Author: Debanujan Nath

Albert Einstein is undoubtedly one of the greatest theoretical physicists of all time. He is well known for his theories of Brownian motion, general relativity, photoelectric effect, Bose-Einstein statistics and many more. In popular culture, it is believed that he became famous for his general theory of relativity, or probably for his explanation of the photoelectric effect (for which he was awarded the 1921 Nobel Prize in physics). However, it is a relatively lesser-known fact that he came to limelight for his quantum calculations of the specific heat of a solid, which led to the determination of limits of validity of the third law of thermodynamics, or Nernstâ€™s heat theorem.

Walther Nernst was surprisingly good at experimenting and much better at understanding the broad picture despite his messy tactics. He also always had an eye for what was contemporary and useful. Nernst was famous and wealthy, so he could study anything he wanted. Nernst made the decision to concentrate on using atmospheric nitrogen to produce fertilisers in the early 1900s. This is because of the findings of William Crooks, who predicted that the contemporary farming methods were depleting the nitrogen content of soil and with population growth, they would soon run out of wheat and millions would starve. Then, Crookes gave that generation of chemists motivation by saying, "it is through the laboratory that starvation may ultimately be turned into plenty." Therefore, Nernst began studying various chemical reactions at various temperatures and pressures. Nernst had an equation stating that the difference between these terms equals the temperature times the entropy (the measure of the randomness or disorder in the system, as found by Rudolf Clausius); thus he understood that at the lowest temperature imaginable, known as absolute zero, the chemical terms he was looking at should be identical. However, in December of 1905, supposedly while giving a lecture, Nernst said that "the realization pressed itself forward", that it looked like these terms not only became "identical at low temperatures", but "they invariably become practically identical some distance before absolute zero is reached." In other words, not only does the temperature go to zero at absolute zero, but also the entropy goes to zero too! Within a few months this "theorem" was being referred to as a "third law of thermodynamics." What is the physical significance of zero entropy? As a biographer of Nernstâ€™s poetically wrote in 1973: "The third law had transformed absolute zero from a state of complete rest into one of perfect orderliness." Nernst called it his "heat theorem" although it wasnâ€™t much of a theory as a "heat postulate" as it was based entirely on assumptions about experimental graphs without any theoretical basis behind it. At first, this "theorem" was, according to one of Nernstâ€™s students, "mainly regarded as a useful rule for calculating chemical equilibria." So, Nernst had made progress towards the construction of fertilisers; nevertheless, he was so enthralled with the ramifications of his "theory" that he turned the task over to Fritz Haber, a fellow scientist. Since entropy cannot be measured directly, Nernst and colleagues used liquid hydrogen as a cooling agent to measure specific heats at extremely low temperatures. Specific heat, often denoted by the symbol C, is a property of a substance that describes its ability to absorb or release heat energy per unit mass. It is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). They discovered that at very low temperatures, the specific heats of all their materials dropped to extremely low values. Indeed, the specific heats would disappear at zero degrees. What does that mean exactly? Evidently, from the definition of specific heat, the object needs no heat for its temperature to increase, which means that the object will not stay at absolute zero.

The absolute zero is not only the coldest temperature, but also unattainable. And so absolute order is unattainable. The lack of a theoretical foundation for his "theory" continued to impede him, but he was convinced about his profound idea. Then, in 1909 or early 1910, Nernst learned about a little-known 1907 work written by Albert Einstein, a patent clerk, which showed that only the application of quantum mechanics can explain how the specific heat can be zero. Actually, Einstein used Max Planckâ€™s quantum hypothesis, which assumed the atoms to be harmonic oscillators with discrete energies but emitting a continuous radiation, with a correction that the radiation is also discrete. Planck didnâ€™t care much about thinking of light as a bunch of particles, writing to Einstein that he felt that light behaves like a wave and is, "described exactly by Maxwellâ€™s equations." Einstein wrote, "For although one has thought before that the motion of molecules obeys the same laws that hold for the motion of bodies in our world of sense perception we now must assume that the diversity of states they can assume is less than for bodies within our experience [and] can only assume the values, 0, hf, 2hf, etc." In his calculation, Einstein used Maxwell- Boltzmann statistics to find the average energy of each atom, and then multiplied the result by 3 (to account for the three independent dimensions in which each atom in the solid could oscillate) to get the total energy of an atom. Then, taking the temperature derivative, he found the specific heat. His results were not so exact (they were modified by Debye in 1912), but his results fitted with the contemporary experimental data. Moreover, the specific heat went to zero asymptotically at zero degrees for *all *solids! As the author Douglas Stone elegantly put it, "Newtonian atoms had frozen to death."

