The Energy System of Matter: A Deduction from Terrestrial Energy Phenomena

In everyday life, rough ideas of heat energy are constantly being obtained by the aid of the senses. This method is, however, only another aspect of transmission, for it will be clear that the sensations of heat and cold are, in themselves, but the evidence of the transformation of heat energy to or from the body.

The process of energy transmission by a flexible band or cord (§ 28) also provides evidence leading to the identification of the peculiar form of energy which is being transmitted. At first sight, it would appear as if this energy were simply energy of motion or kinetic energy. A little reflection, however, on the general conditions of the process must dispel this idea, for it is clear that the precise nature of the energy transmitted has no real connection with the kinetic properties of the system. The latter, truly, influence the rate of transmission and impose certain limits, but evidently, if the pull in the band increases without any increase in its velocity, the actual amount of energy transmitted by the system would increase without altering in any respect the kinetic properties. It becomes necessary, then, to distinguish clearly the energy inherent to, or as it were, latent in the system, from the energy actually transmitted by the system, to recognise the difference between the energy transmitted by moving material and the energy of that material. In this special instance, to identify the form of energy transmitted it must of necessity be associated with the peculiar phenomena of transmission. Now the energy is evidently transmitted by the movement of the connecting belt or band. Before any transmission can take place, however, a certain amount of energy must be stored in the moving system, partly as cohesion or strain energy and partly as energy of motion or kinetic energy. It is this preliminary storage of energy which, in reality, constitutes the transmission machine, and for a given rate of transmission, the energy thus stored will be constant in value. It is obtained at the expense of the applied energy, and, neglecting certain minor processes, will be returned (or transmitted) in its entirety when the moving system once more comes to rest. This stored energy, in fact, works in a reversible process. But when the transmission machine is once constituted, the energy transmitted is then that energy which is being continually applied at the spindle A (Fig. 4) and as continually withdrawn at the spindle B. It must be emphasised that the energy thus transmitted is absolutely different from the kinetic or other energy associated with the moving material of the system. It is the function of this energised material of the band to transmit the energy from A to B, but this is the only relationship which the transmitted energy bears to the material. The energy thus transmitted by the moving material we term mechanical or work energy. We may thus define mechanical or work energy as "that form of energy transmitted by matter in motion."

The idea of work is usually associated with that of a force acting through a certain distance. The form of energy referred to above as work energy is, in the same way, always associated with the idea of a thrust or of a pressure of some kind acting on moving material. Work energy thus bears two aspects, which really correspond to the familiar product of pressure and volume. Both aspects are manifested in transmission. Since work energy is invariably transmitted by matter in motion, every machine for its transmission must possess energy of motion as one of its essential features. As shown above (see also § 28), this energy of motion is really obtained at the expense of the originally applied work energy, and as it remains unaltered in value during the progress of a uniform transmission, it may be regarded as simply transformed work energy, stored or latent in the system, which will be returned in its entirety and in its original form at the termination of the operation. The energy stored against cohesion or other forces may be regarded in the same way. It is really the manifestation of the pressure or thrust aspect of the work energy, just as the kinetic energy is the manifestation of the translational or velocity aspect.

Our definition of work energy given above enables us to recognise its operation in many familiar processes. Take the case of a gas at high pressure confined in a cylinder behind a movable piston. We can at once say that the energy of the gas is work energy because this energy may quite clearly be transmitted from the gas by the movement of the piston. If the latter form part of a steam-engine mechanism of rods and crank, the energy may, by the motion of this mechanism, be transmitted to the crank shaft, and there utilised. This is eminently a case in which energy is transmitted by matter in motion. The moving material comprises the piston, piston-rod, and connecting-rod, which are, one and all, endowed with both cohesive and kinetic energy qualities, and form together the transmission machine. So long as the piston is at rest only one aspect of the work energy of the gas is apparent, namely, the pressure aspect, but immediately motion and transmission take place, both aspects are presented. The work energy of the gas, obtained in the boiler by a transformation of heat energy is thus, by matter in motion, transmitted and made available at the crank shaft. The shaft itself is also commonly utilised for the further transmission of the work energy applied. By the application of the energy at the crank, it is thrown into a state of strain, and at the same time is endowed with kinetic energy of rotation. It thus forms a machine for transmission, and the work energy applied at one point of the shaft may be withdrawn at another point more remote. The transmission is, in reality, effected by the movement of the material of the shaft. So long as the shaft is stationary, it is clear that no actual transmission can be carried out, no matter how great may be the strain imposed. If our engine mechanism were, by a change in design, adapted to the use of a liquid substance as the working material instead of a gas, it is clear that no change would be effected in the general conditions. The energy of a liquid under pressure is again simply work energy, and it would be transmitted by the moving mechanism in precisely the same manner.

