In thermodynamics, Max Planck (1858-1947) was a German physicist noted for his endeavors to formulate an expression for the entropy of radiant heat in agreement with thermodynamics and the electromagnetic theory of light, efforts which launched the quantum revolution. Planck is also noted for his 1897 book Treatise on Thermodynamics, for his 1899 principle of elementary disorder, and significantly for his 1900 postulate of the theory of the existence of "energy elements" (energy quantums) in bodies, the latter of which started the quantum revolution. [2] In relation to his "quantum hypothesis", Planck was one of the first physicists to recognize German physicist Walther Nernst's 1906 heat theorem and to facilitate its status into that of a "third law". Planck was a product of the Berlin school of thermodynamics, through is studies of the works of German physicist Rudolf Clausius, a school he later became a professor at.

Entropy
Planck was the first to define entropy as S = K log W or the entropy of a system proportional to its probability W, as he first stated in 1901. The basis of his argument is that, firstly, based on the theorem that the probabilities of two systems independent of one another is equal to the product of the probabilities of the two systems (W = W1W2); secondly, that the entropy is represented by the sum of entropies (S = S1 + S2); whereby the entropy is proportional to the logarithm of the probability (S = K log W). [4]

Education
In 1867, Planck enrolled in the Maximilians gymnasium school in Munich, where he came under the tutelage of German mathematician Hermann Müller, who took an interest in the youth, and taught him astronomy and mechanics as well as mathematics. It was from Müller that Planck first learned the principle of conservation of energy. Planck graduated from here at the age of 17. In 1874, Plank enrolled at the University of Munich where, under the tutelage of physicist Phillipp von Jolly, he studied the diffusion of hydrogen through heated platinum, but soon transferred to theoretical physics.

In 1877, at the age of 19, Planck went to Berlin for a year of study with physicists Hermann Helmholtz and Gustav Kirchhoff and the mathematician Karl Weierstrass. He wrote that Helmholtz was never quite prepared, spoke slowly, miscalculated endlessly, and bored his listeners, while Kirchhoff spoke in carefully prepared lectures which were dry and monotonous. He soon became close friends with Helmholtz. While there he undertook a program of mostly self-study of German physicist Rudolf Clausius’ writings, which led him to choose heat theory as his field. Planck describes his discovery of Clausius as such: [5]

“One day, I happened to come across the treatises of Rudolf Clausius, whose lucid style and enlightening clarity of reasoning made an enormous impression on me, and I became deeply absorbed in his articles, with an ever increasing enthusiasm. I appreciated especially his exact formulation of the two laws of thermodynamics, and the sharp distinction which he was the first to establish between them.”

In October 1878 Planck passed his qualifying exams and in February 1879 defended his dissertation, Über den zweiten Hauptsatz der mechanischen Wärmetheorie (On the second fundamental theorem of the mechanical theory of heat). He briefly taught mathematics and physics at his former school in Munich. In June 1880 he presented his habilitation thesis, Gleichgewichtszustände isotroper Körper in verschiedenen Temperaturen (Equilibrium states of isotropic bodies at different temperatures). With the completion of his habilitation thesis, Planck became an unpaid private lecturer in Munich, waiting until he was offered an academic position. Although he was initially ignored by the academic community, he furthered his work on the field of heat theory and discovered one after another the same thermodynamical formalism as Gibbs without realizing it. Clausius' ideas on entropy occupied a central role in his work.

Physics professor
In April 1885 the University of Kiel appointed Planck as associate professor of theoretical physics. Further work on entropy and its treatment, especially as applied in physical chemistry, followed. He proposed a thermodynamic basis for Arrhenius' theory of electrolytic dissociation. Within four years he was named the successor to Kirchhoff's position at the University of Berlin — presumably thanks to Helmholtz's intercession — and by 1892 became a full professor. In Berlin, Max Planck joined the local Physical Society. He later wrote about this time, in what has become a famous entropy quotation:

"In those days I was essentially the only theoretical physicist there, whence things were not so easy for me, because I started mentioning entropy, but this was not quite fashionable, since it was regarded as a mathematical spook."

In 1907 Planck was offered Boltzmann's position in Vienna, but turned it down to stay in Berlin. During 1909 he was the Ernest Kempton Adams Lecturer in Theoretical Physics at Columbia University in New York City. He retired from Berlin on 10 January 1926, and was succeeded by Erwin Schrödinger.

Energy elements
In 1900, Planck theorized that the internal energy U of a black body (resonator) could be divided into a discrete number of “energy elements” ε by the expression:

where P is large integer. [1] This supposition later led German-born American physicist Albert Einstein, in 1905, to propose that light itself was composed of quantums of energy, i.e. light quantums. These light quantums later came to be called “photons”, a term introduced in 1926 by American physical chemist Gilbert Lewis. These developments launched the development of quantum thermodynamics.

Quotes
A famous quote by Planck, often misattributed to his quantum theory, is:

“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”

The statement, however, is in regards to the statistical thermodynamics/atomic hypothesis work of Austrian physicist Ludwig Boltzmann and how his work triumphed over German physical chemist Wilhelm Ostwald and the energetics school. [3]

References
1. (a) Planck, Max. (1901). "On the Law of Distribution of Energy in the Normal Spectrum". Annalen der Physik, vol. 4, p. 553 ff.
(b) Planck, Max. (1897). Treatise on Thermodynamics. New York: Dover (reprint).
2. Peacock, Kent A. (2008). The Quantum Revolution (section: Thermodynamics, pgs. 5-14). Greenwood Publishing Group.
3. (a) Planck, Max. (1949). Scientific Autobiography, and Other Papers (pgs. 33-34). Trans. by Frank Gaynor. Philosophical Library.
(b) Hokikian, Jack. (2002). The Science of Disorder: Understanding the Complexity, Uncertainty, and Pollution in Our World (pg. 179). Los Feliz Publishing.
4. Planck, Max (1925). A Survey of Physics (pg. 17). Methuen & Co.
5. Williams, Garnett P. (1997). Chaos Theory Tamed (pg. 382). Joseph Henry Press.

Further reading
● Planck, Max. (1897). Treatise on Thermodynamics. New York: Dover.
● Planck, Max. (1900). “Entropy and Temperature of Radiant Heat.” Annalen der Physik, vol. 1. no 4. April, pg. 719-37.
● Planck, Max. (1909). Eight Lectures on Theoretical Physics. Columbia University Press.
● Planck, Max. (1914). The Theory of Heat Radiation, (translated by Morton Masius). Springer.

External links
● Max Planck – Wikipedia.
● Max Planck – Eric Weisstein’s World of Scientific Biography.
● Planck, Max (1858-1947) – WorldCat Identities.