Reflections on the Motive Power of Heat/Chapter 1

 

 

I.

THE WORK OF SADI CARNOT.

By the Editor.

Nicolas-Leonard-Sadi Carnot was, perhaps, the greatest genius, in the department of physical science at least, that this century has produced. By this I mean that he possessed in highest degree that combination of the imaginative faculty with intellectual acuteness, great logical power and capacity for learning, classifying and organizing in their proper relations, all the facts, phenomena, and laws of natural science which distinguishes the real genius from other men and even from the simply talented man. Only now and then, in the centuries, does such a genius come into view. Euclid was such in mathematics; Newton was such in mechanics; Bacon and Compte were such in logic and philosophy; Lavoisier and Davy were such in chemistry; and Fourier, Thomson, well, and Clausius were such in mathematical physics. Among engineers, we have the examples of Watt as inventor and philosopher, Rankine as his mathematical complement, developing the theory of that art of which Watt illustrated the practical side; we have Hirn as engineer-experimentalist, and philosopher, as well; Corliss as inventor and constructor; and a dozen creators of the machinery of the textile manufactures, in which, in the adjustment of cam-work, the highest genius of the mechanic appears.

But Carnot exhibited that most marked characteristic of real genius, the power of applying such qualities as I have just enumerated to great purposes and with great result while still a youth. Genius is not dependent, as is talent, upon the ripening and the growth of years for its prescience; it is ready at the earliest maturity, and sometimes earlier, to exhibit its marvellous works; as, for example, note Hamilton the mathematician and Mill the logician; the one becoming master of a dozen languages when hardly more than as many years of age, reading Newton's Principia at sixteen and conceiving that wonderful system, quaternions, at eighteen; the other competent to begin the study of Greek at three, learning Latin at seven and reading Plato before he was eight. Carnot had done his grandest work of the century in his province of thought, and had passed into the Unseen, at thirty-six; his one little volume, which has made him immortal, was written when he was but twenty-three or twenty-four. It is unnecessary, here, to enter into the particulars of his life; that has been given us in ample detail in the admirable sketch by his brother which is here republished. It will be quite sufficient to indicate, in a few words, what were the conditions amid which he lived and the relation of his work to that great science of which it was the first exposition.

At the time of Carnot, the opinion of the scientific world was divided, as it had been for centuries, on the question of the true nature of heat and light, and as it still is, to a certain extent, regarding electricity. On the one hand it was held by the best-known physicists that heat is a substance which pervades all bodies in greater or less amount, and that heating and cooling are simply the absorption and the rejection of this “imponderable substance” by the body affected; while, on the other hand, it was asserted by a small but increasing number that heat is a “mode of motion,” a form of energy, not only imponderable, but actually immaterial; a quality of bodies, not a substance, and that it is identical, in its nature, with other forms of recognizable energy, as, for example, mechanical energy. A quarter of a century before Carnot wrote, the experiments of Rumford and of Davy had been crucial in the settlement of the question and in the proof of the correctness of the second of the two opposing parties; but their work had not become so generally known or so fully accepted as to be acknowledged as representative of the right views of the subject. The prevalent opinion, following Newton, was favorable to the first hypothesis; and it was in deference to this opinion that Carnot based his work on an inaccurate hypothesis; though, fortunately, the fact did not seriously militate against its value or his credit and fame.

“With true philosophical caution, he avoids committing himself to this hypothesis; how work is produced from heat.”^[1]

The results of Carnot's reasoning are, fortunately, mainly independent of any hypothesis as to the nature of heat or the method or mechanism of development and transfer or transformation of its energy. Carnot was in error in assuming no loss of heat in a completed cycle and in thus ignoring the permanent transformation of a definite proportion into mechanical energy; but his proposition that efficiency increases with increase of temperature-range is still correct; as is his assertion of its independence of the nature of the working substance.

Carnot's “Réflexions sur la Puissance Motrice du Feu,” published in 1824, escaped notice at the time, was only now and then slightly referred to later, until Clapeyron seized upon its salient ideas and illustrated them by the use of the Watt diagram of energy, and might, perhaps, have still remained unknown to the world except for the fact that Sir William Thomson, that greatest of modern mathematical physicists, fortunately, when still a youth and at the commencement of his own great work, discovered it, revealed its extraordinary merit, and, readjusting Carnot's principles in accordance with the modern views of heat-energy, gave it the place that it is so well entitled to in the list of the era-making books of the age. But it still remained inaccessible to all who could not find the original paper until, only a few years since, it was reprinted by Gauthier-Villars, the great publishing house of Paris, accompanied by a biographical sketch by the younger brother, which it has been thought wise to reproduce with the translation of Carnot's book. In making the translation, also, this later text has been followed; and now, for the first time, so far as is known to the writer, the work of Carnot is made accessible to the reader in English.

