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Kirchhoff's Law and Emissivity


Excerpt from Optical Design Fundamentals for Infrared Systems, Second Edition

Gustav Robert Kirchhoff (1824–1887) stated in 1860 that “at thermal equilibrium, the power radiated by an object must be equal to the power absorbed.” This leads to the observation that if an object absorbs 100 percent of the radiation incident upon it, it must reradiate 100 percent. As already stated, this is the definition of a blackbody radiator.

Most radiation sources are not blackbodies. Some of the energy incident upon them may be reflected or transmitted. The ratio of the radiant emittance W' of such a source and the radiant emittance W of a blackbody at the same temperature is called the emissivity ε of the source:

Equation 1.14

With this relation, different types of radiation sources can be classified as indicated in the figure below, where the curve for the blackbody with ε = 1 is Plank's curve. The curve for a graybody is proportional to Planck's curve for all wavelengths. The spectral radiant emittance for a selective radiator varies not only with temperature but also with wavelength.

Spectral radiant emittance of three types of radiators.

Spectral radiant emittance of three types of radiators.

Citation:

M. Riedl, Optical Design Fundamentals for Infrared Systems, Second Edition, SPIE Press, Bellingham, WA (2001).



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