work upon the contents of the cylinder, steam is liquefied, and the latent heat developed is at once absorbed by B. Carry on this process till the amount of heat given to B is exactly equal to that taken from A in the first operation, and place the cylinder on the non-conductor C. The temperature of the contents is now T, and the amount of caloric in them is precisely the same as before the first operation. Fourth, Press down the piston farther, till it occupies the same position as before the first operation; additional work is done on the contents of the cylinder, a farther amount of steam is liquefied, and the temperature rises. Moreover, it rises to S exactly, by the fundamental axiom, because the volume occupied by the water and steam is the same as before the first operation, and the quantity of caloric they contain is also the same -as much having been abstracted in the third operation as was communicated in the first-while in the second and fourth operations the contents of the cylinder neither gain nor lose caloric, as they are surrounded by non-conductors. Now, during the first two operations, work was done by the steam on the piston, during the last two work was done against the steam; on the whole, the work done by the steam exceeds that done upon it, since evidently the temperature of the contents, for any position of the piston in its ascent, was greater than for the same position in the descent, except at the initial and final positions, where it is the same. Hence the pressure also was greater at each stage in the ascent than at the corresponding stage in the descent, from which the theorem is evident. engine, and the whole amount of caloric which passes from one to the other. We wish to avoid formulæ as far as pos sible, and shall not give any here; since although the above process is exceedingly ingenious and important, it is to a considerable extent vitiated by the assumption of the materiality of heat which is made throughout. To show this, it is only necessary to consider the second operation, where work is supposed to be done by the contents of the cylinder expanding without loss or gain of caloric, a supposition which our present knowledge of the nature of heat shows to be incorrect. But it is quite easy, as we shall soon see, to make the necessary corrections in accordance with the true theory of heat; and it is but bare justice to acknowledge that Carnot himself was by no means satisfied with the caloric hypothesis, and insinuates, as we have already seen, more than a mere suspicion of its correctness. But we owe Carnot much more than this, as we proceed to show; and we shall defer to a later portion of our article an examination of the curious particulars in which his results for the steam-, or air-, engine differ from those now received. If we carefully examine the above cycle of operations we easily see that they are reversible, i.e., that the transference of the given amount of caloric back again from B, to A, by performing the same operations in the opposite order, requires that we expend on the piston, on the whole, as much work as was gained during the direct operations. This most important idea is due also to Carnot, and from it he deduces his test of a perfect engine, or one which yields from the transference of a given quantity of caloric from one body to another (each being at a given temperature) the greatest possible amount of work. And the test is simply that the cycle of operations must be reversible. Hence, on the whole, a certain amount of work has been communicated by the motion of the piston to external bodies; and the contents of the cylinder having been exactly restored to their primitive condition, we are To prove it we need only consider that, if entitled to regard this work as due to the a heat-engine M could made to give more caloric employed in the process. This we work by transferring a given amount of casee was taken from A and wholly transferred | loric from A to B, than a reversible engine to B. It thus appears that caloric does work N does, we may set M and N to work in by being let down from a higher to a lower combination, M driven by the transfer of temperature. And the reader may easily see that if we knew the laws which connect the pressure of saturated steam, and the amount of caloric it contains, with its volume and temperature, it would be possible to apply a rigorous calculation to the various processes of the cycle above explained, and to express by formulæ the amount of work gained on the whole in the series of operations, in terms of the temperature (S and T) of the boiler and condenser of a steam heat, and in turn driving N, which is employed to restore the heat to the source. The compound system would thus in each cycle produce an amount of work equal to the excess of that done by M over that expended on N without on the whole any transference of heat, which is of course absurd. The remarkable consequences deduced by Thomson, by a combination of the methods and results of Fourier and Carnot, with reference to the dissipation of heat, and the final transformations of all forms of energy, of the substance to be experimented on, both though properly belonging to this part of their statements are perfectly general; and, the development of our subject, are left we may add, not only inaccurate, but (with to a future page, so that we' may keep as certain exceptions) not even roughly apclosely as possible to the chronological order, proximate. Mayer professes to found his in presenting the most important additions process on a species of metaphysical reasonto the science. ing as to the indestructibility of force; we A little before the publication of Carnot's have already shown what value is to be atwork, a second method of procuring work tached to speculations of this nature. Befrom heat was discovered by Seebeck. It sides, Mayer gives, as an analogy to the consists in the production of electricity by compression of a body and the consequent the action of heat on heterogeneous conduct-production of heat, the fall of a stone to the ing matter, and the employment