: 6755: 6751: 6746: 6741: 6736: 6731: 6727: 6723: 6720:(12): 370–3. 6719: 6715: 6711: 6704: 6701: 6690:on 2006-09-02 6686: 6679: 6672: 6669: 6658: 6654: 6647: 6644: 6633: 6626: 6623: 6612:on 2007-06-25 6611: 6607: 6600: 6597: 6591: 6587: 6580: 6577: 6565: 6561: 6557: 6551: 6548: 6543: 6537: 6533: 6529: 6525: 6524: 6516: 6513: 6509: 6504: 6501: 6496: 6495: 6490: 6484: 6481: 6476: 6474:0-521-65314-2 6470: 6466: 6459: 6456: 6450: 6445: 6441: 6437: 6433: 6429: 6428: 6423: 6419: 6413: 6410: 6405: 6399: 6396: 6391: 6385: 6382: 6377: 6373: 6369: 6365: 6361: 6357: 6352: 6347: 6343: 6339: 6331: 6328: 6316: 6312: 6305: 6302: 6297: 6295:0-471-81518-7 6291: 6287: 6280: 6277: 6272: 6266: 6262: 6261: 6253: 6250: 6245: 6241: 6237: 6233: 6229: 6225: 6221: 6217: 6209: 6206: 6201: 6199:0-7923-8532-2 6195: 6191: 6187: 6180: 6177: 6173: 6168: 6165: 6162: 6157: 6154: 6150: 6145: 6143: 6141: 6137: 6133: 6128: 6125: 6121: 6116: 6113: 6110: 6107: 6103: 6099: 6094: 6091: 6088: 6083: 6080: 6076: 6072: 6066: 6063: 6059: 6055: 6049: 6046: 6041: 6035: 6031: 6027: 6020: 6017: 6012: 6008: 6001: 5998: 5994: 5990: 5986: 5982: 5978: 5972: 5969: 5964: 5958: 5954: 5953: 5945: 5942: 5939:, Chapter 13. 5938: 5933: 5930: 5927:, Chapter 11. 5926: 5921: 5918: 5915:, Chapter 13. 5914: 5909: 5906: 5902: 5897: 5894: 5888: 5883: 5880: 5878: 5875: 5873: 5870: 5868: 5865: 5863: 5860: 5858: 5855: 5853: 5850: 5848: 5845: 5843: 5840: 5838: 5835: 5833: 5830: 5828: 5825: 5824: 5819: 5817: 5815: 5811: 5806: 5804: 5800: 5784: 5777: 5774: 5771: 5766: 5763: 5760: 5753: 5750: 5746: 5743: 5733: 5731: 5726: 5724: 5720: 5716: 5712: 5708: 5704: 5700: 5684: 5676: 5672: 5667: 5661: 5657: 5653: 5650: 5645: 5642: 5639: 5634: 5631: 5626: 5623: 5617: 5614: 5610: 5607: 5598: 5594: 5590: 5582: 5580: 5577: 5575: 5568: 5564: 5559: 5555: 5547: 5543: 5538: 5534: 5528: 5525: 5518: 5514: 5509: 5505: 5500: 5480: 5475: 5472: 5466: 5460: 5454: 5448: 5441: 5437: 5432: 5428: 5421: 5417: 5412: 5408: 5401: 5397: 5393: 5389:was equal to 5386: 5382: 5378: 5374: 5370: 5366: 5362: 5358: 5352: 5345: 5341: 5337: 5330: 5326: 5322: 5318: 5314: 5310: 5303: 5299: 5295: 5288: 5284: 5280: 5274: 5268: 5262: 5259: 5252: 5248: 5244: 5240: 5236: 5232: 5228: 5224: 5218: 5208: 5202: 5198: 5194: 5190: 5186: 5182: 5178: 5174: 5170: 5166: 5158: 5154: 5150: 5146: 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516: 514: 497: 494: 491: 471: 468: 460: 455: 453: 449: 448:heat capacity 445: 441: 433: 431: 429: 424: 417: 415: 411: 407: 403: 399: 394: 392: 389:still follow 388: 379: 375: 370: 366: 364: 359: 354: 352: 348: 343: 341: 336: 332: 328: 324: 319: 317: 313: 309: 304: 295: 290: 286: 284: 268: 263: 261: 255: 253: 249: 244: 242: 233: 