Planck, the Second Law of Thermodynamics, and Black‐body Radiation

Abstract

Planck’s work on black‐body radiation grew out of a failed attempt to use electrodynamics to show that entropy can never decrease, i.e., that the second law of thermodynamics is not just a statistical but a strict law of nature. This original interest is reflected in his approach to the problem of black‐body radiation. Planck derived the formula for the spectral distribution of black‐body radiation from the formula for the entropy of a resonator interacting with the radiation at its resonance frequency. He initially chose an entropy formula that gave him a black‐body radiation formula proposed by Wien. Deviations from this Wien law at low frequencies led him to adopt a new entropy formula, which gives a law that reduces to the Wien law at high frequencies and to (what is now known as) the Rayleigh‐Jeans law at low frequencies. This new Planck law agreed remarkably well with all experimental data. Planck thus set out to find a derivation of the entropy formula leading to it. Although he continued to resist Boltzmann’s statistical interpretation of the second law for another decade, Planck borrowed some of Boltzmann’s techniques for this derivation. The derivation critically depends on energy elements with sizes proportional to the frequency of the radiation and Planck’s constant as the proportionality constant. Planck’s papers of 1900–01, however, leave open the question of how these energy elements are to be interpreted.