From Joseph Gill

XVI. On the Dynamical Theory of Heat. | By JOSEPH GILL, Esq. | To John Tyndall, Esq., F.R.S. &c.

SIR,

THE kind courtesy with which you received my letter “On the Dynamical Theory of Heat,” inserted in the Philosophical Magazine for August last,¹ encourages me to hope that you will be so good as to give to the following remarks, in continuation of the subject, an opportunity of meeting the notice of scientific men through the same channel. My only object is to elicit truth. I have neither time nor inclination nor ability for scientific controversy, and I long shrunk back from the idea of making public the results of my researches on a subject to which I have given much attention during a large portion of the term of a medium lifetime; but at length my conviction of the truth of some of the glimpses of light which have been afforded me in these intricate researches forced itself into utterance; and my anxiety to see the difficulties which have baffled me removed by abler hands has caused me to persevere in the effort to induce some one of the eminent men who have distinguished themselves in the development of the new science of thermo-dynamics to reconsider these knotty points, and clear away if possible, once for all the doubts and obscurity which still cloud some parts of the subject.

Since the date of my last letter I have read your excellent “Lectures on Heat as a mode of Motion,”² and I feel that the highest praise is due to the ability with which the subject has been divested of technical and mathematical intricacies and brought within the grasp of mind of every earnest reader of average intellect. By thus exhibiting the results of deep and involved researches in “that simple form in which great truths present themselves to those who thoroughly understand them,” an inestimable boon is conferred on numerous readers possessing a knowledge of physics quite sufficient to handle subjects fairly within the range of physical reasoning, though wanting the mathematical knowledge requisite for treating these subjects on the higher scientific plane to which their full theoretical development more properly belongs. It was well remarked by Dr. Lardner,³ that “the phenomena of heat all admit of being explained without the aid of abstruse reasoning, technical language, or mathematical symbols. The subject abounds in examples of the most felicitous processes of induction, from which the general reader may obtain a view of that beautiful logic, the light of which Bacon⁴ first let in on the obscurity in which he found physics involved.” I may truly say that after the perusal of your book I understand the subject better than I did before; but still some of my doubts are unresolved, as you will perceive from the following statements.

Although a fixed equivalence undoubtedly exists between the heat generated by friction and the energy expended in producing the friction, experiment proves that elastic fluids suffer no diminution of heat in the act of producing work, but only a fall of temperature. I have long perceived the difficulties of admitting this hypothesis, as it involves the apparent paradox of a continual investment of energy in the production of molecular motion, of the reconversion of which back again into energy no account can be given. But the results of numerous and varied experiments leave me no alternative, and I must repeat my conviction that heat runs down but does not disappear in the production of work. Even admitting that quantitative heat disappears in the process, still many reasons might be given for doubting that any fixed equivalence exists between the heat disappearing and the work done; but for the present I will confine myself to the simple consideration that, with the disappearance of equal quantities of heat in the expansion of air of constant initial density, different quantities of work should be produced according to the mode of conducting the process.

Imagine a cylinder of 2 cubic feet capacity to contain 1 cubic foot of air of atmospheric pressure at the temperature of 32°F. confined by a piston resting at half stroke, supposed to be without weight or friction. Let the piston be fixed in this position, and heat applied to the air until its temperature is raised 490° above the initial point, and let the quantity of heat required to produce this effect be represented by 100. In this process the air is simply heated, and although statical tension is developed, no dynamical effect is produced, it is merely a preparation for work—a transfer of heat from one substance to another if the heat is taken either ready made, or produced chemically, or a change of some form of energy into heat by friction; but, as long as no work is done by the least air, things are considered to remain in a state of balance or equilibrium.