of the cur- earth or the impact of a number of gravirent to drive an electro-magnetic engine. It tating masses and the consequent heating of is not alluded to by Carnot; and it will all. This, we need scarcely say, is simple tend greatly to the simplicity of this ex-nonsense. His hypothesis might possibly planatory narrative if we defer to a second have been a law of nature, but it never article the consideration of the other physi- could have had any analogy with the gravical agents which the grand principle of con- tation case he compares it to. servation of energy has shown to be so But what it most concerns us to note here intimately related to heat. We shall, there is, that Carnot's fundamental principle is fore, confine ourselves as strictly as possible entirely ignored by both, viz., that no deto the relation between heat and mechanical duction whatever can be made as to the reeffect, which is, however, only one branch lation between heat and mechanical effect, of the dynamical theory. when the body operating or operated upon is in different states at the beginning and end of the experiment. Take, for instance, the second operation in the cycle of Carnot as above explained. For nearly twenty years after the appearance of Carnot's treatise little appears to have been done with reference to the theory of heat. Clapeyron, in 1834, recalled attention to Carnot's reasoning, and usefully ap- The numerical data requisite for the appliplied the principle of Watt's diagram of cation of either of these erroneous methods energy to the geometrical exhibition of the were known at the time for only one or two different quantities involved in the cycle of bodies, and even for these, very inaccurately. operations by which work is derived from So that it is not at all remarkable that the heat by the temporary changes it produces equivalents above given are far from exact. in the volume or molecular state of bodies. Seguin worked with steam, Mayer with air. Then there appeared, almost simultane- It happens that this paucity of data led ously, a group of four or five speculators or Mayer to choose a substance which Joule experimenters whose relative claims have afterwards showed was capable of giving, been since pressed, in some cases, with con- even with the erroneous hypothesis, a result siderable violence. The work of one of not far from the truth; but, even if Mayer these, Rebenstein, we have not seen; that bad in 1842 possessed accurate data, and of another, Colding, is in Danish. Of the therefore been lucky enough to obtain an others, Séguin and Mayer, it seems not very approximate result instead of a very inexact difficult to estimate the claims so far as the one, his determination could never have discovery either of the true theory, or the been called more than a happy guess foundmechanical equivalent, of heat is concerned. ed upon a total neglect of correct reasoning. Séguin in 1839, and Mayer in 1842, gave as When we hear, as has lately been our lot, values of the mechanical equivalent, the first that Mayer is the author of the Dynamical 363 kilogrammètres, or in terms of the or- Theory of Heat; and that he deduced in dinary British units 660 foot-pounds; the 1842, by a simple calculation, as accurate a second the almost identical numbers 365 or value of the dynamical equivalent as Joule 663. It is curious also to observe that the arrived at in 1849, after seven years of methods employed were almost identical: laborious experiment, we wonder whether that of Séguin being founded on the princi- language has any meaning to, those who ple that the work giving out by anybody thus abuse it. Mayer enunciated and apdilating, and thereby losing heat, is the plied a false principle, and got a widely equivalent of the heat lost; while that of erroneous result, which was improved, not Mayer is, that the heat developed by com- by himself but by Joule, years afterwards; pression is the equivalent of the work ex- when, after finding the true result by a legitpended in compressing the body. Neither imate process, he proved that Mayer ought makes the slightest limitation as to the nature to have got a good approximation, and set to work to find the requisite experimental allowed for. The value of the equivalent data. deduced in 1847 from a great number of Merely premising that much of Joule's experiments with water was 781 5 footwork has reference to the general theory of pounds, and with sperm oil, 782-1. In the conservation of energy, and that his first de- paper of 1845, we find his first speculations terminations of the dynamical equivalent of as to the absolute zero of temperature, or heat were obtained by means of the magneto- the temperature of a body absolutely deelectric machine, we shall in accordance with prived of heat. The most interesting of his the definite object we have proposed to our results are, that the absolute zero of temperselves in the present article, confine our ature is 480° Fahr. below the freezing-point present notice of his investigations to those of water, and that a pound of water at 60° strictly bearing on the immediate relation Fahr. possesses, in virtue of its heat, mebetween heat and mechanical effect. chanical energy to the enormous amount of His earliest published experiments of this 415,000 foot-pounds. Changes have since class are described in the Appendix to a been shown to be necessary in these numpaper published in 1843 in the Philosophical bers, but they are comparatively unimporMagazine, as it had the not singular misfor- tant. And it must be regarded as one of tune of being rejected by the Royal Society. the most extraordinary results of physical The valuable discoveries contained in this science, that a pound of water at ordinary paper do not properly belong to our present temperatures contains heat capable (if it subject, but will be carefully considered in could be applied) of raising it to a height of our second article. In the Appendix, how- 80 miles. From friction of Water, 66 66 772-692 foot-pounds. ever, there is described an experimental Finally, in 1849, Joule published the