## Hermann Walther Nernst

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## Nernst, Hermann Walther

# NERNST, HERMANN WALTHER

(*b* . Briesen, West Prussia [now W4brze2no, Poland, 25 June 1864 ; *d.* Zibelle manorial estate, near Bad Muskau, Oberlausitz [now German Democratic Republic], 18 November 1941)

*chemistry, physics.*

Nernst was a physicist, turned chemist, who was quick to seize on novel ideas no matter what their source. His complete theoretical command of the subject matter of physical chemistry was unparalleled. Above all, he was a superb craftsman with keenly developed technical skills and an imaginative intuitive grasp of what was experimentally feasible. Early in his career the application of the principles of physics to chemical problems became his life’s goal. Over a period of four decades his activities in Göttingen and Berlin notably served to extend the boundaries of the traditional domains of both physics and chemistry.

Although Nernst’s early worldwide reputation resulted from a broad range of fundamental contributions to the new developments in physical chemistry, especially in electrolytic solution theory, his crowning achievement was in chemical thermodynamics. For this work Nernst received the Nobel Prize for chemistry in 1920. The Nernst heat theorem of 1906, or the third law of thermodynamics, as Nernst preferred to call it, was at first recognized chiefly as a practical means for computing chemical equilibria. The feasibility of directly calculating the entropy constants for gases from quantum theoretical formulations led to a new recognition of Nernst’s work prior to World War I. During the 1920’s quantum statistical considerations initiated a controversy—even serious reservations in some quarters–over the general validity of Nernst’s theorem for solids. By the late 1920’s, when Nernst no longer was actively engaged in thermodynamic investigations, several special formulations of the heat theorem, and notably that of Francis Simon, led to the acceptance of Nernst’s fundamental idea, in its refined form, as a general law of thermodynamics.

Nernst was the third child of Gustav Nernst, a judge in the Prussian civil service, and Ottilie Nerger. In 1883 he graduated first in his class from the Gymnasium in Graudenz [now Grudziadz, Poland], where his studies had focused on the classics, literature, and the natural sciences. His early ambition was to become a poet. Although that aim faded, he developed a lifelong infatuation for literature and the theater, especially Shakespeare.

From 1883 to 1887 Nernst studied physics at the universities of Zurich, Berlin, Graz, and Würzburg. He attended Heinrich Weber’s physics lectures in Zurich and Helmholtz’ thermodynamics lectures in Berlin . In Graz, Nernst was deeply impressed by Boltzmann and his emphasis on the atomistic interpretation of natural processes. On Boltzmann’s advice Nernst collaborated with his former pupil Albert von Ettingshausen in an investigation of the combined effect of magnetism and the flow of heat on the electric current. They discovered that a magnetic field applied perpendicularly to a temperature gradient gives rise to a potential difference in a metallic conductor. On the basis of this work of 1886 carried out in Graz, Nernst completed his inaugural dissertation the following year under Kohlrausch. Nernst apparently felt that he had taken his thermoelectric investigations as far as he could, for he never returned to the subject. Paul Drude, his future colleague in Göttingen, however, made good use of Nernst’s discovery and the corresponding thermomagnetic and galvanomagnetic effects to develop the electron theory of thermal and electrical conductivity.

The circumstances surrounding Nernst’s studies in Würzburg evidently provided the stimulus and the opportunities for the shift of his interests toward a career dominated by the application of physics to chemical problems. Emil Fischer, who later became Nernst’s colleague in Berlin, and Arrhenius, who had just announced his electrolytic dissociation theory, were both working with Kohlrausch in Würzburg at this time. While Arrhenius and Nernst were visiting Boltzmann in Graz, Arrhenius introduced Nernst to Friedrich Wilhelm Ostwald, with whom he had worked at the Polytechnikum in Riga. With the publication of the volume on *Verwandtschaftslehre* in 1887 in Leipzig, Ostwald’s massive *Lehrbuch der allgemeinen Chemie* had been completed. With van’t Hoff, who was a proponent of the new chemical theory for weak electrolytes, Ostwald launched in 1887 the *Zeitschrift für Physikalische Chemie.* Before the end of the year, Ostwald had accepted a professorship at the University of Leipzig, and Nernst had become his assistant. Although younger by five to ten years than Ostwald, van’t Hoff, and Arrhenius (the three dominant figures in the development of physical chemistry), Nernst soon came to be considered one of the founders of the newly created discipline.

In Leipzig theoretical and experimental chemistry were chemistry were pursued conjointly with impressive zeal. The emphasis fell on the electrolytic theory of ionization; the colligative properties of gases and liquids; and thermodynamics, or “energetics” in the Ostwald sense. Besides Arrhenius, van’t Hoff, and Nernst, others who belonged to Ostwald’s circle included Tammann (Nernst’s successor at Göttingen), Le Blanc (Ostwald’s successor at Leipzig), James Walker, Wilhelm Meyerhoffer, Ernst Otto Beckmann, and Julius Wagner-all pioneers in the establishment and exploration of physical chemistry as an academic discipline.

In the context of this group of *loner,* as they were called, Nernst soon became totally absorbed with the problems of physical chemistry. Within a year he had published his derivation of the law of diffusion for electrolytes in the simple case when only two kinds of ions are present. Thus for the first time (1888) he was able to calculate the diffusion coefficient for infinitely dilute solutions and to show the relationship between ionic mobility, diffusion coefficient, and electromotive force in concentration cells. This in turn was based upon the idea that, for two solutions of differing concentrations separated by a semipermeable partition, the driving force responsible for the diffusion is given by the difference in osmotic pressures on opposite sides of the partition. The fundamental relationship between electromotive force and ionic concentration was developed more fully in his Leipzig *Habilitationsschrift* of 1889,*Die elektromotorische wirksamkeit der lonen.* Applied to ideal solutions, fundamental thermodynamics showed that the electromotive force E, for a galvanic process corresponding to a concentration change from C_{1} to C_{2}, is given by E=RTǀNℱ *ln* C_{1}ǀ_{2}, where R is the gas constant; T is the absolute temperature; N represents the gram equivalents that have reacted; andℱ is Faraday’s constant, so that Nℱ corresponds to the passage of coulombs. Since the electromotive force of a galvanic cell is directly proportional to the free energy of the cell reaction, in this equation there is a crucial connecting link between thermodynamics and electrochemical solution theory. The Nernst equation, however, does not settle the difficulties associated with the determination of ionic concentrations for strong electrolytes and becomes valid only as the solutions approach infinite dilution.

According to the more general theory, the factors that cause the ions to move can be reduced to the following: (1) forces on the ions, both external (such as electrical) and internal (such as concentration gradients and electrostatic forces due to the presence of the ions themselves); (2) random thermal motions of the ions; and (3) the flow of the solution as a whole. The classical Nernst treatment of ionic diffusion (in terms of mobility and transport number) was based on Arrhenius’ theory of electrolytic dissociation and was expressed in terms of the electromotive force of concentration cells and galvanic elements. Nernst had assumed that a metal immersed in an electrolyte acts like a reservoir of ions having properties characteristic of electrolytic solvation pressure. Thus he was able to calculate maximum electric work (electromotive forces) from fundamental principles such as the relation to the gas constant. This work gave Nernst, then in his mid-twenties, an international reputation in electrochemistry.

Nernst’s distribution law, which relates the equilibrium concentrations of a solute distributed between immiscible liquid phases, appeared in two papers in 1890 and 1891. The case that Nernst studied theoretically and experimentally was the distribution of benzoic acid between water (phase *w*) and benzene (phase *b*). According to Nernst, benzoic acid in the water phase is present mainly as C_{6} H_{5} COOH, but a small fraction α dissociates into C_{6} H_{5} COO and H^{+} ions; whereas, benzoic acid in the benzene phase is present mainly as (C_{6} H_{5} COOH)_{2}, but a small fraction β exists as C_{6} H_{5} COOH molecules. Using C* _{w}* and C

*to represent the concentrations (or, more exactly, the activities) of benzoic acid in water and benzene respectively, Nernst was able to show-by taking quantitative account of the ionization of benzoic acid in water and athe incomplete association of benzoic acid in benzene-that at a given temperature the distribution constant*

_{b}*K*(thereafter called the Nernst distribution constant and, later, partition coefficient) was given by K=(1-β)

*C*/(1-α)

_{b}^{2}

*C*Experimentally Nernst was able to confirm this general type of equation in specific cases and to show that since α and β are both small in concentrated solutions, the ratio

_{w}^{2}*C*is approximately constant. It was seen that Henry’s law, according to which the solubility of a gas in liquid is directly proportional to the pressure of the gas above a liquid at equilibrium, is a special case of the more general Nernst distribution equation (1891). In 1872 Berthelot and E. C. Jungfleisch had carried out experimental investigations of the distribution of a substance between two liquid phases. Nernst’s work called attention to the fact that a simple distribution law can be expected to be valid only if, on dissolving, the solute undergoes no changes such as dissociation-that is, only when the concentrations (or activities) of the same molecular species in each phase are considered. The Nernst distribution equation represents an important type of phase equilibrium, and was put to practical use in extraction process calculations and in analyzing the distribution of substances in different parts of a living organism. For example, it was shown that ether tends to concentrate in brain and nerve tissues that are rich in fatty materials rather than in the more aqueous medium of blood.

_{b}/C_{w}^{2}After a semester at Heidelberg, Nernst returned to Leipzig and in 1891 accepted a post as associate professor in physics at the University of Göttingen. In 1892 he married Emma Lohmeyer, the daughter of Ferdinand Lohmeyer, a distinguished surgeon in Göttingen; they had two sons and three daughters. Nernst’s father-in law was an accomplished musician and played the piano and cello with Brahms and the Joachim string quartet. Although exposed to good music in Göttingen and an appreciative and sympathetic listener, Nernst apparently was not endowed with any noteworthy musical talent, as were some of his noteworthy musical talent, as were some of his closest colleagues-Helmholtz, Planck, Einstein, and Simon.

During the early Göttingen period of his career, Nernst’s conception of the goals and significant advances in theoretical chemistry was fashioned and published in his *Theoretische Chemie vom Stand punkte der Avogadroschen Regel und der Thermo dynamik* (1893). This textbook was dedicated to Ettingshausen in Graz *“in treuer Erinnerung an… Lehr- und Wanderjahre.”* As Nernst conceived it, the most important guide to presenting the theoretical treatment of chemical processes was first, to recognize the central importance of Avogadro’s hypothesis, which he referred to as “an almost inexhaustible horn of plenty’ for the molecular theory,” and second, to accentuate the law of energy that governs all natural processes. Convinced that theoretical chemistry had begun to attain a certain maturity, Nernst felt that an independent text book was needed in order to bring together widely different aspects of physics and chemistry. Nernst saw in the development of physical chemistry “not so much the shaping of a new science, as the meeting of two sciences hitherto somewhat independent of each other.” As he indicated in the preface, his objective was to present the latest investigation— “all that the physicist must know of chemistry, and all that the chemist must know of physics.”

The popularity of *Theoretische Chemie* can be attributed to several factors: it was kept up to date with a description of current developments, it was written for students from a not-too-advanced theoretical point of view, it touched upon and interrelated a wide range of phenomena, and it contained an abundance of illustrative materials and descriptions of experiments to facilitate the understanding of the theoretical principles. In Germany until 1926 (the publication date of the fifteenth edition), this work was recognized as the foremost textbook of physical chemistry. Thereafter it was replaced by the texts of Eucken (who followed Tammann at Göttingen) and John Eggert, both of whom were trained under Nernst.

In 1894 Nernst was offered the post of professor of theoretical physics at Munich, left vacant by Boltzmann’s move to Vienna. Instead, he bargained for, and was offered, a chair in physical chemistry and a new Institut für Physikalische Chemie und Elektrochemie in Göttingen-the only such post in Germany, aprat from Ostwald’s in Leipzig. Although Nernst sometimes disagreed with Ostwald on matters of interpretation, he retained a lifelong appreciation of this old master who had turned him in the direction of chemical pursuits. In 1895 Nernst and Schoenflies published their *Einführung in die mathematische Behandlung der Naturwissenschaften,* dedicated to Ostwald; by 1931 it had passed through eleven editions.