Einstein's 1907 paper was at first largely disregarded by the public. He made fruitless attempts for years to persuade other scientists to accept the idea that light acts like both a wave and a particle or to get them interested in quantum mechanics. "This quantum question is so extraordinarily important and difficult that everybody should take the trouble to work on it," Einstein wrote to a friend in May 1909. Planck encouraged Einstein to give his first significant public speech three months later. Though Planck likely expected Einstein to discuss relativity, he instead focused on promoting "a theory of light that can be understood as a kind of fusion of the wave and particle theories." Years later, one of the attendees said that this discussion was shelved because "the chairman of the meeting was Planck, and he immediately said that it was very interesting, but he did not quite agree with it." Einstein continued to work at the patent office in the interim. Actually, Einstein didn't even have much of a reputation inside his own department when he started his first position as a low-level lecturer in October of 1909.

Nernst read Einstein's 1907 article at this point. It was understandable that Nernst was pleased to learn that his theories now had some theoretical support. In correspondence with a friend, Nernst stated, "Einsteinâ€™s 'quantum hypothesis' is probably among the most remarkable thought [constructions] ever; if it is correct, then it indicated completely new paths... for all molecular theories; if it is false, well, then it will remain for all times 'a beautiful memory'." Nernst made the decision to visit Einstein in March 1910 in order to determine whether the young scientist was a genuine genius or a lunatic. Following the encounter, Nernst was so taken aback by Einstein that he referred to him as a "Boltzmann reborn", which is a high regard. Einstein's reputation was immediately impacted. An assistant professor at Zurich Polytechnic was cited as remarking, "Einstein must be a clever fellow if the great Nernst comes all the way from Berlin to Zurich to talk to him."

Even Max Planck addressed the problem by 1912, demonstrating that Nernst's original theory - that the entropy would always go to zero at absolute zero temperature - was false in the case of an object composed of multiple constituents. As a result, the third law was revised to read, "The entropy of a perfect crystal goes to zero at absolute zero temperature." Nernst formulated the third law of thermodynamics, which states that "it is impossible for any procedure to lead to T = 0 [T is temperature] in a finite number of steps," around the same time in 1912. Even now, scientists continue to disagree about the ideal structure for the law.

Nernst determined, in the summer of 1910, that a large international conference on radiation and quantum "issues" is needed. He turned to Ernest Solvay, a wealthy soda manufacturer, and Solvay agreed to the same. Nernst organised the first international physics conference, which took place in Brussels. He asked Solvay to invite 19 of the world's leading scientists, as well as Einstein, in order to support his "heat theorem" (Nernst asked Solvay not to mention that he was the "initiator of the idea of the conference"). Having spent the last few months being absolutely bewildered by quantum mechanics - he had been attempting to rewrite Maxwell's equations to incorporate quantum terms but had found it unmanageable - Einstein had mixed feelings when he received his invitation. In fact, Einstein wrote a depressed letter to a friend the month before he received an invitation to the conference, saying, "I no longer ask whether these quanta really exist. Nor do I try to construct them any longer." He went so far as to call quantum issues "the h-disease," saying that they "look ever more hopeless." Despite wanting to give up on quantum mechanics, Einstein accepted the invitation; it was just too big an honor to ignore. He did, however, lament to a friend that "my twaddle for the Brussels congress weighs down on me," in typical Einsteinian fashion. In a sentimental thank-you message to Solvay following the conference, Einstein said that the congress "will remain forever one of the most beautiful memories of my life." However, he expressed to his buddy Besso his genuine sentiments, saying, "In Brussels... they acknowledged the failure of [quantum] theory with much lamentation but without finding a remedy." Einstein also added that he, "heard nothing that I [he] had not known before," and felt that "nothing positive has come out of it."

But Einstein didnâ€™t know that his talk at the Solvay conference was to have major consequences. The French scientist Marcel Brillouin stated, "From now on we will have to introduce into our physical and chemical ideas a discontinuity, something that changes in jumps, of which we had no notion at all a few years ago." Even the most conservative attendees began to agree with Brillouin. The address made Einstein the talk of the town. When Louis de Broglie, younger brother of one of the attendees of the 1911 Solvay conference - Maurice de Broglie - received the conference notes, he said "I started to think about quanta from the moment that my brother gave me the notes." Another attendee, the illustrious Ernest Rutherford, returned to England and talked to his graduate student, Niels Bohr, about the gathering. And, eventually, de Broglie gave the wave theory of particles and Bohr modelled the atomic structure.

