Black-body radiation is the thermal electromagnetic radiation emitted from a body in thermodynamic equilibrium with its environment. A black body is an idealized opaque and non-reflective body. The radiation emitted is a continuous spectrum over all possible radiation wavelengths that depends only on the body's temperature., Chapter 1., Chapter 13., Chapter 11., Chapter 13.
A perfectly-insulated enclosure which is in thermal equilibrium internally contains black-body radiation and will emit it through a hole made in its wall, provided the hole is small enough to have a negligible effect upon the equilibrium. The thermal radiation spontaneously emitted by many ordinary objects can be approximated as black-body radiation.
Of particular importance, although planets and stars (including the Earth and Sun) are neither in thermal equilibrium with their surroundings nor perfect black bodies, black-body radiation is still a good first approximation for the energy they emit.
A black body at room temperature () radiates mostly in the infrared spectrum, which cannot be perceived by the human eye,Partington, J.R. (1949), p. 466. but can be sensed by some reptiles. As the object increases in temperature to about , the emission spectrum gets stronger and extends into the human visual range, and the object appears dull red. As its temperature increases further, it emits more and more orange, yellow, green, and then blue light (and ultimately beyond violet, ultraviolet).
The term black body was introduced by Gustav Kirchhoff in 1860.From (Kirchhoff, 1860) (Annalen der Physik und Chemie), p. 277: "Der Beweis, welcher für die ausgesprochene Behauptung hier gegeben werden soll, … vollkommen schwarze, oder kürzer schwarze, nennen." (The proof, which shall be given here for the proposition stated [above], 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 [they] neither reflect nor transmit rays. I will call such bodies "completely black [bodies]" or more briefly "black [bodies]".) See also (Kirchhoff, 1860) (Philosophical Magazine), p. 2. Black-body radiation is also called thermal radiation, cavity radiation, complete radiation or temperature radiation.
Theory
Spectrum
Black-body radiation has a characteristic, continuous frequency spectrum that depends only on the body's temperature, called the Planck spectrum or Planck's law. The spectrum is peaked at a characteristic frequency that shifts to higher frequencies with increasing temperature, and at room temperature most of the emission is in the infrared region of the electromagnetic spectrum.Wien, W. (1893). Eine neue Beziehung der Strahlung schwarzer Körper zum zweiten Hauptsatz der Wärmetheorie, Sitzungberichte der Königlich-Preußischen Akademie der Wissenschaften (Berlin), 1893, 1: 55–62.Lummer, O., Pringsheim, E. (1899). Die Vertheilung der Energie im Spectrum des schwarzen Körpers, Verhandlungen der Deutschen Physikalischen Gessellschaft (Leipzig), 1899, 1: 23–41. As the temperature increases past about 500 degrees Celsius, 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.Draper, J.W. (1847). On the production of light by heat, London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, series 3, 30: 345–360. When the body appears white, it is emitting a substantial fraction of its energy as ultraviolet radiation. The Sun, with an effective temperature of approximately 5800 K, is an approximate black body with an emission spectrum peaked in the central, yellow-green part of the visible spectrum, but with significant power in the ultraviolet as well.
Black-body radiation provides insight into the thermodynamic equilibrium state of cavity radiation.
Black body
Most types of matter emit electromagnetic radiation while at a temperature above absolute zero. The radiation represents a conversion of a body's internal energy into electromagnetic energy, and is therefore called thermal radiation. It is a spontaneous process of radiative distribution of entropy.
Conversely, all normal matter absorbs electromagnetic radiation to some degree. An object that absorbs all radiation falling on it, at all wavelengths, is called a black body. When a black body is at a uniform temperature, its emission has a characteristic frequency distribution that depends on the temperature. Its emission is called black-body radiation.
The concept of the black body is an idealization, as perfect black bodies do not exist in nature. Graphite and lamp black have emissivities greater than 0.95, and are good approximations to an ideal black material. Experimentally, black-body radiation may be established best as the steady state equilibrium radiation inside a cavity within 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 black-body radiation emanating from the opening.
