Heat and Thermodynamics

12.4 Kirchhoff′s Law of Radiation

Let a body of monochromatic emissive power e_λ and of absorptivity a_λ be placed inside an enclosure at uniform temperature T. It has already been proved that the amount of radiation crossing unit area at any point inside the enclosure is equal to the emissive power of a black body at the temperature of the enclosure. Then, the quantity of radiation falling per second on unit area of the body is e_λbdλ. The amount of energy absorbed by the body is a_λe_λbdλ. For temperature equilibrium, this must be equal to the quantity of radiation emitted per unit area of the body in one second, that is, e_λdλ. Hence,

 

a_λ e_λb dλ = e_λ dλ

 

or

 

 

Or, the ratio of monochromatic emissive power of a body within the range of wave-length ...