Kirchhoff’s law can be derived in a simplified manner as follows:

Suppose Q is the amount of radiation incident per unit area per second on a body. If As is the absorptive power of the surface, then the amount of radiation absorbed by the body per unit area per second = A_SX Q.

If E_S represents the emissive power of the surface, then the amount of radiation emitted by the surface per unit area per second = E_S.

When the body is in thermal equitbrium with the enclosure,
Amount of radiation emitted by the surface per unit area per second = Amount of radiating absorbed by the per unit area per second.

Thus
                                                                           
For a perfectly black body, As = A_B  =1 and Es may be replaced by E_B where AB and E_B represent the absorptive power and the emissive power of a perfectly black body. Thus we have
                                              
From equation
                                                
or                                       

As EB is constant, the equation gives the expression for the Kirchhoff’s law.

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