The extensive fame of Einstein did not come instantly as he gave his ideas; it took time. As the popular proverb goes: "Only a goldsmith knows the value of gold", Nernst was able to recognize the genius of Einstein. As we all know, after that Einstein would go on to achieve unparalleled fame in the scientific world and beyond, leaving an indelible mark on the course of physics and our understanding of the universe. His legacy lives on, and he remains one of the most celebrated and recognizable figures in the history of science.

### Check this out

"How the 3rd Law of Thermodynamics Made Einstein Famous?" by Kathy Joseph (Kathy Loves Physics & History, YouTube). URL: __https://youtu.be/ueqVVa4iA24?si=oItwFktX5hB0_RBr__

### References

[1] Crookes, W. Address of the President before the British Association for the Advancement

of Science. Science Vol. 8 No. 200 (October 28, 1898) P. 562

[2] Translated in Coffey, P Cathedrals of Science P. 102

[3] Nerst, W. Studies in Chemical Thermodynamics. Nobel Lecture, December 12, 1921 P.

358

[4] Yale Alumni Weekly (Sept, 1906), P. 184

[5] Mandelssohn, K. The World of Walther Nernst (1973) P. 68

[6] Simon, F. The Third Law of Thermodynamics, An Historical Survey. 40th Guthrie

Lecture, Year Book of the Physical Society, 1956 P. 3

[7] Max Planck to Albert Einstein (July 1907), translated and found in Einstein, A, Beck A, and Havas, P, The Collected Papers of Albert Einstein, Vol. 5. Princeton University Press P. 31

[8] Einstein, A. Planckâ€™s Theory of Radiation and the Theory of Specific Heat (1907), translated and found in Einstein, A, Beck A, and Havas, P, The Collected Papers of Albert Einstein, Vol. 2, Princeton University Press P. 218

[9] Stone. Einstein and the Quantum P. 110

[10] Albert Einstein to Jakob Laub (May 17, 1909). Translated and found in Einstein, A, Beck A, and Havas, P, The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press P. 119

[11] Paul Epstein quoted in Stone, Einstein and the Quantum (2013) P. 140

[12] Nernst to A Schuster, (March 10, 1910), Royal Society, found in Barkan, D, Walther Nernst

and the Transition to Modern Physical Science (2011) p. 183

[13] W. Nernst to A Schuster, (March 10, 1910), Royal Society, found in Barkan, D, Walther

Nernst and the Transition to Modern Physical Science (2011) p. 183

[14] George Hevesy recalled in Kuhn, T, Black-body Theory (1987) p. 215

[15] Albert Einstein to Jakob Laub (March 16, 1910), translated and found in Einstein, A, Beck A, and Havas, P, The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 149

[16] Stone. Einstein and the Quantum P. 147- 148

[17] A Survey Of Thermodynamics. Bailyn (1994). American Institute of Physics NY P- 342

[18] Walther Nernst to Ernest Solvay (Nov 27, 1910), translated and found in Mehra, Jagdish,

The Solvay Conferences on Physics (2012) P. 7

[19] Albert Einstein to Michele Besso (May 13, 1911), translated and found in Einstein, A, Beck A, and Havas, P, The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press P. 187

[20] Albert Einstein to Lorentz (Nov 23, 1911), translated and found in Einstein, A, Beck A, and Havas, P, The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press P. 228

[21] Albert Einstein to Michele Besso (September 11, 1911), translated and found in Einstein, A, Beck A, and Havas, P, The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press P. 205

[22] Albert Einstein to Ernest Solvay (Nov 22, 1911), translated and found in Einstein, A, Beck A, and Havas, P, The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press P. 227

[23] Brillouin, W from Solvay, E., Langevin, P., Broglie, M. D., & Institut international de

physique Solvay (1912). La thÃ©orie du rayonnement et les quanta: rapports et discussions de la rÃ©union tenue Ã Bruxelles du 30 octobre au 3 novembre 1911. Paris: Gauthier-Villars.

[25] De Broglie, L, quoted in Stone, Einstein and the Quantum (2011) P. 243

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