Question

Explain Kirchhoff’s Law with its mathematical expression in detail.

Answer 1

Kirchoff’s law of radiation: Kirchoff’s law: It states that at equilibrium temperature, the ratio of total emissive power of any body to absorptivity depends only upon the temperature of the body. Thus when any body is at equilibrium temperature with its surrounding, its emissivity and absorptivity are equal. Consider that the two bodies are kept into a furnace held at constant temperature of T K. Assume that, of the two bodies one is a black body& the other is a non-black body i.e. the body having ‘a’ value less than one. Both the bodies will eventually attain the temperature of T K & the bodies neither become hotter nor cooler than the furnace. At this condition of thermal equilibrium, each body absorbs and emits thermal radiation at the same rate. The rate of absorption & emission for the black body will be different from that of he non-black body. Let the area of non-black body be A1 and A2 respectively. Let ‘I’ be the rate at which radiation falling on bodies per unit area and E1 and E2 be the emissive powers ( emissive power is the total quantity of radiant energy emitted by a body per unit area per unit time)of non-black & black body respectively. At thermal equilibrium, absorption and emission rates are equal, thus,