Kirchhoff’s Law of Heat Radiation

The thermal radiation emission and absorption by a body in thermal equilibrium are covered by Kirchhoff’s law of thermal radiation. It claims that for all wavelengths, the emissive power of a perfect blackbody at a given temperature is equal to the ratio of a body’s emissive power to coefficient of absorption for that body.

Kirchhoff’s law can also be stated as follows: for a body emitting and absorbing thermal radiation in thermal equilibrium, the emissivity is equal to its absorptivity. This is because we can define the emissive power of an ordinary body in comparison to a perfect blackbody through its emissivity.

Symbolically, a=e or more specifically a(λ) = e(λ).

The amount of heat radiated from a given region in a given amount of time is known as emissive power.

Quantity of radiant heat absorbed by body A = Quantity of heat emitted by body A 

or

∴ aQ = R  …(Equation 1)

For the perfect blackbody B,

∴ Q = RB  …(Equation 2)

Dividing Equation 1 and Equation 2, we get

∴ a = R / R_B

or  

∴ R_B = R / a

But R / R_B = e  …(Emissive power)

∴ a = e

Hence, Kirchhoff’s law is theoretically proved.

Surface area (A) and time duration have a direct relationship with the amount of heat radiated (Q) (t). Therefore, it is practical to think about the amount of heat radiated per unit area per unit time (or power emitted per unit area). This is referred to as the body’s Emissive Power or Radiant Power, R, at a specific temperature, T. Dimensions of Emissive power are [L⁰M¹T^-3] and the SI unit is Jm^-2s^-1 or W/m². The composition or polishing of the emitting surface is not a physical quantity. We compare objects made of various materials with the same geometry at the same temperature in order to talk about the material aspect. The maximum emissive power of a perfect blackbody occurs at a specific temperature. Because of this, comparing the emissive power of a given surface to that of the ideal blackbody at a given temperature is convenient.