In physics, a black body is an object that absorbs all electromagnetic radiation that falls onto it. No radiation passes through it and none is reflected, yet in classical physics, it theoretically radiates every possible wavelength of energy. Despite the name, black bodies are not actually black as they radiate energy as well. The amount and type of electromagnetic radiation they emit is directly related to their temperature. Black bodies below around 700 K (426.85 ºC) produce very little radiation at visible wavelengths and appear black (hence the name). Black bodies above this temperature, however, begin to produce radiation at visible wavelengths starting at red, going through orange, yellow, and white before ending up at blue as the temperature increases.

The term "black body" was introduced by Gustav Kirchhoff in 1862. The light emitted by a black body is called black-body radiation, and has a special place in the history of quantum mechanics.

In the laboratory, the closest thing to black-body radiation is the radiation from a small hole entrance to a larger cavity. Any light entering the hole would have to reflect off the walls of the cavity multiple times before it escaped and is almost certain to be absorbed by the walls in the process, regardless of what they are made of or the wavelength of the radiation (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 (i.e., the amount of light emitted from the hole at each wavelength) will be continuous, and will not depend on the material in the cavity (compare with emission spectrum). By a theorem proved by Kirchhoff, this curve depends only on the temperature of the cavity walls.

Calculating this curve was a major challenge in theoretical physics during the late nineteenth century. The problem was finally solved in 1900 by Max Planck as Planck's law of black-body radiation. By making changes to Wien's Radiation Law (not to be confused with Wien's displacement law) consistent with Thermodynamics and Electromagnetism, he found a mathematical formula fitting the experimental data in a satisfactory way. To find a physical interpretation for this formula, Planck had then to assume that the energy of the oscillators in the cavity was quantized (i.e., integral multiples of some quantity). Einstein built on this idea and proposed the quantization of electromagnetic radiation itself in 1905 to explain the photoelectric effect. These theoretical advances eventually resulted in the superseding of classical electromagnetism by quantum electrodynamics. Today, these quanta are called photons. In addition, it led to the development of quantum versions of statistical mechanics, called Fermi-Dirac statistics and Bose-Einstein statistics, each applicable to a different class of particles. See also fermions and bosons.



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 Stefan-Boltzmann law. 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 monotonically with temperature.

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 grey body assumption.



Interestingly, this means that every object around you is emitting electromagnetic waves with wavelengths of all values. Every object in the universe has heat, even the emptiness of space, and when the particles that make up an object vibrate on a microscopic level they radiate electromagnetic waves. These wavelengths are predominantly infrared (heat), but there is also a minute amount of visible light like red, yellow, green and blue. So, right now, you and everything around you is emitting visible light. The reason this light cannot be seen is that it has a very low intensity.

When dealing with non-black surfaces, the deviations from ideal black body behavior are determined by both the geometrical structure and the chemical composition, and 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.

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 black-body radiation emitted by black holes.

To begin, we use the Stefan-Boltzmann law to find the total power (energy/second) the Sun is emitting:

$P\_\; =\; left(\; sigma\; T\_^4$

where

$sigma\; ,$ is the Stefan-boltzmann constant,

$T\_S\; ,$ is the surface temperature of the Sun, and

$R\_S\; ,$ is the radius of the Sun.

where

$R\_\; ,$ is the radius of the Earth and

$D\; ,$ is the distance between the Sun and the Earth.

$P\_\; =\; left(\; sigma\; T\_^4$

where $T\_$ is the surface temperature of the earth.

$P\_\; =\; P\_,$

So plug in equations 1, 2, and 3 into this and we get

$left(\; sigma\; T\_^4$