From the foregoing, it will now be evident to the reader that the energy originally applied to the primary mass (§ 3) of our cosmical system must be work energy. It is this form of energy also which is inherent to each unit of the planetary system associated with the primary. In this system it is of course presented outwardly in the two phases of kinetic energy and energy of strain or distortion. It is apparent, also, that work energy could be transmitted from the primary mass to the separate planets on one condition only, that is, by the movement of some material substance connecting each planet to the primary. Since no such material connection is admitted, the transmission of work energy is clearly impossible.

32. Complete Secondary Cyclical Operation

A general outline of the conditions of working and the relationships of secondary processes has already been given in the General Statement (§ 9), but it still remains to indicate, in a broad way, the general methods whereby these operations are linked to the atmospheric machine. In the example of the simple pendulum, it has been pointed out that the energy processes giving rise to heating at the bearing surfaces and transmission of energy to the air masses are not directly reversible processes, but really form part of a more extensive cyclical operation, in itself, however, complete and self-contained. This cyclical operation may be regarded as a typical illustration of the manner in which separate processes of energy transmission or transformation, such as already described, are combined or united in a continuous chain forming a complete whole.

It has been assumed, in all the experiments with the pendulum, that the operating energy is initially communicated from an outside source, say the hand of the observer. This energy is, therefore, the acting energy which must be traced through all its various phases from its origin to its final destination. At the outset, it may be pointed out that this energy, applied by hand, is obtained from the original rotational energy of the earth by certain definite energy processes. Due to the influences of various incepting fields which emanate from the sun (§§ 17-19), a portion of the earth's rotational energy is transformed into that form of plant energy which is stored in plant tissue, and which, by the physico-chemical processes of digestion, is in turn converted into heat and the various other forms of energy associated with the human frame. This, then, is the origin of the energy communicated to the pendulum. Its progress through that machine has already been described in detail (§§ 21-26). The transformation of energy of motion to energy of position which takes place is in itself a reversible process and may in the meantime be neglected. But the final result of the operations, at the bearing surfaces and in the air masses surrounding the moving pendulum, was shown to be, in each case, that heat energy was communicated to these air masses. The effect of the heat energy thus impressed, is to cause the expansion of the air and its elevation from the surface of the earth in the lines or field of the gravitative attraction, so that this heat energy is transformed, and resides in the air masses as energy of position. The energy then, originally drawn from the rotational energy of the earth, has thus worked through the pendulum machine, and is now stored in the air masses in this form of energy of position. To make the process complete and cyclical this energy must now, therefore, be returned once more to the earth in its original rotational form. This final step is carried out in the atmospheric machine (§ 41). In this machine, therefore, the energy of position possessed by the air masses is, in their descent to their original positions at lower levels, transformed once more into axial or rotational energy. In this fashion this series of secondary processes, involving both transformations and transmissions, is linked to the great atmospheric process. The amount of energy which operates through the particular chain of processes we have described is, of course, exceedingly small, but in this or a similar manner all secondary operations, great or small, are associated with the atmospheric machine. Instances could readily be multiplied, but a little reflection will show how almost every energy operation, no matter what may be its nature, whether physical, chemical, or electrical, leads inevitably to the communication of energy to the atmospheric air masses and to their consequent upraisal.

It is interesting to note the infallible tendency of energy to revert to its original form of axial energy, or energy of rotation, by means of the air machine. All Nature bears witness to this tendency, and although the path of energy through the maze of terrestrial transformation often appears tortuous and uncertain, its final destination is always sure. The secondary operations are thus interlinked into one great whole by their association in the terrestrial energy cycle. Many of these secondary operations are of short duration; others extend over long periods of time. Energy, in some cases, appears to slumber, as in the coal seams of the earth, until an appropriate stimulus is applied, when it enters into active operation once more. The cyclical operations are thus long or short according to the duration of their constituent secondary energy processes. But the balance of Nature is ever preserved. Axial energy, transformed by the working of one cyclical process, is being as continuously returned by the simultaneous operation of others.

