VIII - The Partition of Energy

Summary

IT was shown in 1861 by G. Kirchhoff that in an enclosure at temperature T, the state of the field of radiation depends only on this temperature T, and does not depend on the optical properties of the substances that happen to be present in the enclosure. This state of radiation is called complete or equilibrium radiation, or black-body radiation. It was one of the primary objects of theoretical physics in the nineteenth century to determine this characteristic state of radiation by calculation.

In the preceding paragraph I have stated the broad facts, so that the reader may see the issue. To give these facts their quantitative form, certain refinements of statement are needed. What Kirchhoff actually showed, by means of thermodynamic arguments, is as follows. Let the enclosure contain substances capable of emitting and absorbing radiation of energy frequency v. At any point P in the enclosure, let the specific intensity of radiation for frequency v be I_v; that is to say, in a short time dt through an element of area dS containing P, in a cone of directions of solid angle dω making an angle with θ the normal to dS, the flow of energy is taken to be I_vdvdtdS cos θ dω, dv being a small range of frequencies surrounding v. Further, let k_v be the absorption coefficient of the material at P, j_v the emission coefficient of the same material. These statements mean that a beam of radiation of intensity I_v traversing a thin layer of the material of thickness dl is weakened by the amount dI_v = — k_vpI_v dl, where p is the density; and that the emission of radiant energy from a small element pdv of volume dv in time dt in directions included in dω is j_vp dv dt dω.