Q.Define the absorptive power and the emissive power of a surface at a given temperature and wavelength. State Kirchhoff's law of radiation connecting them, and use it to explain why a good absorber of radiation (such as a black, lamp-soot-coated surface) is also necessarily a good emitter.

The absorptive power (absorptivity) $a$ of a surface is the fraction of the total radiant energy incident on it that the surface actually absorbs, with $0 \le a \le 1$; a perfectly black surface has $a = 1$, absorbing all incident radiation. The emissive power (emissivity) $e$ of a surface is a measure of how efficiently it radiates thermal energy, expressed relative to an ideal black body at the same temperature, with $0 \le e \le 1$; a perfectly black surface has $e = 1$, the maximum possible emissive power.

Kirchhoff's law of radiation states that, for any surface in thermal equilibrium, the ratio $e/a$ (its emissive power divided by its absorptive power) is the same fixed value for every surface at a given wavelength and temperature, equal to the emissive power of a perfectly black body at that same wavelength and temperature. Since this ratio is the same universal value for every surface, a surface cannot have a large $a$ together with a small $e$, or vice versa: if $a$ is close to $1$ (a good absorber), $e$ must also be close to $1$ (a good …

State the two definitions precisely, then state Kirchhoff's law as fixing the ratio $e/a$ across all surfaces, and note the direct logical con …

• Believing absorptive and emissive power are entirely independent properties that could, in principle, take any combination of values. …