PART III

TERRESTRIAL CONDITIONS

33. Gaseous Expansion

Before proceeding to the general description of the atmospheric machine (§ 10), it is desirable to consider one or two features of gaseous reaction which have a somewhat important bearing on its working. Let it be assumed that a mass of gaseous material is confined within the lower portion of a narrow tube ABCD (Fig. 8) assumed to be thermally non-conducting; the upper portion of the tube is in free communication with the atmosphere. The gas within the tube is assumed to be isolated from the atmosphere by a movable piston EF, free to move vertically in the tube, and for the purpose of illustration, assumed also frictionless and weightless. With these assumptions, the pressure on the confined gas will simply be that due to the atmosphere. If heat energy be now applied to the gas, its temperature will rise and expansion will ensue. This expansion will be carried out at constant atmospheric pressure; the gaseous material, as it expands, must lift with it the whole of the superimposed atmospheric column against the downward attractive force of the earth's gravitation on that column. Work is thus done by the expanding gas, and in consequence of this work done, a definite quantity of atmospheric material gains energy of position or potential energy relative to the earth's surface. At the same time, the rise of temperature of the gas will indicate an accession of heat energy to its mass. These familiar phenomena of expansion under constant pressure serve to illustrate the important fact that, when heat energy is applied to a gaseous mass, it really manifests itself therein in two aspects, namely, heat energy and work energy. The increment of heat energy is indicated by the increase in temperature, the increment of work energy by the increase in pressure. In the example just quoted, however, there is no increase in pressure, because the work energy, as rapidly as it is applied to the gas, is transformed or worked down in displacing the atmospheric column resting on the upper side of the moving piston. The energy applied, in the form of heat from the outside source, has in reality been introduced into a definite energy machine, a machine in this case adapted for the complete transformation of work energy into energy of position. As already indicated, when the expansive movement is completed, the volume and temperature of the gaseous mass are both increased but the pressure remains unaltered. While the increase in temperature is the measure and index of a definite increase in the heat energy of the gas, it is important to note that, so far as its work energy is concerned, the gas is finally in precisely the same condition as at the commencement of the operation. Work energy has been, by the working of this energy machine, as it were passed through the gaseous mass into the surrounding atmosphere. The pressure of the gas is the true index of its work energy properties. So long as the pressure remains unaltered, the inherent work energy of the material remains absolutely unaffected. A brief consideration of the nature of work energy as already portrayed (§ 31) will make this clear. Work energy has been defined as "that form of energy transmitted by matter in motion," and it is clear that pressure is the essential factor in any transmission of this nature. Temperature has no direct bearing on it whatever. It is common knowledge, however, that in the application of heat energy to a gaseous substance, the two aspects of pressure and temperature cannot be really dissociated. They are mutually dependent. Any increment of heat energy to the gas is accompanied by an increment of work energy, and vice versa. The precise mode of action of the work energy will, of course, depend on the general circumstances of the energy machine in which it operates. In the case just considered the work energy does not finally reside in the gaseous mass itself, but, by the working of the machine, is communicated to the atmosphere. If, on the other hand, heat energy were applied in the same fashion to a mass of gas in a completely enclosed vessel, that is to say at constant volume instead of at constant pressure, the general phenomena are merely altered in degree according to the change in the precise nature of the energy machine. In the former case, the nature of the energy machine was such that the work energy communicated was expended in its entirety against gravitation. Under what is usually termed constant volume conditions, only a portion of the total work energy communicated is transformed, and the transformation of this portion is carried out, not against gravitation, but against the cohesive forces of the material of the enclosing vessel which restrains the expansion. No matter how great may be the elastic properties of this material, it will be distorted, more or less, by the application of work energy. This distortional movement is the external evidence of the energy process of transformation. Energy is stored in the material against the forces of cohesion (§ 15). But the energy thus stored is only a small proportion of the total work energy which accrues to the gas in the heating process. The remainder is stored in the gas itself, and the evidence of such storage is found simply in the increase of pressure. Different energy machines thus offer different facilities for the transformation or the storage of the applied energy. In every case where the work energy applied has no opportunity of expending itself, its presence will be indicated by an increase in the pressure or work function of the gas.