229: 227: 223: 219: 215: 214:absolute zero 211: 205: 197: 195: 193: 188: 186: 182: 178: 174: 170: 166: 162: 158: 154: 150: 141: 133: 126: 121: 119: 117: 113: 109: 105: 101: 97: 92: 90: 86: 81: 74: 70: 65: 61: 59: 55: 51: 47: 43: 39: 36: 32: 19: 8130: 8111: 8078: 8072: 8040: 8034: 7994: 7988: 7975: 7948: 7930: 7914: 7888: 7877: 7851: 7825: 7795: 7765: 7739: 7712: 7688: 7660: 7632: 7616: 7602: 7572: 7566: 7545:cite journal 7534: 7529:; (1860b). 7513:cite journal 7502: 7497:; (1860a). 7487: 7466: 7439: 7422: 7411:Bibliography 7400: 7395:, p. 58 7388: 7376: 7364: 7352: 7345:Hermann 1971 7340: 7333:Hermann 1971 7324: 7312: 7300: 7288: 7283:, p. 80 7276: 7264: 7259:, p. 11 7252: 7195: 7184: 7178:Stewart 1858 7173: 7148: 7137: 7125: 7113: 7084: 7068: 7063: 7044: 7034: 7014: 7007: 6987: 6980: 6971: 6938: 6934: 6928: 6909: 6905: 6885: 6878: 6846: 6841: 6832: 6828: 6822: 6811:. Retrieved 6801: 6776: 6772: 6762: 6717: 6713: 6703: 6692:. Retrieved 6685:the original 6671: 6660:. Retrieved 6656: 6646: 6635:. Retrieved 6625: 6614:. Retrieved 6610:the original 6599: 6590:HyperPhysics 6589: 6579: 6567:. Retrieved 6559: 6550: 6532:10.1142/p276 6522: 6515: 6510:, p. 22 6503: 6492: 6483: 6464: 6458: 6431: 6425: 6412: 6398: 6384: 6341: 6337: 6330: 6320:December 21, 6318:. Retrieved 6304: 6285: 6279: 6259: 6252: 6219: 6215: 6208: 6189: 6179: 6174:, p. 43 6167: 6156: 6151:, p. 42 6127: 6115: 6105: 6104:, series 3, 6101: 6098:Draper, J.W. 6093: 6082: 6074: 6070: 6065: 6057: 6053: 6048: 6029: 6019: 6011:Blacksmith U 6010: 6000: 5992: 5988: 5984: 5980: 5979:), p. 277: 5976: 5971: 5951: 5944: 5932: 5920: 5908: 5903:, Chapter 1. 5896: 5877:Thermography 5852:Planck's law 5837:Draper point 5809: 5807: 5802: 5798: 5734: 5729: 5727: 5722: 5718: 5714: 5706: 5702: 5698: 5596: 5592: 5586: 5578: 5566: 5562: 5557: 5553: 5545: 5541: 5536: 5532: 5529: 5523: 5516: 5512: 5507: 5503: 5482: 5476: 5470: 5464: 5458: 5452: 5446: 5439: 5435: 5430: 5426: 5419: 5415: 5410: 5406: 5399: 5395: 5391: 5384: 5380: 5376: 5372: 5368: 5364: 5360: 5356: 5350: 5343: 5339: 5335: 5328: 5324: 5320: 5316: 5312: 5308: 5301: 5297: 5293: 5286: 5282: 5278: 5272: 5266: 5263: 5257: 5250: 5246: 5242: 5238: 5234: 5230: 5226: 5222: 5216: 5206: 5203: 5199: 5192: 5188: 5184: 5180: 5176: 5172: 5168: 5164: 5156: 5152: 5148: 5144: 5140: 5136: 5132: 5125: 5121: 5117: 5113: 5109: 5105: 5101: 5097: 5093: 5086: 5082: 5078: 5074: 5070: 5066: 5062: 5058: 5051: 5047: 5043: 5039: 5032: 5028: 5024: 5020: 5014: 5007: 5003: 4999: 4992: 4988: 4984: 4980: 4976: 4972: 4966: 4959: 4955: 4951: 4945: 4939: 4932: 4928: 4924: 4921: 4915: 4912: 4904: 4890: 4874: 4858: 4855:Isaac Newton 4848: 4831: 4822:chromaticity 4800: 4783: 