Black-body radiation has the unique absolutely stable distribution of radiative intensity that can persist in thermodynamic equilibrium inside 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 amount of radiation leaving its surface, called the spectral radiance) is determined solely by the equilibrium temperature and does not depend upon the shape, material or structure of the body. 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).
Black-body radiation becomes a visible glow of light if the temperature of the object is high enough. The Draper point is the temperature at which all solids glow a dim red, about . At , a small opening in the wall of a large uniformly heated opaque-walled cavity (such as an oven), viewed from outside, looks red; at , it looks white. No matter how the oven is constructed, or of what material, as long as it is built so that almost all light entering is absorbed by its walls, it will contain a good approximation to black-body radiation. The spectrum, and therefore color, of the light that comes out will be a function of the cavity temperature alone. A graph of the spectral radiation intensity plotted versus frequency(or wavelength) is called the black-body curve. Different curves are obtained by varying the temperature.
When the body looks black, the absorption is obvious: the amount of light absorbed is all the light that hits the surface. When the black body is much bigger than the wavelength, the light energy absorbed is strictly proportional to the black-body curve. 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.
In the laboratory, black-body radiation is approximated by the radiation from a small hole in a large cavity, a hohlraum, in an entirely opaque body that is only partly reflective, that is maintained at a constant temperature. This technique leads to the alternative term cavity radiation. Any light entering the hole would have to reflect off the walls of the cavity multiple times before it escaped, in which process it is nearly certain to be absorbed. Absorption occurs regardless of the wavelength of the radiation entering (as long as it is small compared to the hole). The hole, then, is a close approximation of a theoretical black body and, if the cavity is heated, the spectrum 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 material in the cavity (compare with emission spectrum).
The radiance or observed intensity is not a function of direction. Therefore, a black body is a perfect Lambertian radiator.
Real objects never behave as full-ideal black bodies, and instead the emitted radiation at a given frequency is a fraction of what the ideal emission would be. The emissivity of a material specifies how well a real body radiates energy as compared with a black body. This emissivity depends on factors such as temperature, emission angle, and wavelength. However, it is typical in engineering to assume that a surface's spectral emissivity and absorptivity do not depend on wavelength so that the emissivity is a constant. This is known as the gray body assumption.
With non-black surfaces, the deviations from ideal black-body behavior are determined by both the surface structure, such as roughness or granularity, and the chemical composition. On a "per wavelength" basis, real objects in states of local thermodynamic equilibrium still follow Kirchhoff's Law: emissivity equals absorptivity, so that an object that does not absorb all incident light will also emit less radiation than an ideal black body; the incomplete absorption can be due to some of the incident light being transmitted through the body or to some of it being reflected at the surface of the body.
In astronomy, objects such as stars are frequently regarded as black bodies, though this is often a poor approximation. An almost perfect black-body spectrum is exhibited by the cosmic microwave background radiation. Hawking radiation is the hypothetical black-body radiation emitted by black holes, 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.
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 () with one square meter of surface area will emit a photon in the visible range (390–750 nm) at an average rate of one photon every 41 seconds, meaning that, for most practical purposes, such a black body does not emit in the visible range.
The study of the laws of black bodies and the failure of classical physics to describe them helped establish the foundations of quantum mechanics.
Additional explanations According to the classical theory of radiation, if each Fourier mode of the equilibrium radiation (in an otherwise empty cavity with perfectly reflective walls) is considered as a degree of freedom capable of exchanging energy, then, according to the equipartition theorem of classical physics, there would be an equal amount of energy in each mode. Since there are an infinite number of modes, this would imply infinite heat capacity, as well as a nonphysical (i.e. not real) spectrum of emitted radiation that grows without bound with increasing frequency, predicting infinite emission power. The problem is known as the ultraviolet catastrophe. Moreover, the classical theory cannot explain the experimentally observed peak in emission spectra (see also Wien's law).