The original manuscript of Carnot has been deposited by his brother in the archives of the French Academy of Sciences, and thus insured perpetual care. The work of Carnot includes not only the treatise which it is the principal object of this translation to give to our readers, but also a considerable amount of hitherto unpublished matter which has been printed by his brother, with the new edition of the book, as illustrative of the breadth and acuteness of the mind of the Founder of the Science of Thermodynamics.

These previously unpublished materials consist of memoranda relating to the specific heats of substances, their variations, and various other facts and data, and principles as well; some of which are now recognized as essential elements of the new science, even of its fundamental part. The book is particularly rich in what have been generally supposed to be the discoveries of later writers, and in enunciations of principles now recognized as those forming the base and the supporting framework of that latest of the sciences. As stated by Tait, in his history of Thermodynamics, the “two grand things” which Carnot originated and introduced were his idea of a “cycle” and the notion of its “reversibility,” when perfect. “Without this work of Carnot, the modern theory of energy, and especially that branch of it which is at present by far the most important in practice, the dynamical theory of heat, could not have attained its now enormous development.” These conceptions, original with our author, have been, in the hands of his successors, Clausius and other Continental writers, particularly, most fruitful of interesting and important results; and Clapeyron's happy thought of so employing the Watt diagram of energy as to render them easy of comprehension has proved a valuable aid in this direction.

The exact experimental data needed for numerical computations in application of Carnot's principles were inaccessible at the date of his writing; they were supplied, later, by Mayer, by Colding, by Joule, and by later investigators. Even the idea of equivalence, according to Hypolyte Carnot, was not originally familiar to the author of this remarkable work; but was gradually developed and defined as he progressed with his philosophy. It is sufficiently distinctly enunciated in his later writings. He then showed a familiarity with those notions which have been ascribed generally to Mayer and which made the latter famous, and with those ideas which are now usually attributed to Joule with similar result. He seems actually to have planned the very kind of research which Joule finally carried out. All these advanced views must, of course, have been developed by Carnot before 1832, the date of his illness and death, and ten or fifteen years earlier than they were made public by those who have since been commonly considered their discoverers. These until lately unpublished notes of Carnot contain equally well-constructed arguments in favor of the now accepted theory of heat as energy. While submitting to the authority of the greatest physicists of his time, and so far as to make their view the basis of his work, to a certain extent, he nevertheless adhered privately to the true idea. His idea of the equivalence of heat and other forms of energy was as distinct and exact as was his notion of the nature of that phenomenon. He states it with perfect accuracy.

In making his measures of heat-energy, he assumes as a unit a measure not now common, but one which may be easily and conveniently reduced to the now general system of measurement. He takes the amount of power required to exert an energy equal to that needed to raise one cubic meter of water through a height of one meter, as his unit; this is 1000 kilogrammeters, taken as his unit of motive power; while he says that this is the equivalent of 2.7 of his units of heat; which latter quantity would be destroyed in its production of this amount of power, or rather work. His unit of heat is thus seen to be 1000 ÷ 2.7, or 370 kilogrammeters. This is almost identical with the figure obtained by Mayer, more than ten years later, and from presumably the same approximate physical data, the best then available, in the absence of a Regnault to determine the exact values. Mayer obtained 365, a number which the later work of Regnault enabled us to prove to be 15 per cent, too low, a conclusion verified experimentally by the labors of Joule and his successors. Carnot was thus a discoverer of the equivalence of the units of heat and work, as well as the revealer of the principles which have come to be known by his name. Had he lived a little longer, there can be little doubt that he would have established the facts, as well as the principles, by convincing proof. His early death frustrated his designs, and deprived the world of one of its noblest intellects, just when it was beginning its marvellous career.

The following sentence from Carnot illustrates in brief his wonderful prescience; one can hardly believe it possible that it should have been written in the first quarter of the nineteenth century: “On peut donc poser en thèse générale que la puissance motrice est en quantité invariable dans la Nature; qu'elle n'est jamais, à proprement parler, ni produite, ni détruite. A la vérité, elle change de forme, c'est a dire qu'elle produit tantôt un genre de mouvement, tantôt un autre; mais elle n'est jamais anéantie.” It is this man who has probably inaugurated the development of the modern science of thermodynamics and the whole range of sciences dependent upon it, and who has thus made it possible to construct a science of the energetics of the universe, and to read the mysteries of every physical phenomenon of nature; it is this man who has done more than any contemporary in his field, and who thus displayed a more brilliant genius than any man of science of the nineteenth century: yet not even his name appears in the biographical dictionaries; and in the Encyclopædia Britannica it is only to be found incidentally in the article on Thermodynamics.

