The great German physicist Max Planck once said, “However many specialties science may split into, it remains fundamentally an indivisible whole.” He declared that the divisions and subdivisions of scientific disciplines were “not based on the nature of things.” And he worked accordingly, moving back and forth between what we would now starkly categorize as physics, philosophy, mathematics, and chemistry. Of the many little-known wrinkles in his long life, Planck’s unsung relationship to physical chemistry was one of the most important.
Most scientists today, if they know anything about Planck, recognize his name at the headwaters of quantum theory. His 1900 discovery of the energy quantum (more like a toe stubbing) launched a revolution that rewrote our physical understanding of matter and its interactions. But his bold steps required a unique mindset. At the age of forty-two, that mindset had been shaped by a wealth of influences, including some that were atypical for a physicist, even in the broad-minded times of the nineteenth century.
When Max Planck was just twenty-one years old, he capped his formal training in theoretical physics with his doctorate thesis, exploring the meaning and utility of entropy. The pillars of thermodynamics were new and wobbly in 1879. Planck’s work on the second law drew very little attention at the time. He refined and clarified entropy as a weather vane for irreversible processes and the flow of time itself. But his professors largely shrugged at his thesis. To make a mark, he would have to apply entropy to something more tangible.
In 1885, Planck began his first professorship in Kiel and pushed his work into the infant field of physical chemistry, including studies of phase transitions and dilute solutions. These interactions with chemistry deeply influenced him. In particular, he embraced the existence and relevance of atoms in the late 1880s, nearly twenty years ahead most physicists.
Applauding the notions of Avogadro and the work of Sweden’s Svante Arrhenius (a physicist turned physical chemist), Planck made critical contributions to thermochemistry and electrochemistry. In his first fifteen years as a professor, he published several papers in the fledgling journal Zeitschrift für physikalische Chemie and set forth other physical chemistry contributions in the leading physics journal of the time, Annalen der Physik. And in terms of our modern notion of “impact,” his most highly ranked offerings were not related to his quantum breakthrough at all. To this day, his most frequently cited papers, both from 1890, swim in electrochemistry: “The Potential Difference between Two Dilute Solutions of Binary Electrolytes,” and “Excitation of Electricity and Heat in Electrolytes.”
Over the next several years, Planck began a new topic and marched toward quantum immortality. But his days with chemistry and his early adoption of atoms played a key role in his quantum breakthrough. From 1894 to 1899, Planck struggled to model thermal radiation, the warm electromagnetic glow emanating from any object with a temperature above absolute zero. He was drawn to its universal character, first noted by his professor Gustav Kirchhoff: The exact assortment of colors (whether visible or not) emerging from any object depends only on that object’s temperature. So yes, if your telephone could be raised to the temperature of the sun, it would emit perfect sunlight. Incredibly, the composition of an object does not influence its emitted thermal spectrum.
After Max Planck’s different approaches for understanding this spectrum (or “black-body radiation”) failed, he turned to a decidedly atomistic set of mathematics, combinatorics. This tool kit applies to flipping coins, counting cards, etc., all based on discrete items or outcomes. In Planck’s 1900 breakthrough, his key step recycled a combinatorics equation used by a colleague years earlier in modeling a gas, molecule by molecule.
When Planck had at last derived nature’s exact mathematical formula for thermal radiation and introduced the world to the fitting parameter h, Planck’s constant, what most excited him was not the quantization of energy. In December 1900, after zipping through his mathematical derivation for a small audience, Planck lingered on the implication for fundamental physical constants. He derived 6.175 x 1023 for what would become known as Avogadro’s number (the number of molecules in one mole of gas), and 2.76 x 1019 for Loschmidt’s number (the number of gas molecules in 1 cubic centimeter at 0˚C and 1 atm). Planck said that the accuracy of his values was “much better than all determinations of those quantities up to now.” Using his cunning fit to available thermal radiation data, he had nailed down those two landmarks of chemistry to within three percent of their contemporary accepted values.
With this step, Planck and his heritage in physical chemistry had, in some sense, pushed physics into a new age of accuracy and precision. The grandchild of his quantum notion, quantum mechanics, would later stand as the most precisely testable theory in all of science.
Image Credit: “Dr. Max Planck” by George Grantham Bain. Public Domain via Wikimedia Commons.
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