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Concept
Stefan–Boltzmann law
Summary
The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Ludwig Boltzmann who derived the law theoretically.
For an ideal absorber/emitter or black body, the Stefan–Boltzmann law states that the total energy radiated per unit surface area per unit time (also known as the radiant exitance) is directly proportional to the fourth power of the black body's temperature, T:
The constant of proportionality, , is called the Stefan–Boltzmann constant. It has a value
5.670374419e-8W m−2 K−4 .
In the general case, the Stefan–Boltzmann law for radiant exitance takes the form:
where is the emissivity of the matter doing the emitting. The emissivity is generally between zero and one, although some exotic materials may have an emissivity greater than one. An emissivity of one corresponds to a black body.
The radiant exitance (previously called radiant emittance), , has dimensions of energy flux (energy per unit time per unit area), and the SI units of measure are joules per second per square metre (J s^-1 m^-2), or equivalently, watts per square metre (W m^-2). The SI unit for absolute temperature, T, is the kelvin (K).
To find the total power, , radiated from an object, multiply the radiant exitance by the object's surface area, :
Matter that does not absorb all incident radiation emits less total energy than a black body. Emissions are reduced by a factor , where the emissivity, , is a material property which, for most matter, satisfies . Emissivity can in general depend on wavelength, direction, and polarization. However, the emissivity which appears in the non-directional form of the Stefan–Boltzmann law is the hemispherical total emissivity, which reflects emissions as totaled over all wavelengths, directions, and polarizations.
The form of the Stefan–Boltzmann law that includes emissivity is applicable to all matter, provided that matter is in a state of local thermodynamic equilibrium (LTE) so that its temperature is well-defined.
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