Art. 68. Second Law of Thermodynamics.--This law was enunciated by Sadi Carnot in 1824, when he wrote an essay on the Motive Power of Heat. Previous to the time of Carnot no definite relation seems to have been suggested between work and heat; Carnot, however, discovered what were those general laws which govern the relation between heat and work. In arriving at his conclusion, he based his results on the truth of the principle of the conservation of energy already referred to ([Art. 52]).
Carnot started his reasoning on the assumption that heat was matter, and therefore indestructible. The two great truths in relation to heat and work, enunciated by Carnot, are known as, first, a Cycle of operations; and, secondly, what he termed a Reversible Cycle. In order to be able to reason upon the work done by a heat-engine, say a steam-engine for example, Carnot stated we must imagine a cycle of operations, by which, at the end of such operations, the steam or water is brought back to exactly the same state in which it was at its start. He calls this a cycle of operations, and of it he says, that only at the conclusion of the cycle are we entitled to reason upon the relation between the work done and the heat spent in doing it. His other idea of the reversible cycle implies that an engine is reversible when, instead of using heat and getting work from it, the engine may be driven through the cycle of operations the reverse way, that is, by taking in work, it can pump back heat to the boiler again. Carnot showed that if you can obtain such a reversible engine, it is a perfect engine. All perfect engines, that is all reversible engines, will do exactly the same amount of work with the same amount of heat, the amount of work being strictly proportionate to the amount of heat consumed. I need hardly point out that the reversible engine, or the perfect engine of Carnot, is only the ideal one, as there is no engine in which all the heat is converted into work, as a great deal of the heat is radiated away and not converted into work at all. Again, working from the standpoint that heat is matter, Carnot reasoned that in the heat-engine the work is performed, not by the actual consumption of heat, but by its transportation from a hot body to a cold one. Thus, by the fall of heat from a higher to a lower temperature, work could be done in the same way that work could be done by allowing water to fall from a higher to a lower level. The quantity of water which reaches the lower level is exactly the same as that which leaves the higher level, as none of the water is destroyed in the fall. He argued, therefore, that the work produced by a heat-engine was produced in a similar manner, the quantity of heat which reaches the condenser being supposed to be equal to that which left the source. Thus the work was done by the heat flowing from a hot body to a cold one, and, in doing this work, it lost its momentum like falling water, and was brought to rest. One of the most important points noted by Carnot is the necessity that, in all engines which derive work from heat, there must be two bodies at different temperatures, that is, a source and a condenser, which correspond to a hot and cold body, so that there may be the passage of heat from the hot to the cold body. In order to get work out of heat it is absolutely necessary to have a hotter and a colder body. From this reasoning we learn, therefore, that work is obtained from heat by using up the heat of the hotter body, part of which is converted into actual work, while part is absorbed by the colder body. So that wherever we have two bodies at different temperatures, according to the second law of thermodynamics, there we have the power of doing work by the transmission of heat, from the body of higher to the one of lower temperature.
That Carnot ultimately came to believe in the dynamical theory of heat, is proved by the following passage taken from his notes on the Motive Power of Heat: “It would be ridiculous to suppose that it is an emission of matter, while the light which accompanies it could only be a movement. Could a motion produce matter? No! undoubtedly, it can only produce a motion. Heat is then the result of motion. It is plain then that it could be produced by the consumption of motive power, and that it could produce this power. Heat is then simply motive power, or rather motion which has changed its form. It is a movement among the particles of bodies. Wherever there is a destruction of motive power, there is at the same time production of heat in quantity exactly proportional to the quantity of motive power destroyed. Reciprocally, whenever there is destruction of heat there is production of motive power.”