Suppose the air to be again at 32°, and the piston free to move when any disturbing cause should be applied. If heat be gradually communicated to the confined air it will expand, raising the piston and with it the superincumbent column of the atmosphere, which may be taken in round numbers at 15 lbs. per square inch. When 490 degrees of temperature have been given to the confined air, its volume will be doubled, and if the piston be 1 square foot area, it will have moved upwards through 1 foot; and it would be said that in its ascent it had performed the work of 144 square inches X 15 lbs. = 2160 lbs. raised 1 foot. In this process 1 cubic foot of air has been heated 490 degrees, as in the former case, but the circumstances are different. In the former case the air was confined to constant volume, and tension was induced, but no work was done. In the present case the air was free to expand, no tension was induced, and work was performed; and as heat was the only energy employed in the operation, we should naturally expect an excess of heat to be used equivalent to the work done. In fact we find that 142 of heat has been thrown into the air in this case, while to heat the air to the same degree under constant volume 100 sufficed; it is therefore said that the difference, represented by 42, has done the work.

The work assumed to be done in the case under consideration, by raising the column of the atmosphere resting on the piston, is not available, it cannot be detached from the apparatus—a circumstance which might induce doubt as to its reality. If it possesses the entity which it appears to have, it should not be impossible to detach it from the matrix where it exists, and to exhibit it in some other form, thus removing the suspicion of imperceived coefficients acting in the phenomena. By altering the circumstances, the work which exists as potential energy in the raised atmospheric column ought, if all real, to be convertible into an equivalent of actual energy, or work done in another shape. By withdrawing the heat from the air in the cylinder, the piston will descend with a power corresponding to the difference of pressure between the total atmospheric pressure outside and the diminished pressure inside; and this power will be equal to half the atmospheric pressure at the beginning of the piston’s stroke, diminishing to nothing at the end, when the confined air will, as a first, occupy 1 cubic foot at atmospheric pressure and 32° temperature. The amount of power obtained in this operation will be less than a quarter of an atmosphere on the area of the piston moved through 1 foot. For simplicity of reasoning we may suppose it to be one quarter of an atmosphere.

In the working of a theoretically perfect thermic engine, all the heat [condensed], or which permanently disappears, is supposed to be converted into work in the proportion of Joule’s equivalent of 772 foot-pounds for every unit of heat, neither more nor less. By means of a regenerator (as used in Stirling’s and Ericsson’s air-engine⁵) of theoretically perfect action, all the heat withdrawn from the air as above described could be stored up in such a way as to be transferred back again to the same air under the same circumstances as before, and the operation could be repeated over and over again indefinitely, with the production of available work, provided that at each stroke of the piston a fresh quantity of heat represented by 42 be thrown into the apparatus. The heat consumed by 1000 strokes of the piston would be 1000 times 42, and the work produced would be 1000 quarters of an atmosphere on the area of piston raised 1 foot.

In the former case 1000 repetitions of the operation, with fresh air and fresh heat each time, would equally consume 1000 times 42 of heat, the 100 of heat remaining unchanged at the end of each operation; but if it is assumed that in each cycle of heating and cooling, expanding and contracting the confined air, work is actually done equal to raising the atmosphere column on the piston through 1 foot (which is the apparent effect), we must allow that the work done by 1000 repetitions of the operation would be 1000 atmospheres on the piston raised 1 foot. How is this apparent discrepancy to be accounted for?

Another serious difficulty in the dynamical theory is the question of the specific heat of air. Regnault’s experiments appear to prove that the specific heat of air is constant at different densities. This result is in accordance with the dynamical theory, and in fact the theory could not stand unless this assumption were admitted. My own experiments have given very different results; but as it might be thought presumptuous to place these experiments in opposition to those of such a high authority as Regnault, I beg to submit the following reasoning to candid scrutiny.

