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).