Let us apply this principle to the solar system, and endeavour to find out whether in that system we have, in relation to the heat thereof, either a cycle of operations or a reversible cycle. We have again to consider the sun as the source of all light and heat in the solar system, radiating forth on every side, year by year, the countless units of heat which go to form the continuance of all planetary life and existence. One of the problems that has confronted scientific men for many years is this, Where does the sun get its supply of heat from? When we remember the incessant loss of heat which the sun suffers through its radiation of heat into space, we are compelled to ask, How is that supply maintained, and how has it been kept up through the countless ages of the past? Several suggestions have been made, and several theories advanced to account for the fact. Mayer, of Germany, suggested that the heat is partly maintained by the falling into the sun of meteors, which, like comets, pursue a path through the heavens, and are subject to the attractive influence of the sun. In the combustion of these meteorites, or meteors, he contended there were the means by which the light and heat of the sun might be maintained. Whatever theory, however, may be suggested as to the maintenance and the source of the continuity of the sun's heat, I do not think it has been suggested by any scientist that the heat emitted and radiated by the sun is ever returned in any way back to the sun from infinite space, whether by reflection or by any other method. So far as I can learn, there are no facts in connection with the solar system which would lead us to make that assumption. On the contrary, experience and experiment teach us that radiation implies loss of heat, and that the body, which so radiates, ultimately becomes cold, unless its internal heat is kept up by some means or other. So that the terms introduced by Carnot in the second law of thermodynamics, viz. that of a Cycle of Operations and of a Reversible Cycle, do not apply to the solar system, and the solar system, viewed from the standpoint of a machine, with the sun as the source of the heat, does not represent a perfect engine, that is, all the heat is not used up in doing work, some of it being radiated out into space. Wherever, however, the heat, that is the aetherial heat waves generated by the sun, comes into contact with a planet, as Mercury, Venus, or Jupiter, then, in accordance with Carnot's reasoning, work is done. Carnot points out that, in order for work to be done, we must have a source and a condenser, that is, two bodies at different temperatures, a hot body and a cold one. Now these conditions of work are satisfactorily fulfilled in the solar system, and as a result work is performed. We have the sun with its huge fires, and its intensity of heat, representing the source or the hot body, while every planet and every meteor and comet, that come under its influence, represent the cold body, and between the two work is always going on. That work is represented by the repulsive power of heat, which I have already indicated, so that, viewed from Carnot's standpoint with relation to the motive power of heat, we find that there are in the solar system those conditions which govern work, and by which, from a mechanical standpoint, work is performed; further, that work takes the form of a repulsive power on every planet or other body upon which the aetherial heat waves fall. Therefore, from the second law of thermodynamics we have another proof of this repulsive power of heat already indicated and referred to in [Art. 63].
Art. 69. Identity of Heat and Light.--We have seen from the preceding articles of this chapter, that heat is due to a periodic wave motion of the Aether, and in the succeeding chapter we shall also see that light is due to some kind of periodic wave motion in the Aether. So that not only heat, but light also, it would appear, is due to certain periodic wave motions that are set up in the Aether by the vibrations of hot or luminous bodies. The question therefore arises, how many wave motions are there in the Aether? Are there different wave motions which in one case produce light, and in the other case produce heat, or are light and heat both produced by the same set of aetherial waves? The identity of light waves with heat waves is manifested by the fact that wherever we get light we get heat, as can be proved in many ways. One of the simplest proofs is found in the common lens or burning-glass, by which the light waves are brought to a focus, and as a result, heat is manifested. Although there is this close identity between light and heat waves, yet there must be some distinction between the heat and light waves, because while light waves affect the eye, heat waves do not. There is actually a difference between the two kinds of waves, and that difference is one of period or length. It must not, however, be thought that there are really two classes or sets of waves in the Aether, one of which could be called light waves, and the other heat waves, but rather the same wave may be manifested in two different forms because of its different wave lengths. In one case the waves may affect the eye, and we have the sensation of sight, but in the other case they affect the body, and we experience the sensation of warmth. An analogy from the waves of sound may make these facts much clearer. We know that sound travels about 1100 feet per second. If, therefore, we have