Conclusions from Kirchhoff s law

Kirchhoff s law shows that a close relationship exists between the emission and absorption capabilities of a body, see 5.1.6. From (5.48) we obtained the following equation for the spectral intensity of any body 

The directional spectral absorptivity of a any radiator agrees with its directional spectral emissivity. 

The directional spectral reflectivity r x of an opaque body can also be traced back to the directional spectral emissivity e x. According to (5.41) and (5.69), it holds that 

This says that one single material function is sufficient for the description of the emission, absorption and reflective capabilities of an opaque body. Table 5.4 shows that it is possible to calculate the emissivities ex, s and from s x. Correspondingly, with known incident spectral intensity Kx of the incident radiation, this also holds for the calculation of ax, a and a from a x as well as of rx, r and r from r x, cf. Tables 5.1 and 5.2. So, only one single material function, e.g. e x = s x(X, f3,ip,T), is actually necessary to record all the radiation properties of a real body6. This is an example of how the laws of thermodynamics limit the number of possible material functions (equations of state) of a system. 

6 However, this is valid with the restriction that the bidirectional reflectivities are not covered, which describe the directional distribution of the reflected radiation see for this the comments in 5.1.5 as well as [5.4], p. 71 ff. 

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