From 1891 to 1904 at Göttingen, Nernst managed to assemble an international group of scholars to cooperate in the intensive and comprehensive investigation of experimental and theoretical physicochemical problems. In Nernst’s institute it was taken for granted that researchers working on various problems would share their ideas and that all of the work was focused in some way on goals that had been clearly set out by Nernst. For example, the electromotive force theory of 1889 gave rise to the theory of lead accumulators (1900), the study of electrocapillarity (1901), and the theory of polarization (1902, 1908). The study of electrolytic phenomena at the liquid-liquid interface (1901) contributed to the formulation of atheory of electrical nerve stimulus important in nerve physiology (1904, 1908). The electromotive force determinations for metals led to investigations of overvoltage and to the suggestion (1900) that the hydrogen From his studies of the influence of the dielectric constant of a solvent on ionic equilibrium (1894) Nernst was led to announce a new method for determining dielectric constants for fluids, using an alternating-current Wheatstone bridge method (1897).

Reminiscent of Helmholtz’ enthusiasm for design and refinement of instruments, Nernst and his co-workers became involved in the constuction of a microbalance and an ingenious expermental method to measure dielectric constants. They also designed special apparatus for the determination of molecular weights by freezing point depression in dilute solutions (1894) and by vapor density measurement at extremely high temperatures (1903). Nernst’s interest in mass action and reaction velocity for gaseous dissociation processes of potential technological significance–as in the case of hydrogen, nitrogen, and ammonia–led to investigations that notably demonstrated his superb mastery of analytical instrumentation. In order to increase the yield in the synthesis of ammonia, he constructed a reaction chamber that could with stand pressures of 75 atmospheres at 1000°C. In 1907 Nernst and Jost achieved a yield of ammonia of about 1 percent at pressures of 50 atmospheres and 685°C., Whereas Haber’s experiments atmosphere and 1000°C. had given a yield of only 0.01 percent. Preoccupied with the heat theorem, Nernst abandoned his research on ammonia, while Haber went on to improve catalytic techniques that made industrial synthesis feasible.

In 1905 Nerns was called to the University of Berlin, upon the retirement of Landolt. It is evident from documents at the archives of Humboldt University that Planck strongly supported Nernst’s appointment to the chair of physical chemistry at Berlin. Planck knew that Nernst was the only one in Europe who might be able to lead Berlin out of its chemical doldrums. Besides, Nernst was a chemist who was so interested in physics that he preferred to be recognized as a physicist doing chemistry rather than as a physical chemist. For example, in his introductory Silliman lecture at Yale in 1906 he remarked that the customary separation of physics and chemistry was not altogether advantageous and was “especially embarrassing in exploring the boundary region where physicists and chemists need to work in concert.”

The situation in physical chemistry at Berlin at this time can be described only as one of mere tolerance for what the *loner* had accomplished. Before the turn of the century the University of Berlin was one of the last strongholds of resistance to the ionic theory of dissociation; thermodynamics also remained almost untouched by chemists. At the university and through his position in the Prussian Academy of Sciences, van’t Hoff had given such activconcerns his blessing, but he was then no longer active in science. As early as 1890/1891 Planck and Helmholtz had lent their support to the ionic theory in general and to Nernst’s outstanding contributions to electrochemistry in particular. They were greeted with such cool response that Helmholtz was led to conclude that, while thermodynamics was of great importance in chemistry in Berlin obviously were not up to it. While Berlin in 1905 was trying to catch up with what had by then become the old physical chemistry of Ostwald, van’t Hoff, and Arrhenius (with its rather exclusive focus on thermodynamics, colligative properties, and ionic theory), Nernst was breaking new ground by defining the limits of applicability of classical thermodynamics for chemical equilibrium, and was simultaneously exploring equilibrium, and was simultaneously exploring problems in chemical kinetics. On the whole, Nernst’s early investigations fit the pattern of chemistry laid out by Ostwald and the *loner.* Until he was about forty years of age, Nernst’s efforts were directed predominantly toward the refinement of methods to explore principles already current among chemists. He managed to do this with exquisite finish and expertise. After moving to Berlin, however, he became totally involved, theoretically, in the exploration of new ideas of thermodynamics.

Around Easter 1905 Nernst drove in his open automobile from Göttingen to Berlin to prepare for new duties, which he was to assume that fall at the chemical institute of the University of Berlin in the Bunsenstrasse. On 23 December Nernst was back in Göttingen to present to the Göttingen Academy his now-classic forty-page “heat theorem” paper, “Ueber die Berechnung chemischer Gleichgewichte aus thermischen Messungen.” It is apparent that the work and deliberations that led to Nernst’s heat theorem and its sequel, the enunciation of the third law of thermodynamics, had been carried out mostly in Göttingen. Undoubtedly that is the reason that led Nernst to present his ideas on this fundamental topic in Göttingen. The paper was published in 1906 in the *Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen.* To comprehend its merits and significance it will be helpful to examine the context in which Nernst’s ideas were formulated and to mention briefly the activities of other investigators upon whose work Nernst was able to build.

The twentieth-century advances associated with the thermodynamics of chemical processes and statistical thermodynamics were made largely from work carried out at the beginning of the century by Boltzmann, Planck, Einstein, and Nernst. The third law of thermodynamics, which had its origin in chemistry, was conceived by Nernst in connection with the search for the mathematical criteria of chemical equilibrium and chemical spontaneity. The solution he proposed for predicting the equilibrium conditions for chemical reactions was a novel one, but the problem itself had been of importance to chemists for over a century. It had taken the form of experimental investigations designed to provide an exhaustive catalog of chemical affinity relationships. An old and certainly puzzling question was why certain chemical reactions go while others do not, or more precisely, how far a given reaction will go before it reaches equilibrium. The more general problem may be stated as follows: Given that one knows the energy changes for the transition of a system (chemical or other) from one equilibrium state to another, is it possible-using only the first and second laws of thermodynamics- to calculate theroretically, for that transition, the quantity of maximum useful work (otherwise known as the Helmholtz available work function)?

By 1900 it was known that the thermodynamic calculation of chemical equilibria, using thermal data alone (that is, heats of reaction, specific heats, and the thermal coefficients for both heats of reaction and specific heats), could not be carried through because of what Haber in 1904 called the thermodynamically indeterminate integration constant *J* that appears in the integrated form of the Gibbs-Helmholtz equation. The theoretically sound point of departure for treating chemical equilibria, indeed, was seen to be the Gibbs-Helmhotz equation, *ΔF = ΔH + T(δΔF/δT) _{p’}* which relates the free energy change ΔF to the heat content or enthapy ΔH and to the entropy change ΔS, the latter being expressed here in the form of the thermal coefficient of free energy change; since

*(δΔF/δT)*=–ΔS.

_{p}The Gibbs-Helmholtz equation, derived from considerations of the first and second laws, was expressed in slightly different form by Gibbs (1875-1879) and Helmholtz (1882-1883). The Gibbs free-energy A (Gibb’s function Ψ) relates to isothermal isochoric processes, whereas the Helmholtz free-energy *F* (Gibbs’ function ζ) relates to isothermal isobaric processes. Throughout our discussion we shall use the Helmholtz free energy and represent it as *ΔF*(Helmhotz’ *freie Energie)* because it is more commonly and more conveniently manipulated in dealing with chemical reactions for which *ΔH* is known. For the sake of uniformity of presentation we shall use the Helmholtz formulation even when Nernst, for example, in some of his papers formulates his heat theorem in the Gibbs form. We recognize that an equivalent expression for the Gibbs free-energy *ΔA* can readily be written so that the change in internal energy *ΔU* (Gibbs’s X) takes the place of *ΔH*(Gibbs’s X) to give

*ΔA* =ΔU+T(δA/δT)_{u}, where (δΔA/δT)_{u} = -ΔS.

Form the Gibbs-Helmholtz equation, *ΔF=ΔH +T(δΔF/δT) _{p},* and the general expression of

*ΔH*as a function of temperature,

*ΔH* =ΔH_{o}+αT+βT^{2}+γT^{3}+…,

and the Kirchhoff law (1858), Δ *C*_{p} = (δΔ *H*/δ *T*)^{p}, where *C _{p}* is the heat capacity at constant pressure, it can readily be shown that the free-energy equation takes the integrated form:

Δ *F* = Δ *H*_{0} - α *TlnT* -β *T*^{2} -γ */2T ^{3}* -…+

*JT.*

In this equation,Δ H_{o} is the heat of reaction at absolute zero, that is, the integration constant in the integrated form of the Kirchhoff law. It can be evaluated empirically from the knowledge of ΔH at any temperature. Likewise, the heat-capacity coefficients, α.β. γ,…,can be calculated from calorimetric data. The only real difficulty encountered in putting this equation into practice is that the integration constant *J* cannot be evaluated calorimetrically and must be obtained from the knowledge of Δ *F*at some temperature.

From the mid-1880’s until the enunciation of Nernst’s theorem in 1906, this integration constant *J* therefore became the focus of a genuine dilemma in chemical thermodynamics because the integrated form of the Gibbs-Helmholtz equation (given above) merely returned the whole problem of predicting the equilibrium conditions for chemical reactions to the experimentalists. The challenge was straightforward: to invent more ingenious techniques to overcome the almost insurmountable analytical difficulties associated with the experimental determination fo Δ *F*. This problem had plagued all the investigators: Arrhenius, van’t Hoff, Ostwald, Le Châtelier, Haber, Richards, Lewis, and, of course, Nernst. The solution that Nernst proposed in 1905 relates to the way in which the *J* of the integrated Gibbs-Helmholtz equation is interpreted and also to the practice of thermochemistry prior to the 1880’s.

During most of the second half of the nineteenth century, chemists used a simple and remarkably serviceable, although theoretically erroneous, energy principle, or rule, to explain and predict the course of chemical reactions. Working independently, H. P. J. Julius Thomsen and Berthelot drew support for the general validity of this energy principle from an enormous number of careful and painstaking calorimetric measurements that were begun in the 1850’s and carried out over a thirtyyear period. It is fair to say that these important thermochemical studies had very little in common with the thermodynamic discussions of the times.

According to the Thomsen-Berthelot principle, the driving force of a chemical reaction, the free energy Δ *F*, is equated simply with the heat of reaction Δ *H* from calorimetric measurements. That is, it was assumed that Δ *F* =Δ *H*. For any given process, say a reaction represented by the chemical equation Y⇄Z, this principle predicts that the magnitude of ΔH a is direct measure of the diving force of the reaction. For exothermic reactions, where ΔH 0, the formation of *Z* from *Y* is favored. For endothermic reactions, where ΔH <0, the formation of *Y* from *Z* is favored. where ΔH = 0, no reaction takes place. The application of this principle gives almsot the right experimental answer most of the time, but not invariably.

Only gradually was the principle seen to be inadequate as experimental data accumulated to show that some exothermic reactions did not proceed spontaneously in the direction of *Z*, while some endothermic reactions did proceed spontaneously in the direction of *Z*. On occasion, isenthalpic reactions (ΔH = 0) were seen to go either way. Also, it was learned from a number of galvanic cell studies, that ΔF for the cell reaction, calculated from the electromotive force *E* (since ΔF= -nℱ E, where ℱ is Faraday’s constant), was in agreement with experiment, where ΔH gave poor results. Likewise, in a few classic cases, where the equilibrium constant *K* could be determined from the equilibrium concentrations of the constituents in the reaction vessel, the driving force could be calculated readily from Δ *F =-RTlnK.* Here too there was good agreement with experiment, where ΔH gave poor results.

In retrospect it seems that all of this should have been self-evident. The course of spontaneous processes must be governed by both the first and second laws of thermodynamics, and not just the first, as the Thomsen-Berthelot principle implies. Accordingly, values for ΔF, calculated from *E* or *K*, but not values of ΔH, should provide reliable information about the driving force or thermodynamic feasibility for chemical spontaneity. Thus, as Nernst and many others recognized clearly at the time, while Δ *H* can be calculated from Δ *F* could, in general, be calculated from Δ *H* only by taking into account the entropy term *dΔ F/dT* that appears in the Gibbs-Helmholtz equation.