a bell which vibrates about 1100 times per second, we should have a wave one foot long. If it vibrated 100 times per second the waves would be 11 feet long, while if it vibrated only 11 times per second, the waves would be 100 feet long. Now the impression made upon the ear depends upon the number of vibrations the bell makes per second, and from the rate of vibration we get the idea of pitch. If the vibrations are very rapid, then we get a note of high pitch, and if the vibrations are slow, then we get a note of low pitch. A note of high pitch, therefore, will correspond to waves of short length, while a low note will correspond to waves of a greater length; so that the greater the rapidity with which a sounding bell vibrates, the shorter will be the length of the sound waves which it generates, and vice versâ. The range of the ear however for sound waves is limited, so that if the vibrations be too rapid or too slow, the ear may not be able to respond to the vibrations, and so no distinct impression of the sound will be conveyed to the brain. It need hardly be pointed out, that both the very short and long waves are of exactly the same character as those of a medium length, which the ear can detect, the only difference being one of rapidity. We do not therefore suggest that in the case of sound, where the vibrations lie outside the compass of the ear, those which lie outside are not sound waves, or that they are different from those which lie within the compass of the ear, and which the ear can detect. Whether the sound waves are long or short, whether they can be detected by the ear or not, we still say that all are sound waves, and that all are due to the vibrations of the sounding body, which vibrations are transmitted through the air, in waves, that fall upon the tympanum or drum of the ear, and set that vibrating, which vibrations are transmitted to the auditory nerve and so give rise to the sensation of hearing. In a similar manner, every atom and every particle of matter, every planet, every sun and star, is constantly in a state of vibration, sending off aetherial waves on every side. Nothing in Nature is absolutely cold, nothing is absolutely still. Therefore all matter, whether in the atomic form, or in the planetary or solar world, is constantly generating aetherial waves, which travel from their source or origin with the velocity of light. If these aetherial waves so generated fall within certain limits, then they affect the eye, and we get the sensation of sight. To do this they must vibrate 5000 billion times per second, and if they fail to do this, they fail to give rise to the sensation of sight. If the aetherial waves fall below this limit, then they affect the body, and give rise to the sensation of heat. For it must be remembered, that as the ear has a certain compass for sound waves, which may vary in different individuals, so the eye has also a certain compass for aetherial waves, with the result that some waves may be too slow or too rapid to affect the eye, and consequently fail to give rise to the sensation of sight. When that is so, the sensation of warmth helps us to detect these longer waves, so that the longer waves would warm us and make their presence felt in that manner. We shall see in the next chapter that there are both shorter and longer waves, which may be detected in other ways. From these facts it can be readily seen, that we have a common origin for both light and heat, and that they are both due to periodic waves in the Aether, and therefore all the laws that govern heat should also govern the phenomena of light. Further, if heat possesses a dynamical value, and if there be such a truth as the motive power of heat, then there ought equally to be a motive power of light; and further, if heat possesses a repulsive motion, then because of the identity of light and heat, light should equally possess this repulsive power, because it is due to similar periodic wave motions in the Aether. With regard to the same laws governing both light and heat, we shall see that this fact also holds good. We have already seen ([Art. 66]) that the intensity of heat is inversely as the square of the distance, and we shall also see in the succeeding chapter that the same law holds good in relation to light. We have seen ([Art. 65]) that the path of a ray of heat is that of a straight line; we shall see in the succeeding chapter that the path of a ray of light is that of a straight line also.
Indeed, there is no law applicable to heat which is not applicable to light. The law of reflection and refraction of heat equally holds good in relation to light; and further, Professor Forbes has shown that heat can be polarized in a similar manner to the polarization of light. This last fact is considered the most conclusive argument as to the identity of light and heat, and proves that the only difference between the two is simply the difference corresponding to the difference between a high note and a low note in sound. That being so, I hope to be able to show that as heat possesses a dynamical value, so light equally possesses a dynamical value, and that as heat is a repulsive motion, then light must equally possess a similar repulsive motion, that motion always being directed from the central body, being caused by the same agency, viz. the waves of the Aether, the common source of both light and heat. I purpose to address myself to this subject in the following chapter, which I have termed Light, a Mode of Motion.
