## The Stefan Boltzmann law

The total power emitted, at all wavelength at a given temperature (M), is represented by the area under the corresponding curve:

Total power emitted = radiant exitance = M =1 M^ dl

= area under the curve for a given temperature T

It is clear from Figure 11.2 that the area under each curve rises rapidly with an increase in temperature.

Josef Stefan (1835-1893) was the first to publish (in 1879) an empirical relation known as Stefan's law, which expressed the observation that the total energy emitted appeared to be proportional to the fourth power of the absolute temperature of the surface. About five years later Ludwig Boltzmann (1844-1906) derived the relation using thermodynamic arguments which is now known as the Stefan-Boltzmann law.

Josef Stefan. Courtesy of Austrian Post.

Stefan-Boltzmann law: M = eaT4

Josef Stefan. Courtesy of Austrian Post.

M = total energy emitted per unit area per sec e = emissivity (= 1 for black surface) a = Stefan-Boltzmann constant

= 5.67 x 10-8 Wm-2 K-4 T = absolute temperature (K)

Ludwig Boltzmann. Courtesy of Austrian Post.
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