Manifestly, the Thomsen-Berthelot principle owed its long-standing practical suscces to the fact that *dΔF/dT* (or the entropy changes) in most chemical reactions is quite small in comparison with ΔF and ΔH. On these premises it became evident that probing into the theoretical significance of the magnitude and sign of *dΔF/dT* might furnish the clue to an explanation of the discrepancies that the thermochemists had tried so diligently, although rather arbitrarily, to bring into line with the Thomsen-Berthelot principle.

Beginning in the early 1890’s, Nernst was alert to the central problem of chemical thermodynamics discussed above. From 1905 until the outbreak of World War I, Nernst with singleness of purpose threw himself into the search for an experimentally demonstrable theoretical solution to this one problem in chemical thermodynamics that had been attacked without success, namely, the calculation, from thermal data, of chemical equilibria as related to the search for criteria of chemical spontaneity.

In *Theoretische Chemie* (1893) Nernst had noted that the Thomsen-Berthelot principle was surprisingly accurate for solids. He proceeded to show that for special cases, such as ideal gases and dilute solutions, for which *ΔH* =0, *ΔF* and therefore *dΔF/dT* should also approach zero. At that time the argued that Δ *F* should have the character of a force function, which, like the gravitational, electrical, and magnetic potential, would be independent of temperature. In 1894 Nernst discussed the Gibbs-Helmholtz equation for the free energy of mixing of concentrated solutions and found a close fit between Δ *F* and Δ *H*, plotted as a function of temperature. In Göttingen, between 1894 and 1905, Nernst carried out some experimental work with gaseous reactions in order to test the Gibbs over a wide range of temperature. His analyses of the high-temperature. His analyses of the high-temperature equilibrium conditions for the formation of nitric oxide (1904, 1906), and the work on the synthesis of ammonia (1907) were motivated by the search for methods of nitrogen fixation from the air, in order to provide a potential source of nitrates for fertilizers and explosives. These were specific practical instances of the application of classical thermodynamic prinicples to the computation of chemical equilibria and the degree of chemical spontaneity for chemical reactions. Their study and the inherent theoretical difficulties connected with the general solution to computing the driving force of chemical reactions, mentioned above, led Nernst to probe the deeper thermodynamic significance of free energies, heats of reaction, and specific heats, especially in the low temperature range.

Other investigators were working along similar lines at about this time. In 1884 in *Comptes rendus*…, in his comprehensive, 225-page paper on chemical equilibrium, under the heading “Constante d’intégration” Le Châtelier recognized the problem in connection with his own equilibrium studies on cements and blast furnace reactions. In 1888 he explored these problems systematically in a memoir published in *Annales des mines,* in which he stated,

It is highly probable that the constant of integration, like the [other] coefficients of the differential equation, is a determinate function of certain physical properties of the reacting substances that are present. The determination of the nature of this function would lead to the complete knowledge of the laws of equilibrium. It would permit us to determine

a prioriindependently of any new experimental data, the complete conditions of equilibrium corresponding to a given to a given chemical reaction. It has hitherto been impossible to determine the exact nature of this constant [“Recherches expérimentales et théoriques sur les équilibres chimiques,” inAnnales des mines,8th ser.,13 (1888), 336].

Nernst later remarked that he had not seen Le Châtelier’s work and, in fact, it is unlikely that he would have examined the *Annales des mines* in connection with his thermodynamic interests.

At Harvard, G. N. Lewis (1899) and T. W. Rich ards (1902) carried out calorimetric and galvanic cell measurements to determine what happens to ΔF and ΔH at low temperatures. For example, Richards found that the thermal coefficient of electromotive force for most galvanic cells *dE/dT* approches zero at low temperatures. Representing graphically the relationship of *E to Δ H* as a function of temperature, he extrapolated to absolute zero. Thus he could conclude that *dΔF/dT* < 0 (since-nℱ(*δE/δT*)_{p} =(*δΔF/δT*)_{p},that *dΔH/dT* >0, and that both become equal to zero as *T* → 0.

At Berkeley, Lewis in 1923 and others since then have maintained that the curves presented by Richards very nearly imply the generalizations that were later embodied in the third law of thermodynamics. Richards’ paper was a suggestive contribution to physical chemistry at the time and was the subject of van’t Hoff’s special memoir in the Boltzmann *Festschrift* of 1904. Haber was influenced by the discussions of both Richards and van’t Hoff and was particularly impressed that for some reactions of low temperatures on Richards’ graph the extrapolated values of Δ *F* and Δ *H* practically overlap. Nevertheless, in spite of the stimulus provided by Richards’ work, it is doubtful that he saw the real implications for thermodynamics of vanishing Δ *F* and Δ *H* values at absolute zero. Nernst later rejected Richards’ priority claim to the third law and implied that Richards work did not reveal even an intimate acquaintance with the second law. Richards own approach had been to focus on the work of compression of atoms as related to chemical affinity. He had pointed out that since the sign and magnitude of both free energy and heat content were dependent upon the sign and magnitude of the heat capacities during the reaction, then *dΔF/dT* must have some fundamental connection with *dΔ H/dT;* and this of course is right.

In his 1904 article in the Boltzmann *Festschrift,* van’t Hoff examined the probable form of the free energy curve in the vicinity of absolute zero. In seeking to give a clearer meaning to the work of Lewis and Richards, van’t Hoff derived a some what different form of the Gibbs-Helmholtz equation was small enough to be disregarded at low temperatures. Nernst later regarded van’t Hoff’s enunciation as a somewhat unsatisfactory hypothesis.

In 1905 Haber published a remarkable book, *Thermodynamik technischer Gasreaktionen.* Of considerable critical insight, this work provided an exhaustive critical survey of the thermodynamic data necessary for the calculation of the free-energy changes of the most important gas reactions. Before Haber, gaseous equilibria had been discussed on a mass-action basis In 1888 Le Châtelier had indicated the significance of specific heats in calculating equilibria over a wide range of temperature, but chemists in general had not recognized the practical importance of his work. On the other hand, Haber was taken seriously because he had treated in detail some well-known and industrially important reactions. Where nineteenth-century chemists had been shy and uneasy about the entropy concept, Haber demonstrated how it could be employed in a practical way.

Most important, Haber attacked head-on the problem that Nernst solved-or thought he had solved-a year later. In 1904 Haber had concluded that if Kopp’s law (the additivity of atomic heat capacities) holds for reactions between solids, the integration constant *J* and therefore the entropy change at absolute zero Δ *S* must have zero value. Lacking knowledge about specific heats at these low temperatures, Haber felt bound to leave open the possibility that the integration constant might have a small finite value owing to deviation from additivity for atomic heat capacities at low temperature. Thus Haber was led to discuss at some length what he called the “thermodynamically indeterminate constant.” Nernst later postulated the validity of Kopp’s law near absolute zero.

In his *Gasreaktionen* (1905) Haber took up the problem of the integration constant in relation to gas reactions. As Planck would later do, Haber explained that the nature of the integration constant should be expressible in terms of heat capacity and entropy constants characteristic of the components of the gaseous reaction In particular he stressed the importance of knowing the variation of these properties with temperature in the vicinity of absolute zero. In the absence of experimental information he proceeded cautiously. Haber could not have formulated, or at least could not have formulated, or at least could not have announced in publication, the heat theorem of Nernst without a great deal more experimental support. Haber’s contribution therefore seems to stand out above the other physical chemists that we have mentioned. Because of insufficient heat capacity information, he simply left open the question of what happens with gases at absolute zero. For gaseous reactions involving no change in the number of molecules he concluded, however, that the integration constant, if not equal to zero, was probably quite small. His experimental data could support this conclusion, and so he adopted it as a guide in setting up his free-energy equations. By the end fo the year Nernst had announced his *Wärme-Theorem,* as he then called it. Haber immediately recognized its immense importance.

During the *Wintersemester* in Berlin, while lecturing on the thermodynamic treatment of chemical processes, Nernst had become more convinced than ever that chemical equilibrium could not be computed from thermal data alone using classical thermodynamics. What was needed, he believed, was a supplementary hypothesis to charaterize was a supplementary hypothesis to characterize the change of free energy in the vicinity of the absolute zero of temperature. Nernst perceived more clearly than any of the other investigators mentioned that the work of transition from one state of a system to another could not be calculated theoretically from energy differences using the laws of thermodynamics. What could be inferred thermodynamically was that Δ *H* and Δ *F* should be equal at absolute zero. This follows simply from the definition of free energy, namely, that Δ *F* =Δ *H - TΔS*for an isothermal process. There was still no way to determine Δ *F* from the knowledge of Δ *H* under any conceivable conditions. A careful study of the available thermochemical data had led Nernst to suspect that the thermal coefficients of heat content *(δΔH/δT)* and free energy *(δΔF/δT)* might approach each other asymptotically in the neighborhood of absolute zero. With as much experimental evidence-scanty at best-as he could muster, Nernst stoutheartedly and with characteristic boldness faced the Göttingen Academy of Sciences to present his *Wârme-Theorem* He must have been rather confident about its significance, because the proof of the title page, as we learn from Simon’s excellent survey of the third law, bore his scribble: “Bitte Revision! Im Ganzen 300 Separata!”

As revealed in the title, the subject of Nernst’s paper was a single issue-the calculation of chemical equilibria from thermal measurements. Like the other investigators, Nernst began with the GibbsHelmholtz equation, but in the Gibbs form, presenting the following integrated form of the equation in terms of the equilibrium constant *K* rather than is terms of free energy:

*lnK =-ΔH _{0}/RT +Σα/RlnT+Σβ/2R T+…+J.*

Like Le Châtelier, Lewis, Richards, and Haber, Nernst noted that all of the quantities in this equation can be obtained by thermal measurements with the exception of the integration constant *J.* Thus, although the form of Nernst’s equation was somewhat different, there was nothing new in it; what is new in this paper is the line of reasoning that Nernst employed to interpret the physical meaning of the equation and to realize the wide chemical implications hidden beneath the constant of integration *J* He correctly supposed that within the whole range of possible temperatures, absolute zero should have a very special thermodynamic significance.

The point of departure for Nernst was to recognize from the Gibbs-Helmholtz equation that if the temperature coefficient of total (internal) energy, *dU/dT (dH/dT* in the Helmholtz form), does not disappear at absolute zero, then the coefficient of free energy, *dA/dT (dF/dT* in the Helmholtz form), must be infinite; and then nothing can be revealed about the *F* curve at absolute zero. This implies a thermodunamically indeterminate *J.* Nernst found his way out of this unacceptable conclusion by shifting from the discussion of gases to that of solids. At this stage of his argument he ignored gaseous reactions, because he knew that for chemical reactions involving gases the sum of the specific heats of the reactants is in general not equal to the sum of the specific heats of the products, since the degrees of freedom may differ. By considering only condensed phases and by assuming that Kopp’s law would apply, he could equate the specific heat sums of products and reactants. If so, *dU/dT (or dH/dT)* would vanish at absolute zero, and *dA/dT* (or *dF/dT*) would be finite. Nernst considered this extrapolation acceptable, since classical theory had indicated that with decreasing temperatures the molecular heats of compounds are equal to the sums of their atomic heats.

Accordingly, Nernst reasoned that *A* and *U* (or *F* and *H*) do not differ markedly at room temperature-nor even at somewhat higher temperature so the *A* (or *F*) curve is not likely to start at a steep angle at absolute zero. He recognized that the simplest assumption would be for the *A* and *U* (or *F* and *H*) curves to run together and become tangent to one another as *T*→0. Referring once again to the integrated form of the Gibbs-Helmholtz equation above, we see that

(δF/δT)_{p} = -α/nT-α-2βT-3/2γT^{2}-…+J.

If we postulate, as Nernst did, that

then *J=0*, and

In other words, Nernst’s hypothesis reveals that as *T*→0 not only does Δ *F-ΔH*→0, but (δΔF/δT)_{p}→0 and *(δΔH/δT) _{p}*→0. We note that there is no suggestion here that either Δ

*F*or Δ

*H*approaches zero as

*T*→0, but only their difference; Δ

*F*and Δ

*H*remain finite quantities, positive or negative approaching each other asymptotically. Nernst recognized that lim was a necessary and sufficient condition for securing a definitive solution to the chemical equilibrium problem, whereas lim

_{p}was necessary but not suffi

*T*→0 cient. The important point about Nernst’s hypothesis is that since

*ΔF-ΔH→0*, as

*T→0*, the integration constant

*J*is known and there is no longer a need to seek special techniques for determining Δ

*F*, since this can now be done purely calorimetrically. The Nernst theorem simply showed how to compute the value of

*J*as the algebraic sum of other empirically determined “chemical constants” for the constituents of a chemical reaction. The experimentally straightforward but nevertheless timeconsuming procedures for carrying out calorimetric measurements at low temperatures later yielded to the perfection of spectroscopic analyses that permits the entropy constants to be calculated with much less effort.

Having postulated his heat theorem for condensed phases in four introductory pages, Nernst turned directly to the question of the determination of the integration constant for gaseous systems. Crediting Le Châtelier and Haber for having recognized the fundamental problem, he proceeded without fanfare or apologies to treat gaseous reactions at sufficiently low temperatures so that all of the constituents could be considered to be in the condensed state. With the help of the van der Waals equation he was able to develop approximation formulas to calculate the free energy for gaseous reactions in the condensed state.

For Nernst this was just the beginning of experimental investigations connected with the theorem, since he sought in various ways to support its theoretical soundness and practical utility. By 1907 his position toward the theorem was essentially fixed–as can be seen from his Silliman lectures. His thesis was that the heat theorem revealed new truths about the relation between “chemical energy and heat,” but he suggested that it also would prove useful beyond the solution of problems of chemical equilibrium and spontaneity. He emphasized that a great deal of experimentation would be necessary in order to decide whether the theorem represents only an approximate principle or an exact law of nature similar to the first and second laws. Irrespective of the theoretical status of the theorem, Nernst maintained that approximations based upon the theorem would provide answers to the all-important question about the driving force for chemical reactivity. In this he was right. Still, he suggested that chemists work over the whole field of thermochemistry from the new point of view and, namely, that they undertake an exhaustive experimental analysis of heats of reaction, specific heats, and temperature coefficients over the entire experimentally feasible temperature range.

Thus, Nernst was led to declare that all that thermodynamics can contribute to chemistry is already implied in the Gibbs-Helmholtz equation, provided that the heat theorem be used to furnish an interpretation of the mode of behavior of nature in the vicinity of the absolute zero of temperature. His line of argument was that *F* cannot in general be equal to *H,* because this is contrary to the results of experiment; that the correct relation between *F* and *H* cannot be found from the first and second laws, because the integrated form of the second-law statement contains a constant that was thus far undetermined; and that therefore if a new law of thermodynamics was to be found, it would have to account for the integration constant as the only remaining thermodynamic problem.

The clue to the theoretical treatment of the problem for Nernst lay in the approximate success at ordinary temperatures of the Thomsen-Berthelot principle. The solution that he provided was to assume that this principle was not only approximate at ordinary temperatures but also in the neighborhood of absolute zero, so that *F* and *H,* plotted as a function of temperature, approach each other asymptotically with contrary slopes. Nernst concluded that this theorem would settle the question by making it possible to predict the thermodynamic stability of any stoichiometrically correct chemical equation, based on calculations derived from thermal data alone.

Nernst’s conception of the overall significance of the heat theorem can be gathered from his own statement at the end of the 1906 paper:

If we now bring the result of our considerations together succinctly, we can say that the goal of thermochemistry, namely the calculation of chemical equilibrium from heat of reaction measurements, seems attainable, provided we seek the aid of a new hypothesis, according to which the curves of free energy and the total energy of chemical reactions between only solid or fluid bodies, become tangent to one another at absolute zero. Even if an exact test of the formulae obtained by the help of the above hypothesis about specific heats is not feasible at low temperatures, the approximation formulae developed in this work are seen to be in agreement with experience. The relationships between heat and chemical affinity seem substantially to have been clarified.

Although unaware of it when he announced his heat theorem, Nernst had laid the foundation for the connection between chemical thermodynamics and the quantum theory set out five years earlier by Planck.

For a over decade after the 1906 paper appeared, virtually the entire facilities and personnel of the physical chemistry institue of the University of Berlin were organized into a huge work program to experimentally test Nernst’s *Wärme-Theorem* The immediate consequence of Nernst’s new idea was that radically different thermochemical techniques were put into practice to elucidate chemical equilibrium. These involved the determination at very low temperatures (in fact as close to zero as possible) of the specific heats and thermal coefficients of specific heats for the constituents of the chemical reactions under investigation. In a series of seven papers published between 1910 and 1914 Nernst and his co-workers (F. Koref, F. A. Lindemann, and F. Schwers) presented impressive experimental evidence to support Nernst’s theorem based on the electrical measurement of electrically induced temperature changes. The rigorous test of the validity of the theorem was soon seen to be an enormously challenging experimental undertaking. To approach this objective the Nernst group constructed ingenious electrical and thermal devices, developed a vacuum calorimeter, and built a small hydrogen liquefier (1911) to achieve temperatures low enough to be able to extrapolate safely to absolute zero. Nernst tackled all these problems imaginatively and successfully, and step by step came increasingly to believe that his hypotheses should be elevated to the rank of a bona fide law of thermodynamics.

Not long after the Nernst heat theorem had become established in its role as a powerful method to predict chemical equilibrium–thus to indicate which reactions were chemically feasible-it was seen that quantum statistical calculations of entropy constants for gases became accessible. As a follow-up to his four classic papers of 1905, Einstein turned to the consideration of radiation theory and treated the specific heat of solids as a problem in quantum mechanics. In Nernst’s 1906 paper there had been no mention of Planck’s quantum ideas of 1900, nor had he taken seriously Einstein’s suggestion in 1907 that quantum theory predicted vanishing heat capacities for solids at absolute zero. During Nernst’s visit to Einstein in Zurich in March 1910, the two men discussed the extent of agreement between the Einstein theory of specific heats and the experiments being conducted at Nernst’s institute in Berlin. On 13 May 1911 Einstein wrote Michele Besso that his theory of specific heats had celebrated true triumphs, since Nernst had experimentally confirmed virtually everything that his theory predicted. Apparently both Nernst and Einstein gloried in the turn of events: Nernst, realizing that his precious heat theorem was linked with and in agreement with predictions from quantum theory; and Einstein, that his revolutionary quantum conceptions were receiving experimental backing from Nernst’s work. Working with Lindemann in 1911, Nernst showed that Einstein’s specific-heat equation was in agreement with his data, except for certain systematic deviations. They also showed that a revised Einstein formula was in still closer agreement with the experimental information except at the every lowest temperatures.

Alert to the significance of the heat theorem for the establishment of the quantum theory, Arnold Sommerfeld, in a lecture at the eighty-third *Naturforscherversammlung* in Karlsruhe in 1911, remarked that the work on blackbody radiation carried out during the first decade of the century at the Physikalisch-technische Reichsanstalt constituted one of the pillars of the quantum theory and added: “Perhaps to be estimated as of equal merit is the work of the Nernst Institute which, in the systematic measurement of specific heats, has furnished a second no less powerful pillar to support the quantum theory.”

The experimental evidence for the quantum theory was one of the central topics of discussion at the first Solvay Congress in Brussels in late October and early November 1911. Nernst had taken the initiative for setting up and organizing the sessions and seeing to it that the leading physicists would be there; the twenty-two participants included Lorentz, Planck, Rubens, Sommerfeld, Wien, Jeans, Einstein, and Lindemann. Einstein reported on his specific heat theory in relation to the Nernst and Lindemann empirical formula for the thermal energy of solids–just before the problem was solved theoretically by Max Born and Theodore von Kármán (1912). About the same time Peter Debye, who had been Sommerfeld’s assistant and was then lecturing on thermodynamics in Zurich, independently presented his theory of specific heat at the Physikalische Gesellschaft in Bern (1912). Born and Kármán had reached their results by a different route than Debye; both had built on the foundations laid by Einstein. For some time these formulations proved satisfactory. Of unique significance was Debye’s deviation of the famous *T*^{3} law that gives for the lowest temperatures the proportionality between atomic heats and the third power of the temperature-a relationship that was seen to fit the facts very well.

In 1910 Planck markedly enhanced the usefulness of Nernst’s theorem by putting it into the form in which it has most frequently been given ever since. In his paper he promoted the idea that not only the entropy differences during the alterations of a system in the vicinity of absolute zero tend to zero, but that the entropy differences of all of the constituents of the system become zero. That is, given that a finite value of *S* is possible only if the specific heats vanish at absolute zero, since otherwise the integral at the lowest limit becomes infinite. The Planck formulation, however, tells more than that namely, that the individual entropies at absolute zero not only are finite but that they are zero. Planck stressed that the Nernst theorem was a major extension of the second law because it permits the calculation of absolute entropies. He also pointed out–but in rather cautiously worded statements-that the entropy form of the Nernst theorem necessarily means that the third law, like the second, is intrinsically connected with probability, atomistics, and statistical implications.

Planck’s formulation of the heat theorem in terms of vanishing entropies at absolute zero did not appeal to Nernst, who considered it both inappropriate and intuitively too unclear. The paradox of Nernst’s position was that his own formulation, which made no reference to entropies, was far more cumbersome and theoretically less elegant. Unquestionably Nernst’s peculiarity on this issue was frowned upon by most members of the scientific community. In principle the application of quantum theory to specific heat considerations for solids could have led before 1905 to the conclusion that lim Δ *S=0*. Such a formulation might have elicited *T→0* more conviction from physicists than Nernst’s heat theorem, because it follows theoretically from quantum mechanics. By contrast, the Nernst heat theorem could not be deduced from the other laws of thermodynamics, and only experimental evidence could serve to establish its correctness. Nernst and his students eventually amassed sufficient empirical evidence to reverse the attitude of scientists toward one of acceptance of Nernst’s heat theorem.

In 1912 Nernst stated his heat theorem in terms of the theoretically decisive principle of the unattainability of absolute zero. According to this principle, it is impossible to build a caloric machine that will allow a substance to be cooled to absolute zero; and from this negative assertion Nernst concluded that the thermal coefficients of all the physical properties of solid bodies would vanish in the approach to absolute zero. The properties of bodies that subsequently were investigated as tests of the third law included direct studies of thermal expansion, surface tension, magnetic and dielectric polarization, and thermoelectric phenomena. More indirect and less unambiguous in an interpretive sense were the studies on fludity, solutions, mixed crystals, frozen-in phases, crystallographic transformations, and chemical reactions-all designed to demonstrate the disappearance of physical properties as *T→0* that is, to show, in Planck’s formulation, that lim

Nernst’s particular way of enunciating the principle of the unattainability of absolute zero was questioned by physicists, even while the principle itself was seen to be important. Rather than providing a proof, Nernst had demonstrated the consistency of the principle with the impossibility of a *perpetuum mobile.* In order to avoid presenting the idea in terms of entropy-temperature graphs, Nernst presented his proof in the form of a Carnot cycle. He showed that a *perpetuum mobile* of the second type results from taking absolute zero as the lowest temperature of the cycle, thus demonstrating that the attainment of absolute zero is theoretically impossible. The way in which the unattainability of absolute zero was deduced from arguments based on the disappearance of specific heats as *T→0* was rather obscure. In 1913 his proof was challenged by Einstein, who reasoned that *Gedankenexperimente* should be possible in principle even if not in practice and that this was not the case for Nernst’s formulation. Nernst stuck to his guns, and so did Einstein.

A long and involved discussion followed about the null-point entropy of frozen-in phases. The best contemporary account of this work was given in 1930 by Franz E. Simon, one of Nernst’s most talented students and colleagues. A more precise formulation of Nernst’s principle was indicated by postulating that the entropies of chemical reaction between pure condensed phases in internal equilibrium vanish as *T→0* The difficulty that emerged from this alternative formulation was one of defining the criteria for equilibrium. Certain condensed phases, like glasses, as well as mixed solid phases of crystals and solutions, are not at equilibrium. Besides, a system may be at equilibrium with respect to atomic or molecular orientations but not with respect to electron or nuclear orientations. As long as residual questions remain about the deep structure of matter there would be no reason to assume that rock-bottom equilibrium can be reached regardless of now close a system approaches absolute zero.

One of the most serious difficulties confronting Nernst was that classical kinetic gas theory predicts that the heat capacity at constant volume *C*_{r} does not tend to zero as *T→0* as the heat theorem demands, but reaches limiting values of 3/2 *R* for monatomic gases, and 5/2 *R* for diatomic gases, and so forth. Thus, even if the Nernst theorem had given a fairly acceptable interpretation of the heat capacities of condensed phases at low tempearatures, it seemed likely that gases might have to be excluded from the theorem. Of course this would have been very detrimental to Nernst’s attempt to elevate the heat theorem to the status of a general law of thermodynamics. Fortunately for Nernst, the developments in quantum mechanics just prior to World War I gave Sackur (1912), Tetrode (1912), and Stern (1913)the means to calculate directly the entropy of a monatomic gas, and later, the entropy of more complex molecules. The calculations agreed tolerably well with the experimental results, showing that theory predicted and experiment confirmed the falling-off of heat capacities at low temperatures.

Nernst interpreted these developments as a step toward confirming his theorem. He proceeded heroically, using some quite primitive arguments and despite the incredulity of many scientists, to postulate (1914) a state of degeneracy *(Entartung)* for gases. Subsequent advances in quantum mechanics showed Nernst to be on the right track. The Bose-Einstein and Fermi-Dirac statistics both confirmed the gas degeneracy idea. The progress of quantum theory notably justified Nernst’s idea, if not the reasons for enunciating it, when it was shown that electrons in metals present an example of degeneracy at much higher temperatures and that the same principle suffices to account for the interior physical conditions of stars at very high temperatures and pressures.

With the outbreak of World War I, Nernst’s academic pursuits virtually came to a halt as he was drawn into military administration, chemical gas warfare, and service as automobile chauffeur for the German army on the move from Belgium to France. As is evident from the preface to Nernst’s 1918 monograph, *Die theoretischen und experimentellen Grundlagen des neuen Wärmesatzes* which was written during a time of “*Trübsal und Not,”* Nernst was able to immerse himself further in the new theoretical physics, namely, quantum mechanics, and to reflect on its meaning and implications for his beloved and not yet controversial *Wärmesatz*. In this volume he presented in a most comprehensive way his mature ideas on chemical thermodynamics.

Until his retirement in 1934 Nernst was again actively involved with the pursuit of physical chemistry at Berlin, but he now took up a number of new topics. With the accumulation of experimental data in the 1920’s, Nernst’s heat theorem, which had enjoyed the successes of early quantum theory, encountered serious difficulties as experimental anomalies with condensed systems appeared that could not be squared with the general theorem. In testing the validity of the third law these anomalies had to be reckoned with. Most of them were identified and examined in terms of their quantum origins. In time they came to be recognized as the quantum effects resulting from the liberation of energy that takes place during the degeneration of various internal degrees of freedom. At lower temperatures these degenerations were seen to lead to greater order or internal equilibrium with respect to each particular quantum effect. Nernst took relatively little part in the discussion of these problems. He felt that his theorem should apply in a straightforward way to all systems using a thermodynamic mode of reasoning and without appealing to statistical considerations. He was convinced that further experimental and theoretical research would confirm his theorem as a general law.

No person contributed more to providing a theoretically satisfying restatement of the third law than Franz Simon in the 1920’s and 1930’s. He had steadily gained a wide reputation as an authority in the newly developing field of cryogenics, on the strength of thermodynamic and statistical reasoning that focused on the meaning of the “internal equilibrium” states of systems. Simon had received his doctorate under Nernst in 1921 with a dissertation on the study of specific heats carried out down to the temperature of liquid hydrogen. This early research on undercooled liquids, glasses, and crystalline substances had revealed a λ-type specific heat anomaly for ammonium chloride. In 1929, using liquid helium as a coolant, he discovered the anomalous specific heat of solid orthohydrogen. His singlestroke adiabatic method for liquefying helium was crucial for the development of low-temperature research in general and led to his own pioneering work on specific heats, magnetic cooling, and nuclear cooling and orientation below 1° K. He perfected a great variety of small-scale experiments and demonstrated the effectiveness of working in vessels with “mathematically thin” walls. Toward the end of his career, while at Oxford, Simon worked on nuclear orientation and cooling, utilizing the magnetic moments of atomic nuclei at very low temperatures in a way that is analogous to the use at higher temperatures of paramagnetic moments to achieve cooling by adiabatic demagnetization. Shortly before his death Simon and his colleagues (especially Kurti) attained temperatures of about 2×10^{-5}^{°} K.

From the very start of Simon’s interest in the third law in 1920, his central concern was to test the general validity of Nernst’s theorem. The desire of some investigators in the 1930’s to restrict the heat theorem to pure crystals was unacceptable to Simon because the theorem could then no longer be considered as a general law. Simon, like Nernst, wanted to demonstrate the authenticity of the heat theorem for all processes to which valid thermodynamic reasoning might be applied. The direction that this concern took was to demonstrate from experimental findings on magnetic properties, super conductivity, and the behavior of liquid helium that the apparent anomalies to the third law could be explained either on the basis of the incorrect extrapolation of specific heats to 0° K. or else to the misapplication of thermodynamics to systems that were not in internal equilibrium. Violations of the third law for chemically homogeneous systems, Simon conjectured, could always be attributed to specific heat anomalies at very low temperatures. For example, he felt that there was no valid reason to assume that nuclear spin systems might not lose their entropy at sufficiently low temperatures. It was basically up to experimentalists to devise sufficiently ingenious analytical techniques to clear up such anomalies. Of course Simon realized that it might not be feasible in practice to go reversibly from a given initial state to a final state within a reasonable length of time, especially with certain chemical reactions for which the chemical kinetics and rates are not favorable. Still, his objective was to explain these anomalies.

It was common knowledge in Berlin that Simon’s “anomaly consciousness” provided the effective stimulus for the high level of achievement of the many *Doktorand* working in his impressive lowtemperature laboratory . Simon’s fundamental argument was that the low-temperature specific heat anomalies that showed up for amorphous solids, nonhomogeneous mixed crystals, solid solutions, and glasses could all be accounted for by recognizing that these systems were not in internal equilibrium but were removed more or less from their most probable entropy states by being “frozen-in..” Thus, unwarranted thermodynamic reasoning was to be avoided for such nonequilibrium systems. Simon supported this view with his own investigations of glasses, showing with X-ray crystal analyses that the state of disorder persists down to the lowest experimentally achievable temperatures. He was able to explain with a clever argument that in such cases, where experimental data on glasses were cited to show that the third law had been violated, the necessary consequence was that it would be possible to reach absolute zero with such substances. Thus the criticism led to a *reductio ad impossibile.* For, wherever entropy differences exist between two states of a system, a reversible adiabatic process from the lower entropy state should lead to absolute zero, provided that the transition be allowed to proceed at a temperature where the initial entropy state is equal to or smaller than the final entropy state at absolute zero . Thus, for systems genuinely in internal equilibrium, nonvanishing entropies (that is, contradictions to the third law) would provide the means for reaching absolute zero.

In 1927 Simon proposed a new formulation of the third law : “At absolute zero the entropy differences disappear between those states of a system between which reversible transitions are possible at least in principle .” In 1930 he expressed similar ideas in another way, namely, that the entropy of all factors within a system that are at equilibrium disappears at absolute zero . In a more acceptable reformulation in 1937 Simon stressed that the entropy contribution of each factor within a system in internal equilibrium becomeszero at absolute zero . This was a rather safe formulation of thet third law, seeing tha it should be possible in principle to discover, at still lower temperatures and by refinement of analytical techniques, additional hitherto unrecognized nonequilibrium factors (frozen-in states) responsible for apparent anomalies. Simon’s formulation was based on the assumption that the lowest energy states of any system are not degenerate . He argued that in that case the apparent contradictions result not from degenerate ground states but rather from a frozen-in disorder that would disappear if the system could somehow be melted out or moved toward greater order catalytically.

The cases of frozen-in disorder that were specially treated by Simon, and that extend beyond the traditional analysis of crystal lattice disorder, concerned foremost disorder in the distribution of isotopes and of magnetic effects at very low temperatures. Examples of the latter were the electron spin disorder of certain paramagnetic salts and nuclear spin systems that would reach internal equilibrium only in the temperature region of 10^{-3} to l0^{-6°}K. Simon argued that there are any number of subsystems that can be studied in connection with the behavior of matter : one subsystem may be in internal equilibrium where another is not . Thus to speak of complete internal equilibrium was to miss the point, because then there would be practically no substance to which thermodynamics would apply . Simon’s third-law statement of 1937 took the simple form : The contribution to the entropy of each Subsystem that is in internal equilibrium disappears at absolute zero.

In his van der Waals centenary lecture in 1937 Simon summarized his views succinctly:

We can state that the present experimental evidence indicates the general validity of Nernst’s theorem as a law of

thermodynamics.The possibility that some future experiment may not be in agreement with the theorem obviously cannot be excluded, but unless there is some reason from a theoretical point of view to expect such a result, to anticipate it is mere speculation. So far, no theoretical argument against the theorem exists. On the contrary the assumption, that the state of lowest energy is that of entropy zero, i.e. that of perfect order is theoretically very plausible. I cannot see, therefore, any justification for withholding from Nernst’s law the status of a general law of thermodynamics [F. Simon, “On the Third Law of Thermodynamics.” inPhysica4no.10 (23 Nov. 1937) 1096]

Over a period of nine years in Berlin, working close to Nernst, Simon published some fifty papers relating to low-temperature studies. Although they contributed to putting Nernst’s law on much firmer theoretical footing, Nernst marshaled the sharpest opposition to the new restatements. Nernst wanted no riders attached to his theorem and told Simon that if this should prove unavoidable, he would be prepared to give up his theorem as a general law of nature. Nernst’s mind was geared to specific heats and to the expression of the theorem in terms of the capacity factor for isothermally unavailble energy, namely the temperature coefficient for free-energy changes. He wanted to have nothing to do with “entropies,” and in his papers he always preferred thermodynamic cycles to entropy diagrams.

It is a paradox that Simon, proceeding from the deep interests in the Nernst theorem that came to dominate his life, subsequently founded a distinguished low-temperature school to demonstrate the theoretical validity of the third law-only to discover that its author did not approve of the conclusions that the investigations led to. In fact, after almost two decades of work, Simon had come to exactly the conclusion that had been Nernst’s deep expectation from the start, namely, that the heat theorem be considered valid as a law of thermodynamics. Simon’s conception, however, of what constitutes validity was intellectually more appealing than Nernst’s had ever been.

The specific problems that claimed Simon’s attention, the search for ways to verify the heat theorem with immense amount of information coming from low-temperature laboratories and the explanation of the numerous anomalies being discovered, are all representative of the general state of dissatisfaction with and confusion about the thrid law that reigned during the 1920’s and 1930’s. The severity of the situation is revealed by a statement made in 1932 by Fowler and Sterne:

We reach therefore the rather ruthless conclusion that

Nernst’s Heat Theorem strictly applied may or may not be true, but is always irrelevant and useless-applied to “ideal solid states” at the absolute zero which are physically useful concepts the theorem though often true is sometimes false, and failing in generality must be rejected altogether. It is no disparagement to Nerst’s great idea that it proves ultimately to be of limited generality. The part that it has played in stimulating a deeper understanding of all these constants, and its reaction on the development of the quantum theory itself cannot be overrated. But its usefulness is past and it should now be eliminated[Review of Modern Physics4(1932), 707]

By the outbreak of World War II, Simon’s views were beginning to find general acceptance. Besides, the need for clarification about various aspects of quantum mechanics and nuclear physics bacame far more pressing than thermodynamics. Formulated initially to explain gas reactions, by 1940 the third law had outlived most of its intended function, and in any case, the entropies were then begining to be treated quantum mechanically and computed largely from spectroscopic data. It may be conjectured, therefore, that all of these matters would have followed, without Nernst’s work, from the logical development of quantum mechanics. In his Guthrie lecture of 1956 Simon responded to this by saying:

Of course, one could say the same of the Second Law, namely that statistical theory would have yielded all the information pronounced first by the empirical statements of Carnot and Clausius. The predictions of the Third Law would eventually have been produced by quantum theory, but I have to remind you only of the fact that we have so far no full quantum statistical explanation of the Third Law to show you that it would have come very much later. Also we must not forget that the Third Law was an extremely strong stimulus to the development of quantum theory and it is perhaps not quite idle to consider how the development would have taken place had Nernst’s deliberations started ten years earlier as they might well have done. Perhaps the quantum of action would have been discovered as a consequence of the disappearing specific heats rather than from the ultra-violet catastrophe of the radiation laws.

