Stefan-boltzmann law

Stefan–Boltzmann law

One of the radiation laws, which states that the amount of energy radiated per unit time from a unit surface area of an ideal blackbody is proportional to the fourth power of the absolute temperature of the blackbody.

The law is written

where E is the emittance of the blackbody, σ the Stefan–Boltzmann constant, and T the absolute temperature of the blackbody. This law was established experimentally by Stefan and was given theoretical support by thermodynamic reasoning due to Boltzmann. This law may be deduced by integrating Planck's law over the entire frequency spectrum.

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A hypothetical body that cannot be excited to radiate by an external source of electromagnetic radiation of any frequency, direction, or state of polarization except in a negligibly small set of directions around that of the source radiation.
The traditional definition of a blackbody—as one that absorbs all the radiation incident on it—is inadequate unless to this definition is added the requirement that the body be large compared with the wavelength of the incident radiation. The concept of radiation incident on a body is from geometrical (or ray) optics, which is never strictly valid (because all bodies are finite) and may break down completely when the body is small compared with the wavelength. This was recognized by Planck, but by almost no one who followed him. Although no strict blackbody exists, some bodies are approximately black over a limited range of frequencies, directions, and polarization states of the exciting radiation.
See blackbody radiation, Planck's radiation law, emissivity.
Planck, M. 1959. The Theory of Heat Radiation. p. 2.