remethod of directly determining the mechan-sults of his latest and most elaborate exical equivalent of heat, so simple, and yet so periments, of which, after what we have effective, as to deserve careful consideration. already said, we need only give the reIt consisted simply in working up and down sults:— in a closed cylinder, filled with water, a piston formed of a number of capillary tubes bound together, so as to constitute a mass with visible pores. The friction of the water when forced to pass through these tubes of course developed heat, which, as well as the work employed in moving the piston, was carefully measured. It is very remarkable, that from the series of experiments, agreeing well with one another, which were made with this simple apparatus, Joule deduced as the dynamical equiva lent of heat 770 foot-pounds, differing by only about a quarter per cent. from the results of his subsequent and far more elaborate determinations. The close agreement of the results of successive trials, was quite sufficient to justify him in publishing this, as, in all probability, a very close approximation to the desired value of the equivalent. Before leaving this part of our subject we shall complete the enumeration of the results of Joule's direct experiments for the determination of the mechanical equivalent, as they are certainly superior in accuracy to those of any other experimenter. Mercury, 774-083 Cast-iron, 774-987 The conclusions of this valuable paper, after all allowance is made for slight but inevitable losses of energy, by sound and other vibrations, are thus given : 1st, The quantity of heat produced by the friction of bodies, whether solid or liquid, is always proportional to the quantity of work expended. 24, The quantity of heat capable of increasing the temperature of a pound of water (weighed in vacuo, and taken at between 55° and 60°) by 1° Fahr., requires for its evolu tion the expenditure of a mechanical force represented by the full of 772 lbs. through the space of one foot. It is only necessary to observe, that the determination is for the value of gravity at Manchester, and must of course be diminished for higher, and increased for lower latitudes, according to a well-known law. As no one has pretended to rival in accuracy the experiments of Joule above mentioned, and as his celebrated result of 1843, so very close to the truth, preceded all other sound attempts at the determination Repeating, in 1845 and 1847, his experiments on the friction of water-but now by of the mechanical equivalent of heat, we means of a horizontal paddle, turned by the descent of known weights-he obtained results gradually converging, as in each successive set of experiments extraneous causes of error were more completely avoided or may pass over the results of direct methods employed by other observers, with the remark, that they agree more of less perfectly with those of Joule. We now come to the consideration of the It may now be asked, does the dynamical theory of heat necessitate any serious change in the important results deduced by Carnot from the caloric hypothesis? This question was answered with greater or less detail in 1849, 1850, and 1851 respectively, by Rankine, Clausius, and W. Thomson. method suggested by Séguin and Mayer, rushing into the second vessel produced, by with which Joule seems to have occupied friction against the connecting tube and the himself experimentally in 1844. We shall sides of the vessel, and amongst its own briefly describe his experiments, though not particles, a development of heat. Thus the in the order in which they were made, this second vessel was heated. But it is obvious change being required for the continuity of that we are not at liberty (without experiour article. Joule compressed air to twenty mental proof) to assume that the loss of atmospheres or so in a strong vessel, which heat in the first vessel will be exactly, or was afterwards screwed to another previ- even nearly, equal to the gain in the second. ously exhausted. A very perfect stop-cock But as experiment has shown them to be prevented all passage of air from one to the almost equal, either the heat produced by other until it was desired. The whole was condensing air, or the cold produced by its placed in a vessel of water, which was expansion from a condensed state, may stirred to bring it to a uniform temperature. legitimately be taken as one of the data for On opening the stop-cock, the air rushed a determination of the mechanical equivafrom the first vessel to the second, so that lent. The last cited paper of Joule's conin a short time the pressure was the same tains five sets of careful experiments made in both. On measuring the temperature of for this purpose by one or other of these the surrounding water again, no change was methods. The extreme results are 823 and perceptible, at least after the proper correc-760 foot-pounds respectively; the mean of tions, determined by separate experiments, the last three sets, chosen as the most likely had been made for the amount of heat pro- to be correct, giving the number 798 footduced by the stirring, etc., during the opera- pounds-only about 3 per cent. too great. tion. This is a most important result, as we shall show immediately, though it is as well to say at once that it is not absolutely exact, as is shown by subsequent experiments capable of even greater accuracy than that just described. The condensed air has been allowed to expand without doing work on external bodies, and though its volume has Rankine's treatment of the subject is been greatly increased, no heat has been based on what he calls the hypothesis of lost, though we might have imagined such Molecular Vortices. He considers the mowould be the case. From this we are en- tions of which we know heat to consist, to titled to conclude, that the heat developed be of the nature of vortices or eddies in the by compressing a gas is (to the amount of ap- ether atmospheres whicn ne imagines to proximation already mentioned) the equiv-surround, in a condensed state, each particle alent of the mechanical