[CHAPTER VII]
LIGHT, A MODE OF MOTION
Art. 70. Light, a Mode of Motion.--No subject has in the past received greater attention from philosophers and scientists than that involved in the question as to “What is Light?” Indeed, it may truthfully be said, that even to-day its exact character is not positively known. That it is due like heat to some periodic wave motion in the Aether is known, but the exact character of that wave motion has yet to be determined. As in the case of heat, so in the case of light, there have been two theories which have contended with each other for supremacy in endeavouring to answer the question as to “What is Light?” Those two theories are known as the Emission or Corpuscular Theory, and the Undulatory or Wave Theory. The corpuscular theory was introduced and developed by Newton in his work on Optics, which ranks second only to the Principia as a work revealing masterly research and scientific genius. Newton supposed that a luminous or lighted body actually emitted minute particles, which were shot out from the body with the velocity of light, that is, at the rate of 186,000 miles per second. These minute particles he termed corpuscles. In the work just referred to regarding this matter, he asks the question, “Are not rays of light very small bodies emitted from shining substances?” These small particles or corpuscles were supposed by him to actually strike the retina of the eye, and so produce the sensation of Sight, in the same way that odorous particles entering the nostril, come into contact with the olfactory nerves and produce the sensation of Smell. In order, however, to account for certain phenomena of light, he was compelled to postulate an aetherial medium to fill all space, in which his luminous corpuscles travelled, and which would excite waves in that medium. In his eighteenth query on this point he asks: “Is not the heat of a warm room conveyed through the vacuum by the vibration of a much subtler medium than air, and is not this medium the same with that medium by which light is reflected or refracted, and by whose vibrations light communicates Heat to bodies, and is put into fits of easy reflection and easy transmission?” The corpuscular theory, however, received its death-blow when, in competition with the wave theory of light, as developed by Young, it was found that the latter theory satisfactorily accounted for certain phenomena as the refraction of light, which the corpuscular theory did not adequately account for. Even while Newton was developing his theory, Huyghens, a contemporary of Newton, was developing another theory which is now known as the undulatory or wave theory. Huyghens drew his conclusions from the analogy of sound. He knew that sounds were propagated by waves through the air, and from the region of the known, endeavoured to carry the principle into the region of the unknown, a strictly philosophical method, and one in accordance with the second Rule of Philosophy. He supposed that light, therefore, like sound, might be due to wave motion, but if it were wave motion, there must have been a medium to propagate the waves. In order to account for this wave motion, he supposed all space to be filled with a luminiferous Aether, which would be to his light waves what air is to sound waves. In this conception he was supported by Euler the mathematician, and in 1690 he was able to give a satisfactory explanation of the reflection and refraction of light, on the hypothesis that light was due to wave motion in the Aether. It was not, however, till the advent of Thomas Young, that the undulatory or wave theory reached its perfection, and finally overthrew its competitor the corpuscular theory. Young made himself thoroughly acquainted with wave motion of all kinds, and applied his knowledge and experience to the phenomena of light, and from the analogies so obtained, he gradually built up the undulatory theory, and gave to it a foundation from which it has not yet been moved. Young made use of the same aetherial medium in order to propagate the wave motion of light in the same way that Huyghens did. From that conception, the Aether has been gradually perfected, until we have the conception which has been presented to the reader in Chapter [IV]., in which I have endeavoured to show that this aetherial medium is matter, but infinitely more rarefied and infinitely more elastic, but notwithstanding its extreme rarefaction and elasticity, it possesses inertia, because it is gravitative. It is this Aether, then, that is concerned in the propagation of light, and is the universal medium which is to light what air is to sound. Young, therefore, having applied himself to the wave motion of sound, from such researches was able to explain the physical cause of colour, and that phenomenon termed interference.