Stefan-Boltzmann Law

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Stefan-Boltzmann law

[′shte‚fän ′bōlts‚män ‚lȯ]
(statistical mechanics)
The total energy radiated from a blackbody is proportional to the fourth power of the temperature of the body. Also known as fourth-power law; Stefan's law of radiation.

Stefan-Boltzmann Law


(or fourth-power law, Stefan’s law), a law asserting that the fourth power of the absolute temperature T of a blackbody is proportional to the energy density ρ of the radiation from the body and to the emissive power u of the body: ρ = aT4, where a is a constant, and u = σT4, where σ is the Stefan-Boltzmann constant.

The law was formulated on the basis of experimental data by J. Stefan in 1879 for the emissive power of any body. Subsequent measurements, however, showed that the law holds only for the emissive power of a blackbody. In 1884 the law was derived theoretically from thermodynamical considerations by L. Boltzmann, who made use of the proportionality, according to classical electrodynamics, of the pressure of equilibrium radiation to the energy density of the radiation. It turned out, however, that the values of the constants a and σ could be determined theoretically only on the basis of Planck’s radiation law, from which the Stefan-Boltzmann law follows.

The Stefan-Boltzmann law is used in the measurement of high temperatures (seeRADIATION PYROMETER).


Landsberg, G. S. Optika, 4th ed. (Obshchii kursfiziki, vol. 3.) Moscow, 1957.
Shpol’skii, E. V. Atomnaia fizika, 6th ed., vol. 1. Moscow, 1974.
References in periodicals archive ?
The linear dependence in our results is due to the circumstance that the Stefan-Boltzmann law holds for a full range of temperatures, but for narrow temperature ranges it reduces well to a linear dependence.
1] [up arrow] values and those calculated by the Stefan-Boltzmann law for snow (emissivity [epsilon] = 0.
Among other things, he originated the law that the total radiation from a black body is proportional to the 4th power of its absolute temperature, known as the Stefan-Boltzmann law.
Such emissions can exceed the Stefan-Boltzmann law by orders of magnitude [18-20].