Table of Contents
Journal of Thermodynamics
Volume 2016, Article ID 9137926, 13 pages
Review Article

Historical Prospective: Boltzmann’s versus Planck’s State Counting—Why Boltzmann Did Not Arrive at Planck’s Distribution Law

1Technical University of Applied Sciences Wildau, Hochschulring 1, 15745 Wildau, Germany
2Kazakh National Pedagogical Abai University, Dostyk avenue 13, Almaty 050010, Kazakhstan

Received 7 August 2015; Accepted 11 November 2015

Academic Editor: Shripad T. Revankar

Copyright © 2016 Peter Enders. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Why does Planck (1900), referring to Boltzmann’s 1877 probabilistic treatment, obtain his quantum distribution function while Boltzmann did not? To answer this question, both treatments are compared on the basis of Boltzmann’s 1868 three-level scheme (configuration—occupation—occupancy). Some calculations by Planck (1900, 1901, and 1913) and Einstein (1907) are also sketched. For obtaining a quantum distribution, it is crucial to stick with a discrete energy spectrum and to make the limit transitions to infinity at the right place. For correct state counting, the concept of interchangeability of particles is superior to that of indistinguishability.