4779: 4767: 4755: 4748: 4671: 4478: 4425: 4421: 4410: 4303: 4300: 4289: 4215: 4204: 3970: 3959: 3795: 3784: 3635: 3569: 3558: 3436: 3338: 3327: 3214: 3211: 3167: 3152: 3036: 3031:perspiration 3016: 2921: 2912: 2737: 2696:Applications 2521: 2519:: the power 2403: 2279: 1792: 1557: 1392: 1318: 1316: 1312: 1142: 1036: 1032:of the body. 696: 693:Planck's law 659: 654: 650: 645: 641: 626: 574:Planck's law 563: 559: 533: 526: 456: 440:Fourier mode 437: 425: 418: 395: 383: 365:assumption. 362: 355: 344: 326: 320: 302: 299: 282: 267:Draper point 264: 259: 256: 245: 238: 208:All normal ( 207: 189: 153:Planck's law 146: 115: 111: 107: 95: 93: 82: 78: 30: 29: 8270:Outer space 8258:Spaceflight 8027:Stewart, B. 7874:Milne, E.A. 7848:Mihalas, D. 7685:Kuhn, T. S. 7462:Hermann, A. 7436:Yung, Y. L. 7347:, p. 7 7335:, p. 6 7329:Paschen, F. 7271:, p. 8 7257:Planck 1914 7216:Siegel 1976 6857:, page 227. 6418:Planck, Max 6344:(2): 5225. 6222:: 355–360. 6216:Measurement 6172:Planck 1914 6149:Planck 1914 6108:: 345–360. 6087:Planck 1914 5901:Loudon 2000 4886:John Leslie 4820:The color ( 4807:fluorescent 4791:ultraviolet 3023:evaporation 1553:9.9 μm 1491:10 m K 1030:temperature 856:solid angle 459:wavelengths 414:black holes 312:temperature 279:6000 K 275:1000 K 241:wavelengths 58:temperature 54:wavelengths 8292:Categories 7926:Planck, M. 7788:Mandel, L. 7762:Loudon, R. 7539:: 783–787. 7507:: 662–665. 7393:Kragh 1999 7281:Milne 1930 6835:: 314–322. 6813:2007-06-24 6694:2007-06-24 6662:2007-06-24 6637:2007-06-24 6616:2007-06-24 5989:, nennen." 5889:References 4797:Light bulb 4774:decoupling 3039:Wien's law 3019:convection 2928:emissivity 2908:emissivity 2487:from 0 to 2273:being the 954:in vacuum; 570:Max Planck 513:Wien's law 421:300 K 372:Nine-year 358:emissivity 353:radiator. 351:Lambertian 331:wavelength 271:798 K 252:lamp black 220:. It is a 204:Black body 198:Black body 179:, with an 96:black body 46:black body 8234:Astronomy 8057:122316368 7928:(1914) . 7818:Mehra, J. 7764:(2000) . 7655:Kragh, H. 7561:(1860c). 7472:MIT Press 7357:Kuhn 1978 6963:119892155 6376:119271232 6351:1212.5225 6315:Space.com 6244:116260472 6161:Wien 1894 5857:Pyrometer 5827:Bolometer 5764:− 5654:− 5646:θ 5643:⁡ 5627:− 4905:In 1859, 4875:In 1858, 4830:CIE 1931 4764:Cosmology 4685:¯ 4682:ε 4648:α 4606:× 4555:× 4457:¯ 4454:ε 4443:α 4440:− 4378:¯ 4375:ε 4370:α 4367:− 4160:¯ 4157:ϵ 4107:¯ 4104:ϵ 4080:¯ 4077:ϵ 3926:σ 3906:π 3837:π 3804:π 3749:α 3746:− 3694:α 3691:− 3664:α 3644:α 3525:π 3500:π 3351:σ 3294:σ 3274:π 3162:radiation 3120:μ 3090:⋅ 3076:− 3068:× 3050:λ 2962:− 2894:ε 2843:− 2825:ε 2822:σ 2773:− 2678:π 2672:ϕ 2665:θ 2658:θ 2655:⁡ 2649:θ 2646:⁡ 2630:π 2621:∫ 2615:π 2603:∫ 2596:Ω 