Stefan–Boltzmann law

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, $T$ :

M^{\circ }=\sigma \,T^{4}.

The constant of proportionality, $\sigma$ , is called the Stefan–Boltzmann constant. It has a value

σ = 5.670374419...×10⁻⁸ W⋅m⁻²⋅K⁻⁴.

In the general case, the Stefan–Boltzmann law for radiant exitance takes the form:

M=\varepsilon \,M^{\circ }=\varepsilon \,\sigma \,T^{4}

where $\varepsilon$ 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.

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