Imagine a vacuum to be made in a cylinder by drawing up its piston by a descending weight, in which operation the work done by the descent of the weight gives an equivalent amount of potential energy in the tendency possessed by the atmospheric column raised by the piston to fall back into the vacuum; and so far things are in a state of equilibrium. Imagine further a second cylinder, twice the size of the former one, full of atmospheric pressure air, which should be compressed into half its original volume by some exterior force applied allowing the developed heat to pass out during the compression. In this operation work has been expended, and heat has been produced, which heat, according to the dynamical theory, would be considered equivalent to the work expended, as by allowing the air to expand back under moderated resistance, restoring to it the heat it had lost, the work done in the compression would be recovered. Now suppose a communication to be made between the two cylinders—the air will rush into the vacuum, and as the contents of the two vessels now filled by the expanded air are equal to the volume which the air originally occupied, it is evident that the pressure will also be equal to what it was before the compression, namely atmospheric pressure. It is clear that no power can be obtained from the expanded air, as it is in equilibrium with the surrounding atmosphere; but the energy which might have been availed of by allowing the atmosphere to fall into the vacuum, and thus produce work, has disappeared. It is impossible to conceive of the annihilation of energy, and we must therefore suppose that it has taken some other shape in the confined air. The dynamical theory does not allow the existence of energy in elastic fluids under any other form than that of molecular motion or heat, consequently there should be more heat in the expanded air; but as the experiments of Gay-Lussac⁶ and Joule have proved that in the expansion of air into a vacuum the temperature of the mass remains constant, we are forced to admit that the specific heat of the expanded air is greater than that of the air in a compressed state: in other words, the susceptibility of air to the influence of heat as affecting the thermometer increases with increase of density.

According to the dynamical theory, a common non-condensing steam-engine, working without expansion, utilizes only about 1/40 of the theoretical power of the steam. By the addition of a condenser this effect is doubled, or the engine gives about 1/20 of useful effect. Such were the deductions published by Regnault, conveying to abstract theorists the idea that the steam-engine is one of the most imperfect of prime movers. Some of the results obtained by M. Hirn⁷ from the practical working of large steam engines were as high as 1/6, none lower than 1/10; and 1/8 may be taken as a possible degree of practical efficiency – better certainly than Regnault’s deductions, but still showing that the steam-engine under the most favourable circumstances is so far from perfection as to throw away 7/8 of the theoretical power of the steam. However, the marked discrepancy between the theoretical deductions and the practical results showed that something was wrong in the theoretical calculation; and the excess of work obtained in Hirn’s results has been accounted for by supposing that some of the steam condenses in the act of expansion in the working of the engine, and that this condensation represents the heat converted into work beyond the theoretical calculation which supposed all the steam to pass into the condenser in the vaporous state. This explanation involves the idea that steam at different densities contains a variable quantity of heat in proportion to the work it can perform; and this inference obtains some slight support from the results of experiment, showing that the total heat of steam increases with increase of density, but by no means enough to account for the greater amount of work it can perform by expansion.

One of M. Hirn’s experiments with an engine cutting off the steam at 1/3 of the stroke showed at the same time a production of work and a creation of heat. In another of his experiments steam was thrown into a sheet-iron vessel immersed in cold water, and it was found that the heat thrown out by the condensing steam was more than that due to its constitution as deduced from calculations of acknowledged correctness. Moreover the fact that steam becomes superheated in the act of free tumultuous expansion is not disputed, though it involves the idea of some other form of energy existing in the steam besides molecular motion. The dynamical theory necessitates the assumption that steam is condensed during expansion in the production of work, as theoretically shown by Clausius and Rankine; and another of Hirn’s experiments would seem to corroborate this assumption. A copper tube upward of 6 feet long and 6 inches diameter, with strong glass ends, was put in communication, by means of stopcocks, with a steam-boiler at one end and with the atmosphere at the other. The tube full of high-pressure steam was perfectly transparent; but the moment the cock communicating with the atmosphere was opened, and part of the steam rushing out allowed the remainder to expand, a cloud was formed in the tube: the steam became quite opake, showing, as it is supposed, the condensation of the steam which should accompany expansion.

On this experiment, I would remark that a film of moisture must exist on the interior surface of the tube, though at the same time the contained mass of steam may be dry, or free from particles of water mechanically suspended in it. The temperature of the copper must be somewhat lower than that of the high-pressure steam, but much higher than the temperatures of the steam at low pressure; consequently, on the sudden lowering of pressure in the tube when the steam is allowed to blow off, an instantaneous “flashing” into steam of the water on the now comparatively hot metal must ensue, with a large amount of priming, or dispersion of the water in the shape of fine spray, probably quite sufficient to account for the opacity observed. The experiment should be made with the tube enclosed in a case with glass heads, filled with steam of the same temperature as the steam inside, to prevent the deposition of moisture on the interior surface of the tube. This precaution would in a degree obviate a serious source of error, though still it should be borne in mind that glass has an attractive power for moisture which prevents its free evaporation at temperatures considerably higher than the regular boiling point under any given pressure.