Throughout his little book, we find numerous proofs of his clearness of view and of the wonderful powers of mind possessed by him. He opens his treatise by asserting that “C'est à la chaleur que doivent être attribués les grands mouvements qui frappent nos regards sur la terre; c'est à elle que sont dues les agitations de l'atmosphère, l'ascension des nuages, la chute des pluies et ties autres météores, les courants d'eau qui sillonnent la surface du globe et dont l'homme est parvenue à employer pour son usage une faible partie; enfin les tremblements de terre, les éruptions volcaniques reconnaissent aussi pour cause la chaleur.”

Carnot was the first to declare that the maximum of work done by heat, in any given case of application of the heat-energy, is determined solely by the range of temperature through which it fell in the operation, and is entirely independent of the nature of the working substance chosen as the medium of transfer of energy and the vehicle of the heat. His assumption of the materiality of heat led, logically, to the conclusion that the same quantity of heat was finally stored in the refrigerator as had, initially, left the furnace, and that the effect produced was a consequence of a fall of temperature analogous to a fall of water; but, aside from this error—which he himself was evidently inclined to regard as such, his process and argument are perfectly correct.^[2]

Throughout his whole work are distributed condensed assertions of principles now well recognized and fully established, which indicate that he not only had anticipated later writers in their establishment, but that he fully understood their real importance in a theory of heat-energy and of heat-engines. In fact, he often italicizes them, placing them as independent paragraphs to more thoroughly impress the reader with their fundamental importance. Thus he says: “Partout où il existe une différence de température, il pent y avoir production de puissance motrice;” and again, this extraordinary anticipation of modern science: “le maximum de puissance résultant de l'emploi de la vapeur est aussi le maximum de puissance motrice réalisable par quelque moyen que ce soit.”

“La puissance motrice de la chaleur est indépendante des agents mis en œuvre pour la réaliser; sa quantité est fixée uniquement par les temperatures des corps entre lesquels se fait, en dernier résultat, le transport du calorique.”

“Lorsqu'un gaz passe, sans changer de température, d'un volume et d'une pression déterminés à une autre pression également déterminée, la quantité de calorique absorbée ou abandonnée est toujours la méme, quelle que soit la nature du gaz choisi comme sujet d'expérience.”

Perhaps as remarkable a discovery as any one of the preceding (and one which, like those, has been rediscovered and confirmed by later physicists; one which was the subject of dispute between Clausius, who proved its truth by the later methods which are now the source of his fame, and the physicists of his earlier days, who had obtained inaccurate measures of the specific heats of the gases;—values which were finally corrected by Regnault, thus proving Carnot and Clausius to be right—is thus stated by Carnot, and is italicized in his manuscript and book:

“La différence entre la chaleur spécifique sous pression constante et la chaleur spécifique sous volume constant est la même pour tous les gaz.”

He bases his conclusion upon the simplest of thermodynamic considerations. He says that the increase of volumes with the same differences of temperature are the same, according to Gay-Lussac and Dalton; and that, therefore, according to the laws of thermodynamics as he has demonstrated them, the heat absorbed with equal augmentations of volume being the same, the two specific heats are constant, and their difference as well. As will be seen on referring to the text, he bases upon this principle a determination of the specific heats of constant volume, taking as his values of the determined specific heats of constant pressure those of Delaroche and Bérard, making the constant difference 0.300, that of air at constant pressure being taken as the standard and as unity. The establishment of this point, in the face of the opposition, and apparently of the facts, of the best physicists of his time, was one of those circumstances which did so much to win for Clausius his great fame. How much greater credit, then, should be given Carnot, who not only anticipated the later physicists in this matter, but who must have enunciated his principle under far more serious discouragements and uncertainty!

It must be remembered, when reading Carnot, that all the “constants of nature” were, in his time, very inaccurately ascertained. It is only since the time of Regnault's grand work that it has been the rule that such determinations have been published only when very exactly determined. No change has been attempted in Carnot's figures, in any respect; as it would be far less satisfactory to read a paraphrased work, and the exact figures are now easily accessible to every one, and his computations may all be made, if desired, on the basis of modern data. Sir William Thomson has already performed this task in the paper appended.

Throughout the whole of this treatise, small as it is, we find distributed a singular number of these anticipations of modern thermodynamic principles. Studying the relation of heat-energy to work done, he concludes:

“La chute du calorique produit plus de puissance motrice dans les degrés inférieurs que dans les degrés supérieurs.”