2589:θ 2586:⁡ 2580:∫ 2547:σ 2539:⋆ 2495:π 2475:θ 2455:π 2432:Ω 2370:π 2365:θ 2362:⁡ 2343:σ 2303:per area 2227:− 2219:× 2162:π 2152:≡ 2149:σ 2141:and with 2118:ν 2109:≡ 2075:π 2060:− 2025:∞ 2016:∫ 2007:by using 1993:π 1986:θ 1980:⁡ 1961:σ 1953:π 1885:π 1829:θ 1823:⁡ 1806:ν 1771:ν 1747:≈ 1711:ν 1659:− 1588:× 1582:× 1567:ν 1533:λ 1468:≈ 1454:− 1443:− 1357:λ 1330:λ 1271:ν 1240:ν 1198:ν 1156:ν 1128:θ 1125:⁡ 1094:θ 1091:⁡ 1074:ν 1045:θ 1004:frequency 990:ν 880:frequency 866:ν 854:per unit 827:ν 789:− 773:ν 737:ν 710:ν 682:Equations 545:ν 529:quantized 498:ν 472:ν 398:astronomy 363:gray body 94:The term 8303:Infrared 8187:Archived 8067:(1894). 8065:Wien, W. 8043:: 1–20. 8029:(1858). 8019:37368520 7974:(2001). 7946:(1979). 7913:(1949). 7824:(1982). 7794:(1995). 7792:Wolf, E. 7738:(1991). 7687:(1978). 7657:(1999). 7631:(1998). 7464:(1971). 7438:(1989). 7421:(1950). 7145:(1960). 6935:The Moon 6917:Archived 6793:15102614 6754:16576330 6676:Lee, B. 6420:(1901). 6077:: 23–41. 6060:: 55–62. 5995:), p. 2. 5987:schwarze 5820:See also 5747:′ 5611:′ 5319:, BB) / 4786:infrared 3007:calories 2924:2 m 2740:infrared 2729:infrared 2572:We used 2216:5.670373 1783:= 17 THz 1585:5.879... 1227:through 618:fermions 590:Einstein 347:radiance 335:spectrum 323:hohlraum 294:Pāhoehoe 248:graphite 210:baryonic 161:infrared 127:Spectrum 71:and its 8282:Science 8222:Physics 8208:Portals 8202:, 2007. 8083:Bibcode 7577:Bibcode 7101:Bibcode 6943:Bibcode 6745:1091498 6722:Bibcode 6569:July 8, 6497:. 2019. 6436:Bibcode 6356:Bibcode 6224:Bibcode 5709:is the 4892:Stokes- 4884:and of 4865:caloric 4845:History 4726:254.356 3676:is the 3364:is the 2906:is the 1520:is the 1002:is the 976:is the 950:is the 924:is the 674:is the 602:photons 226:entropy 169:Celsius 35:thermal 33:is the 8137: 8118: 8055: 8017: 8011:794025 8009: 7960: 7899: 7862: 7836: 7806: 7776: 7750: 7724: 7699: 7673: 7643: 7478: 7450: 7161: 7075: 7051: 7022: 6995: 6961: 6893: 6853: 6791: 6752: 6742: 6538: 6471: 6374: 6292: 6267: 6242: 6196: 6036: 5959: 5697:where 5497:(λ, T) 4860:Optics 4729: 4657: 4619: 4568: 4508: 3971:where 3678:albedo 3570:where 3478: 3339:where 3253: 3204:, and 3184:albedo 3117: 3101: 3084: 2982: 2970:absorb 2910:, and 2878:where 2781:absorb 1693:where 1601: 810:where 622:bosons 523:Jeans. 175:. The 122:Theory 8246:Stars 8053:S2CID 8015:S2CID 7155:408–9 7091:arXiv 6959:S2CID 6688:(PDF) 6681:(PDF) 6372:S2CID 6346:arXiv 6240:S2CID 5797:Here 5477:Thus 5402:, BB) 5346:, BB) 5331:, BB) 5304:, BB) 5289:, BB) 4834:space 4826:locus 4654:0.309 4603:1.496 4552:6.957 3221:power 3065:2.898 2098:with 1524:. So 1481:2.897 852:power 664:5.670 402:stars 273:. 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