I must be allowed to express my opinion that the experiments of M. Hirn are of great practical value, and I submit that the importance of the facts which they furnish is not depreciated by the circumstance that the experimenter, apparently borne down by scientific authority, recently presented to the Academy of Sciences an interpretation of his results in accordance with the dynamical theory. It should also be borne in mind that the results of Hirn’s experiments coincide in the main with those of Séguin made more than twenty five years ago, when his reasoning on the mode of action of the steam-engine pointed out the necessity of supposing a conversion of heat into work, of which, nevertheless, he could find no appreciable indication in the results of the numerous experiments made by him with this express purpose, and conducted with the attention and accuracy suggested by his great scientific knowledge and superior practical skill in thermo-dynamics as then known.

In my experiments above alluded to on the specific heat of air at different densities, I found that certain proportions of surface in the apparatus relative to the masses of air, their condition, and the times occupied by their passage through the calorimeter, were essential to correct results; and I venture to think that some concealed source of error must have existed in Regnault’s experiments on this subject, undetected even by his extraordinary ability in similar researches.

I would also repeat that my long practical acquaintance with the general phenomena of steam, as well as the results of direct experiment, have tended to convince me that the total heat of steam is a constant quantity. I believe that this important point is again engaging the attention of physicists; and it may be well to remark that in the condensation of high-pressure steam there is a tendency to produce heat from the effects of tumultuous expansion, which may seriously affect the results, showing, as in some of Hirn’s experiments, more heat than is due to the constitution of the steam. In the cooling of gases under ordinary circumstances there is no change of state, and the contraction of the volume should result from a gradual shrinking of the sphere of action of each particle in the mass, a process which suggests no idea of tumultuous motion or persuasive action of the particles. In saturated vapours each particle must possess the precise specific amount of heat requisite for its existence in the vaporous state; if heat be added, the vapour becomes a gas; if heat be withdrawn, some of the particles must collapse into liquid. This collapse should evidently be sudden and each particle in assuming the liquid state should, for the moment, leave an almost perfect vacuum in the space it occupied in contact with the cold walls of the condenser. The void is instantly occupied by a fresh particle of vapour, which in its turn collapses, and so the process continues as long as vapour remains to be condensed. It may be conceived that the particles of vapour thus rapidly precipitated into a vacuous space, bounded on the outside by the hard metallic walls of the condenser, must strike with violence against these surfaces, and generate heat by this molecular battering.

It may be replied that the internal work done by the remaining particles of vapour in forcing their fellows down the precipice of the vacuum should cause an amount of chilling of the mass by an actual disappearance of heat equal to that generated by the percussive action of the particles against the sides of the condenser. To this I would answer that, until good account can be given of the actual excess of work-producing power which high-pressure steam is allowed to possess as compared with steam of low pressure, weight for weight, and which is apparently lost by the quiet condensation of the steam in the vessel which contains it, we may suppose some unacknowledged form of energy to exist in the steam distinct from mere molecular motion, though always acting in cooperation with it, and more than sufficient to cause the violent fall of the vapour particles against the walls of the condenser, thus generating heat in excess of what is fairly due to the constitution of the steam.

The very nature of the steam suggests the idea that, as far as quantitative heat is concerned, each individual particles should have a fixed specific temperature the general temperature of any given mass resulting simply from the number of particles in a given space, or, in other words, the distance of the particle from each other, and consequently the amplitude of their molecular motions. Thus it is certainly reasonable to conceive of a fall of temperature in expanding steam without any idea of absolute loss of heat. However this may be, I would beg to impress on the attention of physicists who may be making further experimental researches on this interesting point, the importance of guarding against all probable causes of error which can be foreseen, keeping in mind the results obtained by Seguin and Hirn, and also the experiments of Siemens, in which high-pressure steam seemed to superheat itself by tumultuous expansion.

I remain, Sir, | Your most obedient Servant, | JOSEPH GILL | Palermo, January 4, 1864.

Phil. Mag. 27, 84-91.