effect expended in of matter. From this he has deduced many the compression, and thus that Séguin's and useful results, but the theory itself, though Mayer's unwarranted assumption is very skilfully developed, can scarcely be considnearly true for air. Why, then, was Mayer's ered as a very probable representation of value of the mechanical equivalent so erro- the actual thermal motions in bodies. neous? Simply because the direct determination of the specific heat of air is an exceed ingly difficult and delicate operation, and had been only very roughly effected before 1842. Rankine and Thomson first theoretically assigned the true value, founding their calculations on Joule's experimental results from the friction of fluids. Joule, by a direct process, obtained a closely accordant value; and finally Regnault, also by direct experiment, obtained exactly the number predicted from theory. What actually took place in Joule's experiment was, the air in the first vessel, suddenly expanding, produced mechanical effect in forcing a portion of its mass with great velocity into the second vessel; this it did at the expense of its store of energy in the form of heat. Thus the first vessel was cooled to a certain extent. The air Clausius also, while adapting successfully Carnot's method to the true fundamental propositions in Thermo-dynamics, has somewhat confused his reasoning (instead of simplifying it) by introducing at once as a hypothesis Mayer's unwarrantable assumption, so far as regards the development of heat by the compression of a gas. In this he was, no doubt, justified by Joule's experiments last mentioned, but he missed in consequence some valuable results which, though discoverable in permanent gases, become especially prominent in liquefiable gases, such as sulphurous acid and carbonic acid; but it is to be observed to his credit, that he does not assume any such extension of the hypothesis to solids and liquids as was contemplated by Mayer. One of the most valuable of the results thus deduced by Rankine and Clausius is as follows:-If saturated steam at any high the proposition in 1850, by a process stricttemperature is allowed to expand, pressing ly analogous to that of Carnot, already out a piston, in a vessel impervious to heat, given; but based on the additional axiom, that "It is impossible for a self-acting ma chine, unaided by any external agency, to convey heat from one body to another at a higher temperature." Thomson, from one of whose papers* we have taken this notice, gives the above not very evident axiom in the more convincing form: "It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects." Carnot showed that, on his principles, the amount of work done by transference of a given amount of heat increased indefinitely with the increasing difference of temperatures of the source and refrigerator; and of course it follows from this that the airengine, in which a much greater range of temperature may be employed with safety than in the steam-engine, should be the more effective of the two. The introduction of In its new form, the theory of the motive the true theory leaves this result unaffected power of heat is based upon the two fol- except in degree; in fact it shows that the lowing propositions: the first of which, work to be derived from a given amount of though really announced by Davy, was only heat leaving the source increases indeed definitely received in science in consequence with the excess of temperature of the source of Joule's experiments; the second is the over the reservoir; but, far from increasing axiom of Carnot (already given, with its indefinitely as Carnot's theory showed, it has demonstration on the caloric theory), as as a superior limit, which it never reaches, adapted by Clausius to the dynamical the mechanical equivalent of the heat which theory. J. When equal quantities of mechanical effect are produced by any means whatever from purely thermal sources, or lost in purely thermal effects, equal quantities of heat are put out of existence, or are generated. II. If an engine be such that, when it is worked backward, the physical and mechanical agencies in every part of its motions are all reversed, it produces as much mechanical effect as can be produced by any thermodynamic engine, with the same temperatures of source and refrigerator, from a given quantity of heat. leaves the source. In fact, the ratio of the heat taken in to that ejected is that of the absolute temperature of the source to the absolute temperature of the refrigerator.t Thus, in the most favourable circumstances, the steam engine, and even the air-engine, are exceedingly imperfect; giving at most only about one-tenth of the mechanical equivalent of the heat spent. The theory of what have been called Caloric Engines, where ether, or chloroform, or some such easily vaporized liquid is used in connexion with air or steam to utilize as much as possible of the applied heat, has been given by various investigators, including those last mentioned, but it appears that in practice the method has not realized the anticipa tions of its proposers. In order to prove the second proposition, we must consider in what respect Carnot's proof has become inapplicable, and we find it to be this: we have no right now to asA most remarkable result of the applisume, as he did, that in a complete cycle of cation of Carnot's reasoning was given by J. operations in which his fundamental condi. Thomson in 1849. From this reasoning tion is satisfied (i. e., the medium brought it is obviously demonstrable, as shown by exactly to its primitive state) as much heat W. Thomson, that water at the freezinghas been given out to the refrigerator as has point may, without any expenditure of work been absorbed from the source; because the on the whole, be converted into ice by a mefirst of our new propositions shows that this is only true when the medium has had as much work done upon it as it has exerted on external bodies. Clausius proved *On the Dynamical Theory of Heat, etc., by W. Thomson, Trans. R. S. E. 1851. W. Thomson, Trans. R.S.E. 1851. |