Pursuing an Idea: Planck’s Quantum Theory of Ideal Gas * Massimiliano Badino † 1 Prelude: One Hundred Years of ‘Quantitude’ Many years later, as he faced the firing squad, Erwin Planck was to remember that distant afternoon when his father took him to discover the quantum. It was indeed in a day at the beginning of the last century, during a walk in the Grunewald Forest, that Max Planck in- formed his youngest son that his recent discovery was the greatest since the time of Newton. After that day, physics was never the same again. From the mysterious realm of the interac- tion between matter and radiation, the quantum spread out both in the theory of radiation and in the theory of matter and eventually changed our picture of the physical world. Planck played a foremost role in this revolution till the mid-1920 and especially his work on the ap- plication of quantum hypothesis to the ideal gas was instrumental in setting the stage for quantum mechanics. In this paper I will give a cursory outline of this work and, centering on the argumen- tative structure, I will argue that Planck’s theory of gas was framed according to a theoretical strategy he had already adopted in his previous work on radiation theory. The thrust of this strategy consists in focussing on the general features of the system and leaving aside spe- cific assumptions on the micro-processes. Throughout the years Planck reconfigured and reorganized his arguments and the great flexibility of his theoretical strategy allowed him to maintain a consistent outlook on the problem. The development of Planck’s theory of quan- tum gas can be divided into three phases. Firstly the lecture at the Wolfskehl Conference held in Göttingen in 1913 where Planck presented a sketchy account of the phase equilib- rium between gas and condensate. Secondly, after some destructive criticisms against his initial attempt, Planck changed radically the approach and elaborate a more mature theory in 1916 and then in 1921. In the third phase, from 1921 to 1925, Planck was mostly concerned with the defense of his theory. In this paper I will especially focus on a particular problem, namely on the justification of the extensivity term for entropy. This problem will be our key to enter Planck’s theory of quantum gas. 2 From the Wärmestrahlung to the Wolfskehl Lecture Thermodynamics and gas theory had been the protagonists of 19th century physics. How- ever, at the turn of the century, many quandaries still remained to solve and new ones sud- * German translation in Dieter Hoffmann (ed.) Max Planck und die moderne Physik, Springer, Berlin, 2010. † Max-Planck-Institut für Wissenschaftsgeschichte, Boltzmannstrasse 22, 14195 Berlin; Fritz-Haber-Institut der Max Planck Gesellschaft, Faradayweg 4-6, 14195 Berlin. 1