Radiation, Blackbodies & Kirchhoff's Law

The sun warms us across 150 million kilometres of empty space. No conduction, no convection: radiation.

Thermal radiation#

Every body emits energy that travels through space like light and, when it falls on another body, is partly absorbed, raising that body’s thermal energy. This energy is called thermal radiation (or radiant energy). “Radiation” names both the process and the energy itself.

Prévost’s theory of exchange (1792)#

• All bodies radiate at all temperatures, at a rate depending on the surface, its area and its temperature (faster when hotter).
• They also absorb part of the radiation from surrounding bodies.
• Radiating more than it absorbs, a body cools; less, it warms.

A body left in a room settles at room temperature, yet is still radiating: it must now absorb exactly as fast as it emits. Put a hotter body in the room and it emits faster than it absorbs, so it cools; a colder one warms.

Blackbodies#

Hang a polished body and a black-painted one in a room. Both reach room temperature and receive the same radiation. The polished one reflects most of it and absorbs little; the black one absorbs most. Since neither changes temperature, the black one must also emit faster. Good absorbers are good emitters.

A perfect blackbody is an ideal; lampblack, reflecting about 1%, comes close. Better: a small hole in a cavity blackened inside, with a cone opposite the hole. Radiation entering the hole bounces round and is absorbed long before it can find its way out.

Kirchhoff’s law#

Proof: put a body A and an identical-shaped blackbody B in an enclosure, all at one temperature. Both receive radiation ΔU in time Δt. B absorbs all of it and, staying at constant temperature, emits the same: ΔU = kE₀. A absorbs aΔU and must emit as much: aΔU = kE. Dividing: