The German physicist Rudolf Julius Emanuel Clausius (1822-1888) was one of the chief architects of thermodynamics and the kinetic theory of gases.

Born on Jan. 2, 1822, in Köslin, Pomerania, R. J. E. Clausius was the sixth son of the 18 children of the Reverend C. E. G. Clausius, a Lutheran pastor and councilor of the Royal Government School Board in Köslin. Young Clausius received much of his primary and secondary education in the private school which his father established in Uckermünde. After graduating from the gymnasium in Stettin, Clausius enrolled at the University of Berlin, and in 1844 he obtained his teacher's certificate.

During the next 6 years Clausius taught physics at the Friedrich Werder Gymnasium in Berlin. He received his doctoral degree in 1848 from the University of Halle with a dissertation which gave for the first time the explanation of the blue sky and red sunset in terms of the selective reflection of various wavelengths of light by particles present in the atmosphere. In 1850 Clausius became professor of physics at the Royal Artillery and Engineering School in Berlin and also obtained the rank of privat-dozent at the University of Berlin.

Theories of Heat

Clausius presented his paper "On the Motive Power of Heat and on the Laws Which Can Be Deduced from It for the Theory of Heat" in 1850. Its significance can best be gauged by the comments of James Clerk Maxwell, who years later wrote that Clausius "first stated the principle of Carnot in a manner consistent with the true theory of heat." The "true theory" was the consideration of heat as a mechanical process.

Sadi Carnot's explanation of his very successful theory of the efficiency of steam engines seemed, however, to contradict the mechanical theory. In Carnot's words, "no heat was lost" when a steam engine produced work by going through its cycles. Clausius insisted that the "new theory" could only be a mechanical one. More importantly, he showed that it was quite consistent with the mechanical theory to assume that when work was done by heat one part of the heat was "lost," or rather was transformed into work. This part of the heat and the other part which was rejected into the cold reservoir of the engine stood, in Clausius's words, in a "certain definite relation to the quantity of work produced."

Two subsequent papers published in 1851 by Clausius clarified merely some details of his first memoir, but in 1854 he confronted once more the fundamentals. What became known as his fourth memoir carried the title "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat." In it Clausius proposed to make Carnot's theorem a particular form of the general proposition, "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time." With a penetrating analysis, Clausius showed that the Carnot cycle corresponded to the integral (dQ/T), the value of which was zero for a reversible, or ideal, process. For an irreversible, or real, process the corresponding value could only be positive.

Herein lay a proposition of utmost importance, but its full meaning was not spelled out by Clausius until about 10 years later. Meanwhile, he moved to Zurich to serve as professor of physics at the Swiss Federal Technical Institute. Two years later he also assumed professorship at the University of Zurich. In Zurich he married Adelheid Rimpau; they had six children.

Kinetic Theory of Gases

The scientific fruits of Clausius's first years in Zurich related to the kinetic theory of gases. Clausius achieved his task in two papers: "On the Kind of Motion Which We Call Warmth" (1857) and "On the Average Length of Paths Which Are Traversed by Single Molecules in the Molecular Motion of Gaseous Bodies" (1858). From the assumption that molecules move in a straight path Clausius calculated the average velocity of hydrogen molecules at normal temperature and pressure. Because the value, about 2,000 meters per second, seemed to contradict the low rate of gaseous diffusion, Clausius offered as explanation the important notion of the free mean path of molecules.

A few years later, in 1862, Clausius published his paper "On the Thermal Conductivity of Gaseous Bodies," in which he successfully derived from theoretical considerations the experimentally known data in question. He deserved indeed the praises heaped on him by Maxwell, who referred to Clausius as the first who "gave us precise ideas about the motion of agitation of molecules." Maxwell also described the adoption of mechanical principles to molecular studies as being "to a great extent the work of Prof. Clausius."

The year 1862 also saw the return of Clausius's full attention to thermodynamics. The results spoke for themselves. In the paper known as his sixth memoir, "On the Application of the Theorem of the Equivalence of Transformations to Interior Work," he concluded that it was "impossible practically to arrive at the absolute zero of temperature by any alteration of the condition of a body."

Concept of Entropy

On April 24, 1865, Clausius read before the Philosophical Society of Zurich his best-remembered paper, or ninth memoir, "On Several Convenient Forms of the Fundamental Equations of the Mechanical Theory of Heat." In it the word "entropy" was used for the first time. The word, as Clausius noted, was coined by him from the Greek toe, or transformation: "I have intentionally formed the word entropy so as to be as similar as possible to the word energy; for the two magnitudes to be denoted by these words are so nearly allied in their physical meanings, that a certain similarity in designation appears to be desirable."

In nontechnical parlance, entropy stands for the inevitable transformation of some part of the energy in any real physical process into a form which is no longer utilizable. Clausius disclosed the far-reaching, cosmic consequences of his analysis of the foundations of thermodynamics: "If for the entire universe we conceive the same magnitude to be determined, consistently and with due regard to all circumstances, which for a single body I have called entropy, and if at the same time we introduce the other and simpler conception of energy, we may express in the following manner the fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat. (1) The energy of the universe is constant. (2) The entropy of the universe tends to a maximum."

In 1869 Clausius accepted an invitation to become professor of physics at the University of Bonn after having spent 2 years in the same capacity at the University of Würzburg. The University of Bonn represented the last phase of Clausius's academic career. There he wrote in 1870 his last important paper on thermodynamics, which contained the notion of virial. In 1876 he published a second, considerably enlarged and revised version of what was mainly a collection of his memoirs which had been printed in 1864 under the title Abhandlungen über die mechanische Wärmetheorie. The new edition, entitled Die mechanische Wärmetheorie (The Mechanical Theory of Heat), was for several decades the standard for textbooks on thermodynamics. The second part of the book deals with the analysis of electrical phenomena on the basis of mechanical principles, a topic which dominated Clausius's attention in Bonn.

Clausius's wife died in 1875. Eleven years later he married Sophie Sack, by whom he had one son. In the summer of 1886 he began to show symptoms of acute anemia. Nevertheless he carried on with the work of seeing to print the third edition of his Wärmetheorie, and he even held examinations from his sickbed. He was the embodiment of sincerity and conscientiousness to the end, which came on Aug. 24, 1888.

Further Reading

• In French, R. Clausius, sa vie, ses travaux et leur portée métaphysique (1890), is a booklet by F. Folie, a close friend of the Clausius family and director of the Brussels Observatory. The major documents representing the emergence of thermodynamics as a full-fledged branch of physics are collected in W. F. Magie, ed., The Second Law of Thermodynamics: Memoirs by Carnot, Clausius and Thomson (1899). A good critical account of the steps leading to the full formulation of the second law of thermodynamics is given in Frederick O. Koenig's essay, "On the History of Science and of the Second Law of Thermodynamics," in Herbert McLean Evans, ed., Men and Moments in the History of Science (1959).