Things do not always develop in the most direct or logical way; they depend on many chance observations, on personalities and sometimes even on economic needs…. I hope I have shown you how a great mind tackled a very obscure situation, at first only in order to elucidate some relatively narrow field, and how later, as the result of all the interaction and cross-fertilization with other fields, the Third Law emerged in all its generality, as we know it to-day

[year Book of the Physical Society (1951), 21]

Irrespective of the status and intrinsic long-range merts of the third law, an impressive number of fringe benefits resulted from the stimuli coming from the Nernst syndrome. Over a period of about three decades a prodigious amount of good low temperature research had been carried out in highly specialized centers for cryogenic investigation, namely, Berlin, Cracow, Paris, London, Toronto, Leiden, Oxford, and Berkeley. In the process of testing the Nernst theorem, important advances were achieved, especially in the study of the low temperature properties of matter, the physics and chemistry of solid-state phenomena, gas degeneracy, corresponding states, zero-point energies,λ point phenomena, magnetic cooling, superconductivity, and superfluidity. More immediately important than the gradual opening of these domains of experimental inquiry was the immediate support that the heat theorem gave to quantum mechanics in the early days of its development, before the results of spectroscopy and the Bohr theory of atomic structure were available.

Over the years Nernst became increasingly possessive about his role in the genesis of the third law. In Berlin, within the shadow of the colossal achievements of Planck and Einstein, Nernst–perhaps understandably-became rather defenseive about the merits of his own contributions. Several students of Nernst tell the story–the versions differ somewhat, but not their essential message that in his lectures Nernst liked to refer to the first law of thermodynamics as having been discovered independently by three investigators (presumably Mayer, Joule, and Helmholtz) and the second law, by two independent investigators (Carnot and Clausius). Concerning the third law of thermodynamics Nernst would say, “Well, this I have just done by myself.” According to another version of this anecdote, which also seems to suit his character, Nernst added that it therefore should be obvious that there never could be a fourth law of thermodynamics. In any case, we know that Nernst became rather adamant in insisting that his heat theorem (*mein Wärmesatz,* as he called it) was more than a way of calculating chemical equilibria; it was in fact a law of thermodynamics on a par with the first and second laws. Indeed, after the theoretical low–temperature quantum mechanical interpretation of specific heats by Planck and Einstein, Nernst believed that the collapse of his heat theorem, if possible, would necessarily have to be accompained by the simultaneous rejection of Planck’s and Einstein’s views.

Nernst’s participation in the extensions, criticisms, and reformulations of his heat theorem was rather that of a spectator; it was his students who were involved in new contributions. Nernst was totally absorbed in other scientific matters. Thus while low–temperature investigations continued to command the attention of experimentalists and theoreticians alike, he explored new leads in photochemistry, chemical kinetics, and chemical astrophysics. This phase of Nernst’s career coincides with the Weimar Republic–an incredibly fertile period for the physical sciences. Berlin was an international whirlpool of scientific activity and a hotbed for the germination of radically new perspectives in physics and chemistry. Thus, the more narrowly focused thermodynamic approach to physical chemistry that had marked the approach of Ostwald in Leipzig, and to some extend even the prewar focus in Berlin, was enlarged and upgraded to accommodate new advances in chemical reaction kinetics, photochemistry, quantum mechanics, spectroscopy, nuclear physics, and radiochemistry.

When Ostwald resigned from his chair in physical chemistry at the University of Leipzig in 1905 to pursue his literary and philosophical predilections, the center for physical chemistry in Germany shifted for a decade to Nernst and his group of collaborators in Berlin. After World War I physical chemistry was pursued in Berlin as vigorously as before, but by then other university centers had also been launched or reinforced. The most consolidated activity in the physical sciences in the 1920’s however, was at the University of Berlin, the Technische Universität, the Kaiser Whilelm Institut, and the Physikalisch–technische Reichsanstalt–all located within a few miles of each other. It was most fortunate that such government–sponsored institutions had broad–minded and enlightened officials in charge of the funding.

From 1919 to 1933 the most prominent physical chemists include, besides Nernst, whose commanding position was unassailable, four outstanding experimentalists: Fritz Haber, director of the Kaiser Wilhelm Institut for Physical Chemistry and Electrochemistry at Dahlem: Max Bodenstein, a superb experimentalist, who became Nernst’s successor in the chair of physical chemistry at the University of Berlin in 1922; Max Volmer, head of the institute for physical chemistry at the Technische Universität; and K. F. Bonhoeffer, Nernst’s student, who joined Haber’s institute in 1922 and who, more than any of the others mentioned here, took full advantage of the new methods and advances made available in the 1920’s. Bonhoeffer later followed Le Blanc in Leipzig.

The whir of excitement generated in seminars, colloquiums, and laboratories by the brilliant constellation of physicists and chemists in Berlin was contagious. The wave of activity was closely related to Nernst’s own interests, both in regard to testing the validity and exploring the implications of his heat theorem and in other developments relevant to the new problems in physical chemistry that he had undertaken. Planck and Einstein were working on quantum mechanics and thermodynamics; Laue, on crystal interference; Erwin Schrödinger and Fritz London, on the applications of wave mechanics: Paschen and Ladenburg, on spectroscopy: Otto Warburg, on photochemistry; Otto Hahn, on radiochemistry; Gustav Hertz, on isotype separation by gaseous diffusion; Herbert Freundlich, on capillary and colloid phenomena and Michael Polanyi on chemical kinetics. Because of his prominence in the Berlin scientific community. Nernst was at one time or another in contact with all of these investigators.

Like virtually all of his colleagues named here, Nernst had come from a socially prestigious and quite wealthy family. Money was therefore seldom a problem. On the other hand, overwork and high performance expectations did introduce considerable anxiety and discomfort. Among the scientifically elite, solitary retreats from Berlin *zur Erholung*at health resorts and other oases of tranquillity and relaxation became standard fare.

When he returned to his physical chemistry institute in Berlin, Nernst *est revenu á ses premières amours,* as Bodenstein put it. There he was to become entrenched once again in more decisively chemical topics than third-law investigations. In the first instance he worked on photochemistry. According to Einstein’s photochemical equivalence law of 1912, a molecule that absorbs one energy quantum of radiation *hv* in a primary photochemical process can initiate secondary chemical reactions no longer dependent on the illumnination. This law seemed to hold in a number of instances, but it had been demonstrated that for the formation of HCl from H_{2} and Cl_{2}*(dieboshafte Chlorknallgasreaktion)* at least 10^{6} molecules were formed per quantum in place of two as might be expected from the equation Cl_{2}+*hv* =2Cl. In 1918 Nernst suggested a simple and ingenious solution to this problem the idea of a “chain reaction” . In this case the suggested process was

Cl_{2}+*hv*=2Cl

Cl+H_{2}=HCl+H

H+Cl_{2}=HCl+Cl, and so forth

Nernst’s theory was fully justified in 1925 by James Franck’s calculations of the energy of dissociation of Cl_{2} based on absorption-spectrum studies. Nerst’s co-workers mainly John Eggert Walter Noddack, Friedrich Bonhoeffer, and Max Bodenstein subsequently set the high standards in photochemical investigations that came to be so essential in the field of chemical kinetics. It was shown that chain reactioins of the type suggested by Nernst can be initiated by means other than light for example, alpha particle bombardment, sparks, and the introduction of sodium vapor. It was also demonstrated that the chain process is terminated only by the removal of the active molecules by wall collision or reaction with other molecules.

Nernst left his university post in 1922 to succeed Emil Warburg as president of the Physikalischtechnische Reichsanstalt; but his ambitious plans for major organizational changes were wrecked by severe inflation . After two years of frustration, Nernst returned in 1924 to the university to fill the vacant post of professor of physics that had been created by Heinrich Rubens’ death . Until his retirement in 1934, Nernst continued to devote his efforts to physical chemistry and to serve as director of the physical laboratory .

In the late 1920’s Nerst turned his attention to cosmological questioins. He was inspired in part by discussions of these matters with Einstein, but the principal motivation for this late-in-life escapade into physicochemical astrophysics was a basic uneasiness about the idea that the universe should have a passing existence, its so-called heat-death *(Wärmetod)* being predicted from the second law. The problem essentially was: Why was it that the degradatioin of energy had not yet reached its maximum? (We should say: Why had the entropy not yet reached a maximum?) Nernst, however, never put itthat way; he scrupulously avoided the term “entropy,” although, of course not its mathematical equivalent, namely, the capacity factor for isothermally unavailable energy, dQ_{rev}/T. In an attempt to explain away the *Wärmetod* of the universe, Nernst explored various hypotheses. He argued that cosmological questioins about the begining and the end of the universe were scientifically meaningless. Bypostulating fluctutations in the zero-point energy in space, or in the ether, as he preferred to put it, he reasoned that a steady-state theory might find scientific support in terms of the balance between energy degradation and energy creation as seen in the appearance of new stars and novae, and in the stages of stellar classificatioins that range fromnew to steady-state systems.As a source of energy for these new creations in the universeNernst postulated what he called the null point energy of the ether *(die Nullpunktsenergie des Lichtäthers)*

Nernst had talked about such matters as early as 1912, and in 1921 he had written a small volume on the subject, *Das Weltgebäude im Lichte der neueren Forschung* He continued to explore related ideas in a number of papers on chemical astrophysics (1928), the specific heat of gases at stellar temperatures and pressures (1929), the physics of stellar evolution (1935), and the interstellar radiation temperature (1938). He endeavored–somewhat naively, it appears in retrospect- to provide a thermodynamic synthesis of the observed stellar sequence, the red shift, and so on; but his ideas on a steady-state universe and nuclear processes as the source of stellar energy were later seen to be not completely outlandish.

In all of his work Nernst displayed a cagey, dubious attitude toward the long-range value of abstract, theoretical premises. Committed to “hypotheses” and “theorems” that could be shown to be fruitful in leading to new discoveries, he exhibited little concern for the search–Einstein or Planck fashion-for answers to broad and general philosophical questions. For example, he classed Einstein’s theory of Brownian motion above that of relativity because of the former’s real physical content. Nernst’s dominant inclination was toward experimental investigatioins and phenomena that could be visualized. Interested in reliable experimental results, he was never fussy about how clumsy or makeshift his apparatus looked. Sometimes he built his own equipment (tranformers, pressure and temperature regulators, measuring devices, and even a microbalance); and almost of all the apparatus in Nernst’s laboratory was constructed on the premises. The instruments were made as small as possible and were assembled with the minimum waste of materials. In the use of materials or energy Nernst was inordinately frugal, and he looked with contempt upon the misuse of natural resources.

Pure and applied research were identical for Nernst, because theoretical questions were formulated within the context of ongoing experimental investigations. Upon examining his papers, one gets the impression that the areas of pure scientific activity that Nernstinvestigated grew out of his intense preoccupation with challenging experimental and instrumental situations. It also is singularly evident that Nernst had a deep and sincere interest in the technical applications of physics and chemistry. He was passionately enthusiastic about motor cars, tried out one after another when they came on the market, and investigated various combustible fuels.