Fig. 8

The principles which underlie the above phenomena can readily be applied to other cases of gaseous expansion. It is a matter of common experience that if a given mass of gaseous material be introduced into a vessel which has been exhausted by an air-pump or other device for the production of a vacuum, the whole space within the vessel is instantly permeated by the gas, which will expand until its volume is precisely that of the containing vessel. Further phenomena of the operation are that the expanding gas suffers a decrease in temperature and pressure corresponding to the degree or ratio of the expansion. Before the expansive process took place the gaseous mass, as indicated by its initial temperature and pressure, is endowed with a definite quantity of energy in the form of heat and work energy. After expansion, these quantities are diminished, as indicated by its final and lower temperature and pressure. The operation of expansion has thus involved an expenditure of energy. This expenditure takes place in virtue of the movement of the gaseous material (§ 4). It is obvious that if the volume of the whole is to be increased, each portion of the expanding gas requires to move relatively to the remainder. This movement is carried out in the lines of the earth's gravitative attraction, and to a certain extent over the surface of the containing vessel. In some respects, it thus corresponds simply to the movement of a body over the earth's surface (§ 16). It is also carried out against the viscous or frictional forces existing throughout the gaseous material itself (§ 29). Assuming no influx of energy from without, the energy expended in the movement of the gaseous material must be obtained at the expense of the inherent heat and work energy of the gas, and these two functions will decrease simultaneously. The heat and work energy of the gas or its inherent energy is thus taken to provide the energy necessary for the expansive movement. This energy, however, does not leave the gas, but still resides therein in a form akin to that of energy of position or separation. It will be clear also, that the reverse operation cannot, in this case, be carried out; the gas cannot move back to its original volume in the same fashion as it expanded into the vacuum, so that the energy utilised in this way for separation cannot be directly returned.

The expansion of the gas has been assumed above to take place into a vacuous space, but a little consideration will show that this condition cannot be properly or even approximately fulfilled under ordinary experimental conditions. The smallest quantity of gas introduced into the exhausted vessel will at once completely fill the vacuous space, and, on this account, the whole expansion of the gas does not in reality take place in vacuo at all. To study the action of the gas under the latter conditions, it is necessary to look on the operation of expansion in a more general way, which might be presented as follows.

34. Gravitational Equilibrium of Gases

Consider a planetary body, in general nature similar to the earth, but, unlike the earth, possessing no atmosphere whatever. The space surrounding such a celestial mass may then be considered as a perfect vacuum. Now let it be further assumed that in virtue of some change in the conditions, a portion of the material of the planetary mass is volatilised and a mass of gas thereby liberated over its surface. The gas is assumed to correspond in temperature to that portion of the planet's surface with which it is in contact. It is clear that, in the circumstances, the gas, in virtue of its elastic and energetic properties, will expand in all directions. It will completely envelop the planet, and it will also move radially outwards into space. In these respects, its expansion will correspond to that of a gas introduced into a vacuous space of unlimited extent.

The question now arises as to the nature of the action of the gaseous substance in these circumstances. It is clear that the radial or outward movement of the gas from the planetary surface is made directly against the gravitative attraction of the planet on the gaseous mass. In other words, matter or material is being moved in the lines or field of this gravitative force. This movement, accordingly, will be productive of an energy transformation (§ 4). In its initial or surface condition each portion of the gaseous mass is possessed of a perfectly definite amount of energy indicated by and dependent on that condition. As it moves upwards from the surface, it does work against gravity in the raising of its own mass. But as the mass is thus raised, it is gaining energy of position (§ 20), and as it has absolutely no communication with any external source of energy in its ascent, the energy of position thus gained can only be obtained at the expense of its initial inherent heat and work energy. The operation is, in fact, a simple transformation of this inherent energy into energy of position, a transformation in which gravity is the incepting agency. The external evidence of transformation will be a fall in temperature of the material. Since the action is exactly similar for all ascending particles, it is evident that as the altitude of the gaseous mass increases the temperature will correspondingly diminish. This diminution will proceed so long as the gaseous particles continue to ascend, and until an elevation is finally attained at which their inherent energy is entirely converted into energy of position. The expansion of the gas, and the associated transformation of energy, thus leads to the erection of a gaseous column in space, the temperature of which steadily diminishes from the base to the summit. At the latter elevation, the inherent energy of the gaseous particles which attain to it is completely transformed or worked out against gravity in the ascent; the energy possessed by the gas at this elevation is, therefore, entirely energy of position; the energy properties of heat and work have entirely vanished, and the temperature will, therefore, at this elevation, be absolute zero. It is important to note also that in the building of such a column or gaseous spherical envelope round the planet, the total energy of any gaseous particle of that column will remain unchanged throughout the process. No matter where the particle may be situated in the column, its total energy must always be expressed by its heat and work energy properties together with its energy of position. This sum is always a constant quantity. For if the particle descends from a higher to a lower altitude, its total energy is still unchanged, because a definite transformation of its energy of position takes place corresponding to its fall, and this transformed energy duly appears in its original form of heat and work energy in accordance with the decreased altitude of the particle. Since the temperature of the column remains unchanged at the base surface and only decreases in the ascent, it is clear that the entire heat and work energy of the originally liberated gaseous mass is not expended in the movement against gravity. Every gaseous particle—excepting those on the absolute outer surface of the gaseous envelope—has still the property of temperature. It is evident, therefore, that in the constitution of the column, only a portion of the total original heat and work energy of the gaseous substance is transformed into energy of position.