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 ?
In Section 2.1, we also obtain the mass and radiation rate characteristics for the Schwarzschild black hole as a function of time by using the Stefan-Boltzmann law. In Section 3, we study the thermodynamics of Reissner-Nordstrom black holes taking into account the effect of the GUP.
If one assumes that the energy loss is dominated by photons, then one can apply the Stefan-Boltzmann law to estimate the energy radiated as a function of time
The power per unit area radiated can be determined by integrating the Planck distribution over all wavelengths, yielding the Stefan-Boltzmann law
Quasithermodynamics and a correction to the Stefan-Boltzmann law. Mathematical Notes, 83(1), 72-79.
In their Nature Communications article, the authors argue that this does not constitute a violation of the Stefan-Boltzmann law, because the effective "emitting surface" is now governed by the transmitter, which is essentially transparent [21].
Stefan-Boltzmann Law. Here the a parameter is [alpha] = ([beta], 0,0,0) and the generalized Bogoliubov transformation takes the form
The first two terms are associated with the Stefan-Boltzmann law and the Casimir effect at zero temperature.
This result was used to implement the prescription of Thermo Field Dynamics, which allows dealing with some phenomena at finite temperature, such as the analogous Casimir effect and Stefan-Boltzmann law. We point out that we projected the mean energy and pressure in the space of coordinates in order to recover the results of literature.
Voltage across and current through the lamp are recorded at the time of spectra capture, and the power and temperature data are fit with the Stefan-Boltzmann law. This experiment is further expanded by investigating the lamp's resistance as a function of temperature.
Additionally, the Stefan-Boltzmann law is related to the Planck distribution by solving the following for P;
For instance, the pressure calculated in that theory depends on temperature, T linearly [25], but in SR theory pressure is proportional to [T.sup.4] (also known as Stefan-Boltzmann law) [26].
Steven and Giddings., "Hawking radiation, the Stefan-Boltzmann law, and unitarization," Physics Letters B, vol.