We to-day admit that, since the one degree at a low temperature, and the corresponding quantity of heat, are larger fractions of the total temperature, and the total heat stored in the substance, than the one degree at a higher point on the scale of absolute temperature, this principle of Carnot has become obvious.

In the enunciation of the essential principles of efficiency of the heat-engine, we find the proofs of this same wonderful prescience. He asserts that, for best effect: “(1) The temperature of the working fluid must be raised to the highest degree possible, in order to secure a commensurate range of temperature; (2) The cooling must be carried to the lowest point on the scale that may be found practicable; (3) The passage of the fluid from the upper to the lower limit of temperature must be produced by expansion;” i.e., “it is necessary that the cooling of the gas shall occur spontaneously by its rarefaction;” which is simply his method of stating the now universally understood principle that, for highest efficiency, the expansion must be adiabatic, from a maximum to a minimum temperature. He goes on to explain these principles, and then says that the advantage of high-pressure engines lies “essentiellement dans la faculté de rendre utile une plus grande chute de calorique.” This principle, as a practical system of operation, had already, as he tells us, been enunciated by M. Clément, and had been practised, as we well know, since the days of its originator, Watt; but Carnot saw clearly the thermodynamic principle which underlies it, and as clearly states it, for the first time.

He sees clearly, too, the reasons for the attempts of Hornblower and of Woolf, premature as they proved and as he also sees, in the introduction of the compound engine, and even suggests that this idea might be still further developed by the use of a triple-expansion engine, a type which is to-day just coming into use, more than a half-century after Carnot's date. He recognizes the advantages of the compound engine in better distribution of pressures and in distribution of the work of expansion, but does not, of course, perceive the then undiscovered limitation of the efficiency of the simple engine, due to “cylinder condensation,” which has finally led, perhaps more than any other circumstance, to its displacement so largely by the multi-cylinder machine. No one has more exactly and plainly stated the respective advantages to be claimed for air and the gases, used as working fluids in heat-engines, than does Carnot; nor does any one to-day better recognize the difficulties which lie in the path to success in that direction, in the necessity of finding a means of handling them at high temperatures and of securing high mean pressures.

His closing paragraph shows his extraordinary foresight, and the precision with which that wonderful intellect detected the practical elements of the problem which the engineer, from the days of Savery, of Newcomen, and of Watt, has been called upon to study, and the importance of the work, which he began, in the development of a theory of the action, or of the operation, of the heat-engines, which should give effective assistance in the development of their improved forms:

“On ne doit pas se flatter de mettre jamais à profit, dans la pratique, toute la puissance des combustibles. Les tentatives que l'on ferait pour approcher ce résultat seraient même plus nuisibles qu'utiles, si elles faisaient négliger d'autres considérations importantes. L'économie du combustible n'est qu'une des conditions à remplir par les machines à feu; dans beaucoup de circonstances, elle n'est que secondaire: elle doit souvent céder le pas à la sûreté, à la solidité, à la durée de la machine, au peu de place qu'il faut lui faire occuper, au peu de frais de son établissement, etc. Savoir apprécier, dans chaque cas, à leur juste valeur, les considérations de convenance et d'économic qui peuvent se présenter; savoir discerner les plus importantes de celles qui sont seulement accessoires, les balancer toutes convenablement entre elles, afin de parvenir, par les moyens les plus faciles, au meilleur résultat: tel doit être le principal talent de l'homme appelé à diriger, à co-ordonner entre eux les travaux de ses semblables, à les faire concourir vers un but utile de quelque genre qu'il soit.”

Such was the work and such the character of this wonderful man. Those whose desire to follow more closely and to witness the process of development of the work of which this initial paper of Carnot was the introductory, should study the contribution of Sir William Thomson to this development, as published in 1849,—a paper which constitutes that physicist the virtual discoverer of Carnot and the godfather of the man and his thoughts. This paper constitutes the final chapter of this little book.

From that time the additional progress so rapidly made in the new science was as inevitable as the development of a gold-field, once the precious metal has been found in paying quantities in the hitherto unvisited cañons and gorges of a distant and unexplored mountain-range. But great as is the work since done, and great as have been the discoveries and the discoverers of later years, none claims our gratitude and compels our respect in greater degree than does the original discoverer—

 

Sadi Carnot.

 

1. Tait: Thermodynamics, p. 13.
2. Account of Carnot's Theory of the Motive Power of Heat; Sir Wm. Thomson; Trans. Roy. Soc. of Edinburgh, xvi. 1849; and Math. and Phys. Papers, xli. vol. 1 (Cambridge, 1882), p. 113. In this paper the corrections due to the introduction of the dynamic theory are first applied.