On Monte Generoso, Nernst constructed a device for the study of the conversion of atmospheric electricity into useable energy. His experimental investigations(1899-1900) on the electrolytic conduction of solids at very high temperatures were put to use in 1904 in the Nernst lamp, which replaced the older, more fragile, and less efficient carbon filaments by rare-earth oxide wires. His lamp netted him considerable income (he sold the patents outright),but it was relatively short-lived because of the introduction of the tungsten lamp. Several decades later, theoretical interest in similar studies was reinstated in connection with the investigation of the mechanism of ionic conduction in semiconductors.

Nernst’s irrepressible, zealous openness to scientific discoveries and their technological application is visible in the way that he followed the new studies of radiatioin, quantum chemistry radioactivity, astrophysics, and cosmic rays. On the whole his flair for the fundamentally novel was sound; his suggestions were occasionally based on inadequate comprehension of the situation or overly ambitious speculations. For example, in 1922 Nernst examined the scientifically plausible but musically shallow idea that the concert grand might be replaced with a small piano that was magnetically controlled and furnished with loudspeaker amplificatioin.Nernst called his instrument the *Neo-Bechstein flügel*. The balance of harmonics for such extrascientific activities was *physique amusante*

The story of how Nernst exercised his entrepreneurial talents within the Berlin scientific community of Weimar Germany has been depicted recently with sympathetic deference,vivdness of detail, and personal involvement, by Kurt Mendelsohn. Nernst played the conspicuous role of organizer for the first Solvay Conference of 1911. He was the effective promoter in the creation of a post for Einstein at the Berlin Academy of Sciences. He was the Prime mover for the establishment of the Kaiser Wilhelm Institut. He was also a founder of the Deutsche elektrochemische Gesellschaft (later called Deutsche Bunsengesellschaft) and for several years edited its*Zeitschriftfür Elektrochemie.*with J. A. W. Borchers, beginning in 1895, Nerst edited the *Jahrabuch für Elektrochemie*

In 1913 Planck and Nernst traveled to Zurich to entice Einstein, then thirty-four years of age, to join them in Berlin. Although his light-quantum theory had not yet found favor with them and the general theory of relativity was still in process of formulation, they were able to offer Einstein a position at the Royal Prussian Academy of Sciences, the directorship of research at the Kaiser Wilhelm Institut, the rank of professor, a special salary, and teaching at his option. The normal requirement for renewal of his German nationality was waived. Einstein accepted the offer.

Some of Nernst’s closest colleagues in Berlin, notably Bodenstein, Simon, and Einstein, have told us something about his nonconformist personality. He was short, bald, energetic, impulsive, and candid; his external life was a scenario of innocence, simple charm, and sincerity. It is evident that his personal demeanor did not fit the traditional model of the German professor and *Herr Geheimrat* His life was quite devoid of academic pedantry, pretense, and deception. In 1942 Einstein commented that Nerst was a personality so original that he had never met anyone who resembled him in any essential way; “So long as his egocentric weakness did not enter the picture, he exhibited an objectivity rarely found, an infalliable sense for the essential and a genuine passion for knowledge of the deep interrelations of nature”

Bodenstein, who was closely associated with Nernst and succeeded him in the chair of physical chemistry, remarked in his 1942 address to the German Chemical Society in Berlin that the huge measure of success that Nernst enjoyed in so many areas of science was due to a remarkably clear, prosaic, and mobile mind unhampered by any fear of being wrong. Bodenstein said, “Nernst possessed in a quite extraordinary way a feeling for what is scientifically possible. As a hunter he would forgive me for saying that he had an unusually fine nose for the true and, besides, a blissful phantasy that allowed him to represent graphically difficult matters to himself and to us”.Bodenstein made a special point of Nernst’s predilection for fertile and lively phantasy and inventions *(geistvolle Apercus)* thrown out freely and spontaneously: “Sometimes [they were] explored more closely, sometimes conducive to further formulation, sometimes lighting up like meteors, and soon thereafter falling into oblivion”. His phantasies were easy-come-easy-go, unless they turned out to exhibit great promise.

Self-confident, highly disciplined, and exacting with his students and assistants, Nernst was nevertheless generous and totally impartial, shared ideas freely, and graciously offered help to those able to appreciate his train of thought. When a student disappointed Nernst in regard to some matter, he would say,“For God’s sake don’t tell anyone that you studied under me!” The impressive list of his students included outstanding personalities such as Bodenstein, Bonhoeffer, Volmer, Eucken, Langmuir, Bjerrum, Warburg, Lindemann (later, Chuirchill’s scientific adviser), and Simon, who, driven from Germany in 1933, became director of the Clarendon Laboratory at Oxford. In 1895 an English student, Miss Moltbly, was the first woman to receive the doctorate in experimental physics in Germany, working under Nernst; and Lotte Pusch, who married Volmer, was Nernst’s lecture assistant in Berlin.

Nernst’s dealings with others frequently were punctuated with a sarcastic sense of humour and spontaneous with remarks or innuendo concocted to suit the occasion. Behind this facade lay hidden one of the most gifted, versatile, and penetrating minds of the times. If not exactly devoted to him, those with whom he came in contact invariably admired him. To judge from the accounts of his many students, the anecdotes told by and about his funny little man, although undoubtedly apocryphal, seem to be legion. Not notably brilliant as a day-by-day lecturer Nernst was, nevertheless, long remembered by his students, especially for the personal anecdotes and jokes that he introduced into the classroom and for the salty enthusiasm that he radiated from the podium. This was conspicuous whenever he had a chance to speak about the most recent scientific achievements –and especially his own. In fact, he would then so intimately relate the new scientific developments to his own researches and interpretatioins that students often came away supposing that he and his assistants had worked out most physical chemistry. In examinations Nernst was easy on the students; his motto was “Das Wissen ist der Tod der Forschung”

Fond of travel, Nernst visited both North and South America. He was keen on outdoor life, especially on hunting, and took great delight in the role of country gentleman by inviting his guests to a hare-shooting spree at his country estate in Zibelle. He was an enthusiastic carp farmer, arguing on the basis of second-law considerations that fish were a better investment from an energy standpoint than warm-blooded livestock. An avid automobile fan, he owned one of the first automobiles in Göttingen at the end of the nineteenth century and published several investigations on the maximum efficiency of the internal combustion engine (1905-1913). The story has often been told that a special nitrous oxide injector had been installed in his fuel combustion system so that he could call upon this auxiliary energy thrust to go uphill with ease.

Nernst had a deep love for his country, but he was never narrow-mindedly nationalistic. Both of his sons were killed during World War I, and he himself offered his own services to the military when called upon. He was, however, so singularly free from prejudice and so saturated with practical common sense that it was out of the question for him to cover up his almost childlike good nature or to act in an expedient way to protect himself against potential dangers. In August 1920 Nernst joined Arnold Sommerfeld and Otto Rubens to send a public letter to all the major Berlin newspapers in order to protest the position of anti-Semitic organizations that had sought to identify the theory of relativity with Dada. These organizations had even singled out its originator, Einstein, as a plagiarist. After 1933 Nernst did not get along at all with the Nazis and accordingly was no longer welcome in official circles. Like Laue, Planck, Haber, and Von Mises, Nernst refused to cooperate with the anti-Einstein forces in the academy in Berlin in April 1933, or with the subsequent fascist-inspired patronization of *Deutsche Physik* He warned the faculty at the University of Berlin that the pro-Nazi position of such scientists as Philip Lenard and Johannes Stark would jeopardize the cooperative efforts and free exchange of information among physicists in Berlin.

Two of Nernst’s daughters had married men of “non-Aryan” origin and were unable to be with the family during difficult days. Nernst died of a heart attack in 1941 at his estate in Zibelle, now on the German-Polish border about ninety miles southeast of Berlin. Little information about his last years was available in those circles that once had claimed him in their front ranks.

## BIBLIOGRAPHY

I. Original Works. The most complete list of Nernst’s publications is in Lord Cherwell [F. A. Lindemann] and F.Simon, “Walther Nernst, 1864-1941,” in *Obituary Notices of Fellows of the Royal Society of London***4** (1942-1944, 101-112. Works published before 1900 include “Ueber das Auftreten elektromotorischer Kräfte an Metallplatten, welche von einem Wärmestrome durchflossen werden and sich im magnetischen Felde befinden,” in *Annalen der physik***29** (1886),343-347, written with A. von Ettingshausen; “Ueber die elektromotorischen Krafte, welche durch den Magnetismus in von einem Wärmestrome durchflossenen Metallplatten geweckt werden” *ibid* 31 (1887), 760-789, his inaugural diss. at Würzburz; “zur Kinetik der in Lösung befindlichen Körper 1.Theorie der Diffusioin,” *in Zeitschrift für physikalische Chemie* 2(1888), 613-637; “Ueber freie lonen,”:*ibid* 3(1889), 120-130, written with W. Ostwald; “Die elektromotorische Wirksamkeit der Ionen,” *ibid* 4(1889) 129-181, his *Habilitationsschrift*at Leipzig; “Ueber die Verteilung eines Stoffes zwischen zwei Lösungsmitteln,” in *Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen* (1890), 401-416;“Ueber das Henry sche Gesetz,” *ibid* (1891), 1-14; “Verteilung eines Stoffes zwischen zwei Lösungsmitteln und Dampfraum,” in*Zeitschrift für physikalische Chemie,* 8 (1891), 110-139: *Theoretische Chemie vom Standpunkte der Avogadroschen Regel und der Thermodynamik* (Göttingen, 1893), originally written as an introduction to O. Dammer, *Handbuch der anorganischen Chemie* (Stuttgart, 1892), which by 1926 had gone through 15 eds.,including translations into English; “Ueber die mitder Vermischung konzentrierter Lösungen verbundene Aenderung der freien Energie,” *in Annalen der physik* 53(1894), 57-68; “Methode zur Bestimmung von Dielektrizitätskonstanten,” in *Zeitschrift für physikalische Chemie***14** (1894), 622–663; “Ueber den Gefrierpunkt verdünnter Lösungen,” *ibid* 15(1894), 681-693, written with R.Abbegg *Einführung in die mathematische Behandlung der Naturwissenschaften-Kurzgefasstes Lehrbuch der Differential-und Integralrechnung mit besonderer Berücksichtigung der Chemie*(Munich-Leipzig, 1895; 11th ed..,1931), written with A.Schönflies *Die Ziele der physikalischen Chemie, Festrede 1896 zur Einweihung zu Göttingen* (Göottingen, 1896); “Ueber die Verwendung schneller elektrischer Schwingungen in der Brückenkombination,” *in Annalen der physik* 60 (1897), 600-624, “Zur Theorie der elektrischen Reizung” in *Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen* (1889), 194-198; and “Ueber die elektrolytische Leitung fester Körper bei sehr hohen Temperaturen,” in *Zeitschrift für Elektro chemie***6** (1899), 41-43

