Kirchhoff's Law

Kirchhoff's Law of Thermal Emission was formulated in 1859 [1]. It is at the same time the simplest and least understood law in physics. Kirchhoff’s law states that given thermal equilibrium with an enclosure, the radiation inside will be always black, or normal, in a manner which is independent of the nature of the walls, or the objects they contain. This is known as the concept of universality. That is, that the radiation within an enclosure can always be described by a universal function dependent only on temperature and frequency. This universal function was first given to us by Max Planck, in 1900 [2]. Kirchhoff’s law stands at the heart of all of modern astrophysics. It is the basis for setting the temperature of the stars, for the gaseous model of the Sun, and for believing that we now know the temperature of the entire universe.

Tragically, Kirchhoff’s belief that radiation within an enclosure was independent of the nature of the walls is not correct. Kirchhoff arrived at universality because he did not properly address reflection within cavities. As a result, the proper law of thermal emission was brought to us by Balfour Stewart, in 1858 [3]. Like Kirchhoff’s law, Stewart’s law properly equates the emissivity and absorptivity of an object at thermal equilibrium, but it does not lead to universality. Stewart’s law states that the radiation is determined not only by temperature and frequency, but also by the nature of the walls. These problems have been addressed in detail [4,5,6,7,8]. Far from being universal, Planck's formulation, while correct, is restricted to objects which on Earth are best approximated by graphite or soot [6]. The universal nature of radiation in thermal equilibrium is not a valid concept.

Scientists and engineers are invited to review and judge these questions for themselves.

Pierre-Marie Robitaille, Ph.D.
Professor of Radiology and Chemical Physics
The Ohio State University

[1] G. Kirchhoff. Über das Verhältnis zwischen dem Emissionsvermöogen und dem Absorptionsvermögen. der Körper für Wärme und Licht. Poggendorfs Annalen der Physik und Chemie, 1860, v. 109, 275–301 [English translation - On the relation between the radiating and the absorbing powers of different bodies for light and heat. Phil. Mag., 1860, ser. 4, v. 20, 1–21].
[2] M. Planck. Über das Gesetz der Energieverteilung im Normalspektrum. Annalen der Physik, 1901, v. 4, 553–563 [English translation by D. ter Haar: M. Planck. On the theory of the energy distribution law in the normal spectrum. The old quantum theory. Pergamon Press, 1967, 82–90].
[3] B. Stewart. An account of some experiments on radiant heat, involving an extension of Prévost's theory of exchanges. Trans. Royal Soc. Edinburgh., 1858, v. 22(1), 1–20.
[4] P-M. L. Robitaille. On the validity of Kirchhoff’s law of thermal emission. IEEE Trans. Plasma Sci., 2003, v. 31(6), 1263–1267.
[5] P-M. L. Robitaille. A critical analysis of universality and Kirchhoff’s law: a return to Stewart’s law of thermal emission. Progress in Physics, 2008, v. 3, 30–35. (also in arXiv: 0805.1625)
[6] P-M. L. Robitaille. Blackbody radiation and the carbon particle. Progress in Physics, 2008, v. 3, 36-55.
[7] P-M. L. Robitaille. An analysis of universality in blackbody radiation. Progress in Physics, 2006, v. 2, 22–23 (also in arXiv:physics/0507007)
[8] P-M. L. Robitaille. Kirchhoff's Law of Thermal Emission: 150 Years. Progress in Physics, 2009, v. 4, 3-13.

modified on April 10, 2010