For the radiation from a black body in thermal equilibrium, see Black-body radiation As the temperature of a black body decreases, its intensity also decreases and its peak moves to longer wavelengths. Shown for comparison is the classical Rayleigh–Jeans law and its ultraviolet catastrophe A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A white body is one with a "rough surface [that] reflects all incident rays completely and uniformly in all directions."[1] A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic radiation called black-body radiation. The radiation is emitted according to Planck's law, meaning that it has a spectrum that is determined by the temperature alone (see figure at right), not by the body's shape or composition. An ideal black body in thermal equilibrium has two notable properties:[2] It is an ideal emitter: at every frequency, it emits as much or more thermal radiative energy as any other body at the same temperature. It is a diffuse emitter: the energy is radiated isotropically, independent of direction. An approximate realization of a black surface is a hole in the wall of a large insulated enclosure (an oven). Any light entering the hole is reflected or absorbed at the internal surfaces of the body and is unlikely to re-emerge, making the hole a nearly perfect absorber. When the radiation confined in such an enclosure is in thermal equilibrium, the radiation emitted from the hole will be as great as from any body at that equilibrium temperature. Real materials emit energy at a fraction—called the emissivity—of black-body energy levels. By definition, a black body in thermal equilibrium has an emissivity of ε = 1.0. A source with lower emissivity independent of frequency often is referred to as a gray body.[3][4] Construction of black bodies with emissivity as close to one as possible remains a topic of current interest.[5] In astronomy, the radiation from stars and planets is sometimes characterized in terms of an effective temperature, the temperature of a black body that would emit the same total flux of electromagnetic energy. Contents

Definition Edit

The idea of a black body originally was introduced by Gustav Kirchhoff in 1860 as follows: ...the supposition that bodies can be imagined which, for infinitely small thicknesses, completely absorb all incident rays, and neither reflect nor transmit any. I shall call such bodies perfectly black, or, more briefly, black bodies.[6] A more modern definition drops the reference to "infinitely small thicknesses":[7] An ideal body is now defined, called a blackbody. A blackbody allows all incident radiation to pass into it (no reflected energy) and internally absorbs all the incident radiation (no energy transmitted through the body). This is true for radiation of all wavelengths and for all angles of incidence. Hence the blackbody is a perfect absorber for all incident radiation.[8]

Idealizations Edit

This section describes some concepts developed in connection with black bodies. An approximate realization of a black body as a tiny hole in an insulated enclosure Cavity with a hole Edit A widely used model of a black surface is a small hole in a cavity with walls that are opaque to radiation.[8] Radiation incident on the hole will pass into the cavity, and is very unlikely to be re-emitted if the cavity is large. The hole is not quite a perfect black surface — in particular, if the wavelength of the incident radiation is longer than the diameter of the hole, part will be reflected. Similarly, even in perfect thermal equilibrium, the radiation inside a finite-sized cavity will not have an ideal Planck spectrum for wavelengths comparable to or larger than the size of the cavity.[9] Suppose the cavity is held at a fixed temperature T and the radiation trapped inside the enclosure is at thermal equilibrium with the enclosure. The hole in the enclosure will allow some radiation to escape. If the hole is small, radiation passing in and out of the hole has negligible effect upon the equilibrium of the radiation inside the cavity. This escaping radiation will approximate black-body radiation that exhibits a distribution in energy characteristic of the temperature T and does not depend upon the properties of the cavity or the hole, at least for wavelengths smaller than the size of the hole.[9] See the figure in the Introduction for the spectrum as a function of the frequency of the radiation, which is related to the energy of the radiation by the equation E=hf, with E = energy, h = Planck's constant, f = frequency. At any given time the radiation in the cavity may not be in thermal equilibrium, but the second law of thermodynamics states that if left undisturbed it will eventually reach equilibrium,[10] although the time it takes to do so may be very long.[11] Typically, equilibrium is reached by continual absorption and emission of radiation by material in the cavity or its walls.[12][13][14][15] Radiation entering the cavity will be "thermalized"; by this mechanism: the energy will be redistributed until the ensemble of photons achieves a Planck distribution. The time taken for thermalization is much faster with condensed matter present than with rarefied matter such as a dilute gas. At temperatures below billions of Kelvin, direct photon–photon interactions[16] are usually negligible compared to interactions with matter.[17] Photons are an example of an interacting boson gas,[18] and as described by the H-theorem,[19] under very general conditions any interacting boson gas will approach thermal equilibrium. Transmission, absorption, and reflection Edit A body's behavior with regard to thermal radiation is characterized by its transmission τ, absorption α, and reflection ρ. The boundary of a body forms an interface with its surroundings, and this interface may be rough or smooth. A nonreflecting interface separating regions with different refractive indices must be rough, because the laws of reflection and refraction governed by the Fresnel equations for a smooth interface require a reflected ray when the refractive indices of the material and its surroundings differ.[20] A few idealized types of behavior are given particular names: An opaque body is one that transmits none of the radiation that reaches it, although some may be reflected.[21][22] That is, τ=0 and α+ρ=1 A transparent body is one that transmits all the radiation that reaches it. That is, τ=1 and α=ρ=0. A gray body is one where α, ρ and τ are uniform for all wavelengths. This term also is used to mean a body for which α is temperature and wavelength independent. A white body is one for which all incident radiation is reflected uniformly in all directions: τ=0, α=0, and ρ=1. For a black body, τ=0, α=1, and ρ=0. Planck offers a theoretical model for perfectly black bodies, which he noted do not exist in nature: besides their opaque interior, they have interfaces that are perfectly transmitting and non-reflective.[23] Kirchhoff's perfect black bodies Edit Kirchhoff in 1860 introduced the theoretical concept of a perfect black body with a completely absorbing surface layer of infinitely small thickness, but Planck noted some severe restrictions upon this idea. Planck noted three requirements upon a black body: the body must (i) allow radiation to enter but not reflect; (ii) possess a minimum thickness adequate to absorb the incident radiation and prevent its re-emission; (iii) satisfy severe limitations upon scattering to prevent radiation from entering and bouncing back out. As a consequence, Kirchhoff's perfect black bodies that absorb all the radiation that falls on them cannot be realized in an infinitely thin surface layer, and impose conditions upon scattering of the light within the black body that are difficult to satisfy.[24][25]

Realizations Edit

Radiative cooling Edit

See also Edit

References Edit