Between 1900 and the end of World War I, Nernst published “Ueber die Gaspolarisation im Bleiakkumulator,” *ibid.,***6** (1900), 549-550, written with P. Dolezalek; “Ueber Elektrodenpotentiale,” *ibid.,* 7 (1900), 253-255; “Ueber die Leitfähigkeit fester Mischungen bei hohen Temperaturen,” in *Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen* (1900).,328-330 written with H. Reynolds; and “Ueber die Bedeutung elektrischer Methoden und Theorien für die Chemie,” in *Verhandlungen der Gesellschaft deutscher Naturforscher und Ärzte,***1** (1901), 83-99. See also “Ueber elektrolytische Erscheinungen an der Grenzfläche zweier Löosungsmittel,” in *Nachrichten von der Gesellschaft**der Wissenchaften zu Göttingen* (1901), 54-61, written with E. H. Riesenfeld, also in *Annalen der Physik* 8 (1902), 600–608; “Ueber die Wanderung galvanischer Polarisation durch Platin-und Palladium platten,” in *Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen* (1902), 146-159, written with A. Lessing; “Ueber Molekulargewichtsbestimmungen beisehr hohen Temperaturen,” *ibid* (1903), 75-82 “Bildung von Stickoxyd bei hohen Temperaturen” *ibid*(1904), 261-276; “Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen,” in *Zeitschrifit für Elektrochemie* 10 (1904), 664-668, written with J. O. W. Barratt; “physikalisch- chemie **47** (1904), 52-55; “Betrachtungen über den Verbrennungsprozess in den Gasmotoren,” *Zeitschrift des Vereins deutscher Ingenieure,* 49(1905), 1426-1431; “Ueber die Berechnung chemischer Glechgewichte aus thermischen Messungen,” in *Nachrichen von der Gesellschaft der Wissenschaften zu Göttingen* (1906), 1-40, the classic enunciation of the third law of thermodynamics; “Ueber die Bildung von Stickoxyd bei hohen Temperaturen,” in *Zeitschrift für anorganische Chemie***49** (1906), 213-228; “Ueber das Ammoniakgleichgewicht,” in*Zeitschrift für Elektro chemie* 13 (1907), 521-524 written with F.Jost “Die Entwicklung der allgemeinen and physikalischen Chemie in den letzten 40 Jahren,” in *Berichte der Deutschen chemischen Gesellschaft***40** (1907),4617-4626, an address in celebration of the fortieth anniversarty of the German Chemical Society in Berlin, 11 Nov. 1907, also trans. in *Annual Report of the Board of Regents of the Smithsonian Institution for 1908* (1909), 245-253; *Experimental and Theoretical Applications of Thermodynamics to Chemistry* (New York-London, 1907), Silliman lectures at Yale University delivered in 1906; “Zur Theorie des elektrischen Reizes” in *pflüger’s Archiv für die gesamte Physiologie de Menschen und der Tiere* 122 (1908), 275-314; “Zur Theorie der galvanischen Polarisation. Anwendungen zur Berechnung der Reizwirkungen elektrischer Ströme,”in *Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin* (1908),3-13; “Zur Theorie der eletrischen Nervenreizung,” in *Zeitschrift für Eletrochemie***14** (1908),545-549; “Untersuchungen über die spezifische Wärme bei tiefen Temperaturen, I-III, and V-VIII,” in *Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin* (1910), 247-261, 262-282; (1911).306-315, 494-501; (1912) 1160-1171, 1172-1176;(1914), 355-370, written with F.Koref F. A. Linmdemann, and F.Schwers; “Ueber neuere Probleme der Wärmethorie,” *ibid* (1911), 65-90; “Der Energiequanten fester Stoffe,” in *Annalen der Physik* 4th ser., 36 (1911)395-437; “Zur Thorie der spezifischen Wärme and über die Anwendung der Lehre von den Energiequanten auf physikalishch-chemische Fragen übnerhaupt,” *Zeitschrift für Elerochemie***17** (1911). 265-275; “Ueber einen Apparat zur Verflussigung von Wasserstoff,” *ibid* 17 (1911),735-737; “Spezifische Wärme und Quantentheorie,” *ibid.,* 817-827, written with F.A. Lindemann; “Application de la théorie des quanta à divers problèmes physico-chimiques,” in P.Lanagevin and de Broglie, eds., *La théorie du rayonnement et les quanta, rapports et discussions de la réunion tenue à Bruxelles, du 30 Octobre au 3 Novembre 1911 sous les auspices de M.E. Solvay* (Paris.1912); “Thermodynamik und spezifische Wärme,” in *Sitzungsberichte der Preussischen Akademie der Wissenchaften zu Berlin* (1912),134-140; “Zur Thermodynamik kondensierter Systeme,” *ibid* (1913), 971-985; “Ueber den maximalen Nutzeffedckt von Verbrennungsmotoren,” in *Zeitschrift für Elektrochemie* 19 (1913),669-702; “Ueber die Anwendung des neuen Wärmesatzes auf Gase,” *ibid*20 (1914), 357-360; “Zur Anwendung des Einsteinschen photochemischen Aequivalentgesetzes,” *ibid*24 (1918), 335-336; and *Die theoretischen und experimentellen Grundlagen des neuen Wärmesatzes* (Halle-Salle, 1918), of which the English eds. of 1918 and 1926 were entitled *The New Heat Theorem, Its Foundations in Theory and Experiment*

Works published during the Weimar Republic include “Zur Theorie photochemischer Vorgänge,” in *Physikalische Zeitschrift***21** (1920), 602-605 written with W.Noddack; *Das Weltgebäude im Lichte der neueren For schung* (Berlin,1921); “Zur Theorie photochemischer Vorgänge,” in *Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin* (1923).110-115, written with W.Noddack; and “physico-chemical Consideratioins in Astrophysics,” in *Journal of the Franklin Institute***206** (1928), 135-142.

Later writings are “Physikalische Betrachtungen zur Entwicklungs theorie der Sterne,” in *Zeitschrift für Physik***97** (1935), 511-534; “Einige weitere Anwendungen der Physik auf die Sternentwicklung,” in *Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin* (1935), 473-479; and “Die Strahlungstemperatur des Universums,” in *Annalen der Physik* 5th ser., **32** (1938),44-48.

II. Secondary Literature. On Nernst and his work, see Kurt Bennewitz and Franz Simon , “Zur Frage der Nullpunktsenergie,” in *Zeitschrift für Physik***16** (1923), 183-199; Max Bodenstein, “Walther Nernst, 25.6.1864-18.11.1941,” in *Berichte der Deutschen chemischen Gesellschaft* 75(1942),79-104; K.F. Bonhoeffer ed., “Dem Andenken an Walther Nernst,” in *Naturwissenschaftern***31** (1943),257-275,305-322,397-415, which contains articles on current topics related to Nernst’s work by J.J. Hermans, Erich Lange, L.Ebert, Carl Wagner, K. Bennewitz, K.F. Bonhoefferm G. Damkohler, H. von Wartenberg, Rudolf Edse, A. Eucken, K. Clusius, W. Schottky, G. Weitzel,. P. Harteck, and J. Eggert; Max Born andTheodore von Karman, “Ueber Schwingungen im Raumgitter,” *Physikalische Zeiutschrifit***13** (1912),297-309; Peter Debye., “Zur Theorie der spezifischen Wärmen,” *Annalen der physik***39** (1912), 789-839; and the following literature by John Eggert: “Das Nernstsche Wärmetheorem und Seine Bewährung durch Affnitätsmessungen,” in *Naturwissensfchaften***35** (1915),452–456; “Einführung in die Grundlagen des Nernstschen Wärmetheorems,” *ibid.,* 7 (1919) 883-889,917-921; and “Walther Nernst. Zur hundertsten Wiederkehr seines Geburtstages am 25 Juni 1964,” in *Angewandte chemie***76** (1964), 445-455.

See also the following works by Albert Einstein; “Die Planck’sche Theorie der Strahlung und die Theorie der spezifischen Wärme,” in *Annalen der physik***22** (1907), 180-190, 800; “Thermodynamische Begründung des photochemischen Aequivalentgesetzes,” *ibid.,***37** (1912), 832-838;38(1912),881-884; “Letat actuel du problème des chaleurs spéfiques,” in P.Langevin and de Broglie, eds.,*La théorie du rayonnemet et les quanta*… (Paris,1912), 407-449; “The Work and Personality of Walther Nernst,” in *Scientific Monthly***54** (1942), 195-196; and *Albert Einstein-Michele Besso Correspondence, 1903-1955* (Paris,1972),19-21.

Other literature includes Arnold Eucken, “Anhang Die Entwicklung der Quantentheorie vom Herbst 1911 bis Sommer 1913,” in *Die Theorie der Strahlung und der Quanten (Abhandlungen der Deutschen Bunsen-Gesellschaft für angewandte physikalische Chemie)*7 (1914),371-405; R.H. Fowler and T.E. Sterne, “Statistical Mechanics With Particular Reference to the Vapor Pressures and Entropies of Crystals,” in *Review of Modern physics***4** (1932),635-722; P. Günther “Die kosmologischen Betrachtungen von Nernst,” in *Zeitschrift für angewandte Chemie und Zentralblatt für technische Chemie***37** (1924), 454-457; Werner Haberditzl, “Walther Nernst und die Traditionen der physikalischen Chemie an der Berliner Universität,” in *Forschen and Wirken, Festschrift zur 150-Jahr-Feieer der Humboldt-Universität zu Berlin*I,(Berlin, 1960), 401-416; Paul Harteck, “Physical Chemists in Berlin, 1919-1933;” in *Journal of Chemical Education*37 (1960),462-466; Martin J.Klein, “Einstein, specifric Heats, and the Early Quantum Theory,”in *Science,***148** (1965),173-180; Hans-Günthehr Körber,ed.,*Aus dem wissenschaftlichen Briefuechsel Withelm Ostwalds.*2 vols,(Berlin,1961,1969);N.Kurti, “Franz Eugen Simon,1893-1956,” in *Bioigraphical Memoirs of Fellows of the Royal Society***4** (1958),225-256; Henri Le Châtelier. “Recherches expérimentales et théoriques sur les equuilibres chimiques,” in *Annales des mines et des carburants* 13(1888),157-382; G. N. Lewis, “The Development and Application of a General Equatioin for Free Energy and Physio-Chemicalk Equilibrium,” in *Proceedings of the American Academy of Arts and Sciences***35** (1899),3-38;G.N.Lewis and Merie Randall,*Thermodynamics and the Free Energyt of Chemical Substances* (New York,1923),435-454; Kurt Mendelsohn,*The World of Walther Nernst. The Rise and Fall of German Science 1864-1941* (Pittsburgh,1973); *Nobel Lectures in Chemistry,1901-1921* (Amsterdam,1966),347-364; James R. Partington, “The Nernst Memorial Lecture,” in*Journal of the Chemical Society***3** (1953), 2853-2872; Max Planck, “La Loi du rayonnement nooir et l’hypothèse des quantités élémentaires d’action,” in P.Langevin and de Broglie, eds.,*La théorie du rayonnemnet et les quanta*… (Paris 1912), 93-132; “Ueber neuere thermodynamische Theorien (Nernstsches Wärmetheorem and Quanten–Hyupothese)” in *Berichte der Deuschen chemischen Geselklschaft***45** (1912), 5-23; and T.W.Richards, “Die Bedeutung der Änderung des Atomvolums,” in *Zeitschrift für Physikalische Chemie***42** (1902),129-154.

Other works on Nernst and his work are E. H. Riesenfeld, “Walther Nernst zu seinem sechzigsten Geburstag,”in *Zeitschrift für angewandte Chemie und Zentralblatt für technische Chemie***37** (1924), 437-439; Otto Sackur, “Die Bedeutunbg des elementaren Wirkungsquantumns für die Gastheoirie and die Berechnung dert chemischen Konstanten,” *Festschrift W.Nernst* (Halle-Salle,1912),405-423; and the following works by Franz Simon: “Die Bestimmung derfreien Energuie,” in *Geiger-Scheel Hanbuch der Physik***10** (1926),350-404; “Zur Frage der Entropie amorpher Substanzen,” in *Zeitschrifit für physik***38** (1926), 227-336, written with F. Lange; “Zum Prinzip von der Unerreichbarkeit dees absoluten Nullpunktes,” in *Zeitschrift für Physik***41** (1927), 806-809; “Fünfuyndzwanzig Jahre Nernstecher Wärmesatz,” in *Ergebnisse der exakten Naturwissenschaften***9** (1930),222-274; “Anbei Heliumtemperaturen,” in *Naturwissenschaften***18** (1930),34-35, written with Kurt Mendelsohgn and M. Ruhemann; “On the Third Law of Thermodynamics,” in *physics***4** (1937), 1089-1096; and “The Third Law of Thermodytnamics. An Historical Survety,” in *Yearbook of the physical Society* (London, 1956),1-22. See also Arnold Soimmerfeld, “Das Plancksche Wirkungsquantumn and seune allgemeine Bedeutung für die Moleküphysik,” in *Physikalische Zeitschrift,***12** (1911), 1057-1068; Otto Stern, “Zur kinetischen Theorie des Dampfdrucks einatomiger Stoffe and über die Entropie-Konstante einatomiger Gase,” *ibid.,***14** (1913), 629-632; and H.Tetrode, “Die chemische Koinstante der Gase und das elementare Wirkungsquantum,” in*Annalen der Physik***38** (1912), 434-442; **39** (1912),255-256.

Erwin N. Hiebert