Abstract
Nicolas Léonard Sadi Carnot (1796–1832) was born in the Palais du Petit- Luxembourg in Paris. His father, a famous mathematician and minister of war under Napoleon, named his son after the eminent medieval Persian poet Sadi of Shiraz. Carnot attended the Charlemagne Lycée before enrolling at the age of 16 in the École Polytechnique, the elite military academy which attracted many famous scientists and mathematicians during the age of the French Revolution: Biot, Arago, Laplace, Fourier, Gay-Lussac, Ampère, and Poisson. After his graduation in 1814, Carnot served as a cadet sub-lieutenant in the engineer corps at Metz, a position which he found increasingly frustrating and confining after Napoleon’s defeat at Waterloo and his father’s consequent retirement and exile to Magdeburg, Germany. So in 1819 Carnot took an examination and was appointed a lieutenant in the French general staff. After attaining a furlough he increasingly turned his attention to the study of scientific matters, particularly the writings of Pascal and the design of steam engines. This latter interest would eventually lead to his only publication in 1824. Carnot’s Réflexions sur la puissance mortice du feu went largely unnoticed until after his death from cholera at the age of 36. Several years later, Clausius and Kelvin developed Carnot’s seminal ideas on heat engines into one of the foundations of modern science: the second law of thermodynamics. The reading selections that follow are from an 1897 English translation by Robert Henry Thurston (Fig. 3.1).
Wherever there exists a difference of temperature, motive-power can be produced.
—Sadi Carnot
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Notes
- 1.
Much of the present introduction was derived from a biographical sketch of Sadi Carnot written by his younger brother, Hippolyte, which can be found in Chap. II of Carnot, S., Reflections on the Motive Power of Heat, second ed., John Wiley & Sons and Chapman & Hall, New York and London, 1897.
- 2.
Sadi Camot’s Réflexions sur la puissance motrice du feu (Paris, Bachelier 1824) was long ago completely exhausted. As but a small number of copies were printed, this remarkable work remained long unknown to the earlier writers on Thermodynamics. It was therefore for the benefit of savants unable to study a work out of print, as well as to render honor to the memory of Sadi Carnot, that the new publishers of the Annales Scientifique de l’École Normale supérieure (ii. series,t. 1, 1872) published a new edition, from which this translation is reproduced.
- 3.
It may be said that coal-mining has increased tenfold in England since the invention of the steam-engine. It is almost equally true in regard to the mining of copper, tin, and iron. The results produced in a half-century by the steam-engine in the mines of England are to-day paralleled in the gold and silver mines of the New World—mines of which the working declined from day to day, principally on account of the insufficiency of the motors employed in the draining and the extraction of the minerals.
- 4.
We say, to lessen the dangers of journeys. In fact, although the use of the steam-engine on ships is attended by some danger which has been greatly exaggerated, this is more than compensated by the power of following always an appointed and well-known route, of resisting the force of the winds which would drive the ship towards the shore, the shoals, or the rocks.
- 5.
We use here the expression motive power to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.
- 6.
We distinguish here the steam-engine from the heat-engine in general. The latter may make use of any agent whatever, of the vapor of water or of any other, to develop the motive power of heat.
- 7.
Certain engines at high pressure throw the steam out into the atmosphere instead of the condenser. They are used specially in places where it would be difficult to procure a stream of cold water sufficient to produce condensation.
- 8.
The existence of water in the liquid state here necessarily assumed, since without it the steam-engine could not be fed, supposes the existence of a pressure capable of preventing this water from vaporizing, consequently of a pressure equal or superior to the tension of vapor at that temperature. If such a pressure were not exerted by the atmospheric air, there would be instantly produced a quantity of steam sufficient to give rise to that tension, and it would be necessary always to overcome this pressure in order to throw out the steam from the engines into the new atmosphere. Now this is evidently equivalent to overcoming the tension which the steam retains after its condensation, as effected by ordinary means.
If a very high temperature existed at the surface of our globe, as it seems certain that it exists in its interior, all the waters of the ocean would be in a state of vapor in the atmosphere, and no portion of it would be found in a liquid state.
- 9.
It is considered unnecessary to explain here what is quantity of caloric or quantity of heat (for we employ these two expressions indifferently), or to describe how we measure these quantities by the calorimeter. Nor will we explain what is meant by latent heat, degree of temperature, specific heat, etc. The reader should be familiarized with these terms through the study of the elementary treatises of physics or of chemistry.
- 10.
We may perhaps wonder here that the body \(b\) being at the same temperature as the steam is able to condense it. Doubtless this is not strictly possible, but the slightest difference of temperature will determine the condensation, which suffices to establish the justice of our reasoning. It is thus that, in the differential calculus, it is sufficient that we can conceive the neglected quantities indefinitely reducible in proportion to the quantities retained in the equations, to make certain of the exact result.
The body \(b\) condenses the steam without changing its own temperature—this results from our supposition. We have admitted that this body may be maintained at a constant temperature. We take away the caloric as the steam furnishes it. This is the condition in which the metal of the condenser is found when the liquefaction of the steam is accomplished by applying cold water externally, as was formerly done in several engines. Similarly, the water of a reservoir can be maintained at a constant level if the liquid flows out at one side as it flows in at the other.
One could even conceive the bodies \(a\) and \(b\) maintaining the same temperature, although they might lose or gain certain quantities of heat. If, for example, the body \(a\) were a mass of steam ready to become liquid, and the body \(b\) a mass of ice ready to melt, these bodies might, as we know, furnish or receive caloric without thermometric change.
- 11.
We assume here no chemical action between the bodies employed to realize the motive power of heat. The chemical action which takes place in the furnace is, in some sort, a preliminary action,—an operation destined not to produce immediately motive power, but to destroy the equilibrium of the caloric, to produce a difference of temperature which may finally give rise to motion.
- 12.
This kind of loss is found in all steam-engines. In fact, the water destined to feed the boiler is always cooler than the water which it already contains. There occurs between them a useless re-establishment of equilibrium of caloric. We are easily convinced, à posteriori, that this reestablishment of equilibrium causes a loss of motive power if we reflect that it would have been possible to previously heat the feed-water by using it as condensing-water in a small accessory engine, when the steam drawn from the large boiler might have been used, and where the condensation might be produced at a temperature intermediate between that of the boiler and that of the principal condenser. The power produced by the small engine would have cost no loss of heat, since all that which had been used would have returned into the boiler with the water of condensation.
- 13.
The matter here dealt with being entirely new, we are obliged to employ expressions not in use as yet, and which perhaps are less clear than is desirable.
- 14.
Equation 3.3 for the work done by an expanding gas can only be used when the pressure exerted by the gas is nearly the same as the external pressure attempting (in vain) to restrain its expansion. During such an expansion, the gas pressure is uniform throughout. Equation. 3.3 cannot be used when the gas expands rapidly against a much weaker restraining force, for example, when a balloon is popped and an initially high pressure gas rushes into a surrounding low-pressure gas. There is no work done by the gas in such a “free expansion.” For a more sophisticated treatment of this topic, and its relationship to entropy, see Rudolph Clausius’ discussion of reversible and irreversible processes in Chap. 6 of the present volume.
- 15.
Molar volume is the volume per mole of gas.
- 16.
The division of heat into internal energy and external work will be discussed in more detail by Rudolph Clausius; see Chap. 6.
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Kuehn, K. (2016). Steam Engines and Heat Flow. In: A Student's Guide Through the Great Physics Texts. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-21828-1_3
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