Energy Density and Intensity of Thermal Radiation

Radiation is associated with energy density u, which is the energy per unit volume, and an intensity I, which is defined as follows the energy incident on a small area d 3 due to radiation from a solid angle dQ, which makes an angle 0 with the normal to the surface Ja = IcosQdCldG (Fig. 11.1) [1]. 

The energy density u and intensity of radiation / could also be defined for a particular frequency as 

Gustav Kirchhoff (1824-1887) (Courtesy the E. F. Smith Collection, Van Pelt-Dietrich Library, University of Pennsylvania) 

As noted by Gustav Kirchhoff (1824-1887), thermal radiation that is in equilibrium simultaneously with several substances should not change with the introduction or removal of a substance. Hence /(v) and m(v) associated with thermal radiation must be functions only of the temperature T, independent of the substances with which it is in equilibrium. 

A body in thermal equilibrium with radiation is continuously emitting and absorbing radiation. The emissivity, ek v,T)dv, of a body k is defined as the intensity of radiation emitted by that body in the frequency range v and v + dv at a temperature T absorptivity, ak y,T)dv, is defined as the fraction of the incident intensity /(v) that is absorbed in the frequency range v and v + dv at a temperature T. By considering the balance of emitted and absorbed energy (Fig. 11.2), Kirchhoff also deduced that the ratio of emissivity ek v, T) and the absorptivity akiy,T) of a substance k must equal independent of the 

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