The Stefan—Boltzmann law describes the power radiated from a black body in terms of its temperature. The value of the constant is. The radiance watts per square metre per steradian is given by. The SI unit for absolute temperature T is the kelvin. Wavelength- and subwavelength-scale particles,  metamaterials ,  and other nanostructures are not subject to ray-optical limits and may be designed to exceed the Stefan—Boltzmann law. In , John Tyndall presented measurements of the infrared emission by a platinum filament and the corresponding color of the filament.
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The Stefan—Boltzmann law describes the power radiated from a black body in terms of its temperature. The value of the constant is. The radiance watts per square metre per steradian is given by. The SI unit for absolute temperature T is the kelvin. Wavelength- and subwavelength-scale particles,  metamaterials ,  and other nanostructures are not subject to ray-optical limits and may be designed to exceed the Stefan—Boltzmann law.
In , John Tyndall presented measurements of the infrared emission by a platinum filament and the corresponding color of the filament. Following Bartoli, Boltzmann considered an ideal heat engine using electromagnetic radiation instead of an ideal gas as working matter. The law was almost immediately experimentally verified. Heinrich Weber in pointed out deviations at higher temperatures, but perfect accuracy within measurement uncertainties was confirmed up to temperatures of K by With his law Stefan also determined the temperature of the Sun 's surface.
A round lamella was placed at such a distance from the measuring device that it would be seen at the same angle as the Sun. Precise measurements of atmospheric absorption were not made until and This was the first sensible value for the temperature of the Sun. The temperature of stars other than the Sun can be approximated using a similar means by treating the emitted energy as a black body radiation. This same formula can be used to compute the approximate radius of a main sequence star relative to the sun:.
With the Stefan—Boltzmann law, astronomers can easily infer the radii of stars. The law is also met in the thermodynamics of black holes in so-called Hawking radiation. At Earth, this energy is passing through a sphere with a radius of a 0 , the distance between the Earth and the Sun, and the irradiance received power per unit area is given by. The radiant flux i. Because the Stefan—Boltzmann law uses a fourth power, it has a stabilizing effect on the exchange and the flux emitted by Earth tends to be equal to the flux absorbed, close to the steady state where:.
The Earth has an albedo of 0. The effect of albedo on temperature can be approximated by assuming that the energy absorbed is multiplied by 0.
This approximation reduces the temperature by a factor of 0. The above temperature is Earth's as seen from space, not ground temperature but an average over all emitting bodies of Earth from surface to high altitude.
In the above discussion, we have assumed that the whole surface of the earth is at one temperature. Another interesting question is to ask what the temperature of a blackbody surface on the earth would be assuming that it reaches equilibrium with the sunlight falling on it.
This of course depends on the angle of the sun on the surface and on how much air the sunlight has gone through.
Above the atmosphere, the result is even higher: K. We can think of the earth's surface as "trying" to reach equilibrium temperature during the day, but being cooled by the atmosphere, and "trying" to reach equilibrium with starlight and possibly moonlight at night, but being warmed by the atmosphere.
This relation is:. Now, from the fundamental thermodynamic relation. The last equality comes from the following Maxwell relation :. After separating the differentials the equality becomes. The law can be derived by considering a small flat black body surface radiating out into a half-sphere. Note that the cosine appears because black bodies are Lambertian i. Finally, this proof started out only considering a small flat surface. However, any differentiable surface can be approximated by a collection of small flat surfaces.
So long as the geometry of the surface does not cause the blackbody to reabsorb its own radiation, the total energy radiated is just the sum of the energies radiated by each surface; and the total surface area is just the sum of the areas of each surface—so this law holds for all convex blackbodies, too, so long as the surface has the same temperature throughout.
The law extends to radiation from non-convex bodies by using the fact that the convex hull of a black body radiates as though it were itself a black body.
The total energy density U can be similarly calculated, except the integration is over the whole sphere and there is no cosine, and the energy flux U c should be divided by the velocity c to give the energy density U :. From Wikipedia, the free encyclopedia. See also: Black body , Black-body radiation , Planck's law , and Thermal radiation. Absorption and scattering of light by small particles. Conference on Lasers and Electro-Optics OSA Technical Digest.
Optical Society of America. Philosophical Magazine. Lehrbuch der Experimentalphysik [ Textbook of experimental physics ] in German. Leipzig, Germany: B. Thus, while the temperature climbed only somewhat more than double, the intensity of the radiation increased from See also: Wisniak, Jaime November Indian Journal of Chemical Technology.
Annalen der Physik und Chemie in German. Bibcode : AnP Comptes Rendus in French. London, England: Richard and John E. Australian Telescope Outreach and Education. Retrieved Newport Corporation. Archived from the original on October 29, Archived from the original PDF on Blackbody radiation laws. Categories : Laws of thermodynamics Power laws Heat transfer. Namespaces Article Talk. Views Read Edit View history.
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Hukum Stefan-Boltzmann. Dasanama lan kosok bali saka Stefan-Boltzmann law ing bausastra dasanama Basa Inggris. The relation 1 1. From 1 1. Longair, Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Lambert M.