Kirchhoff's law--: It states that at any temperature, the ratio of emissive power to the absorptive power for a given wavelength in same for all bodies and is equal to the emissive power of a black body.
Suppose eλ and aλ be the emissive and absorptive power of a body at a given wavelength λ and the body is laced in an isothermal enclosure. dϕ respectively the quantity of heat received by the body per unit time, per unit surface area, within the wavelength λ and λ + dλ.
Energy absorbed by the body = aλ dθ and energy reflected by the body = (1 - aλ) dθ.
The body also emits energy eλ dλ per unit time per unit surface area.
Hence, (1 - aλ) dθ + cλ dλ = dθ
or, eλ dλ = aλ dθ
When the body is perfectly black
(emissive power of a black body)
This is the proof of kirchhoff's law.
