Part 7

FIG. 1. ]

This preliminary idea being established, let us imagine an elastic fluid, atmospheric air for example, shut up in a cylindrical vessel, abcd (Fig. 1), provided with a movable diaphragm or piston, cd. Let there be also two bodies, A and B, kept each at a constant temperature, that of A being higher than that of B. Let us picture to ourselves now the series of operations which are to be described:

(1) Contact of the body A with the air enclosed in the space abcd or with the wall of this space—a wall that we will suppose to transmit the caloric readily. The air becomes by such contact of the same temperature as the body A; cd is the actual position of the piston.

(2) The piston gradually rises and takes the position ef. The body A is all the time in contact with the air, which is thus kept at a constant temperature during the rarefaction. The body A furnishes the caloric necessary to keep the temperature constant.

(3) The body A is removed, and the air is then no longer in contact with any body capable of furnishing it with caloric. The piston meanwhile continues to move, and passes from the position ef to the position gh. The air is rarefied without receiving caloric, and its temperature falls. Let us imagine that it falls thus till it becomes equal to that of the body B; at this instant the piston stops, remaining at the position gh.

(4) The air is placed in contact with the body B; it is compressed by the return of the piston as it is moved from the position gh to the position cd. This air remains, however, at a constant temperature because of its contact with the body B, to which it yields its caloric.

(5) The body B is removed, and the compression of the air is continued, which being then isolated, its temperature rises. The compression is continued till the air acquires the temperature of the body A. The piston passes during this time from the position cd to the position ik.

(6) The air is again placed in contact with the body A. The piston returns from the position ik to the position ef; the temperature remains unchanged.

(7) The step described under number 3 is renewed, then successively the steps 4, 5, 6, 3, 4, 5, 6, 3, 4, 5; and so on.

In these various operations the piston is subject to an effort of greater or less magnitude, exerted by the air enclosed in the cylinder; the elastic force of this air varies as much by reason of the changes in volume as of changes of temperature. But it should be remarked that with equal volumes, that is, for the similar positions of the piston, the temperature is higher during the movements of dilatation than during the movements of compression. During the former the elastic force of the air is found to be greater, and consequently the quantity of motive power produced by the movements of dilatation is more considerable than that consumed to produce the movements of compression. Thus we should obtain an excess of motive power—an excess which we could employ for any purpose whatever. The air, then, has served as a heat-engine; we have, in fact, employed it in the most advantageous manner possible, for no useless re-establishment of equilibrium has been effected in the caloric.

All the above-described operations may be executed in an inverse sense and order. Let us imagine that, after the sixth period, that is to say the piston having arrived at the position ef, we cause it to return to the position ik, and that at the same time we keep the air in contact with the body A. The caloric furnished by this body during the sixth period would return to its source, that is, to the body A, and the conditions would then become precisely the same as they were at the end of the fifth period. If now we take away the body A, and if we cause the piston to move from ef to cd, the temperature of the air will diminish as many degrees as it increased during the fifth period, and will become that of the body B. We may evidently continue a series of operations the inverse of those already described. It is only necessary under the same circumstances to execute for each period a movement of dilatation instead of a movement of compression, and reciprocally.

The result of these first operations has been the production of a certain quantity of motive power and the removal of caloric from the body A to the body B. The result of the inverse operations is the consumption of the motive power produced and the return of the caloric from the body B to the body A; so that these two series of operations annul each other, after a fashion, one neutralizing the other.

The impossibility of making the caloric produce a greater quantity of motive power than that which we obtained from it by our first series of operations, is now easily proved. It is demonstrated by reasoning very similar to that employed at page 56; the reasoning will here be even more exact. The air which we have used to develop the motive power is restored at the end of each cycle of operations exactly to the state in which it was at first found, while, as we have already remarked, this would not be precisely the case with the vapor of water.

We have chosen atmospheric air as the instrument which should develop the motive power of heat, but it is evident that the reasoning would have been the same for all other gaseous substances, and even for all other bodies susceptible of change of temperature through successive contractions and dilatations, which comprehends all natural substances, or at least all those which are adapted to realize the motive power of heat. Thus we are led to establish this general proposition:

The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of the caloric.

We must understand here that each of the methods of developing motive power attains the perfection of which it is susceptible. This condition is found to be fulfilled if, as we remarked above, there is produced in the body no other change of temperature than that due to change of volume, or, what is the same thing in other words, if there is no contact between bodies of sensibly different temperatures.

Different methods of realizing motive power may be taken, as in the employment of different substances, or in the use of the same substance in two different states—for example, of a gas at two different densities.

This leads us naturally to those interesting researches on the aeriform fluids—researches which lead us also to new results in regard to the motive power of heat, and give us the means of verifying, in some particular cases, the fundamental proposition above stated.

We readily see that our demonstration would have been simplified by supposing the temperatures of the bodies A and B to differ very little. Then the movements of the piston being slight during the periods 3 and 5, these periods might have been suppressed without influencing sensibly the production of motive power. A very little change of volume should suffice in fact to produce a very slight change of temperature, and this slight change of volume may be neglected in presence of that of the periods 4 and 6, of which the extent is unlimited.

If we suppress periods 3 and 5, in the series of operations above described, it is reduced to the following:

(1) Contact of the gas confined in abcd (Fig. 2) with the body A, passage of the piston from cd to ef.

FIG. 2. FIG. 3. ]

(2) Removal of the body A, contact of the gas confined in abef with the body B, return of the piston from ef to cd.

(3) Removal of the body B, contact of the gas with the body A, passage of the piston from cd to ef, that is, repetition of the first period, and so on.

The motive power resulting from the ensemble of operations 1 and 2 will evidently be the difference between that which is produced by the expansion of the gas while it is at the temperature of the body A, and that which is consumed to compress this gas while it is at the temperature of the body B.

Let us suppose that operations 1 and 2 be performed on two gases of different chemical natures but under the same pressure—under atmospheric pressure, for example. These two gases will behave exactly alike under the same circumstances, that is, their expansive forces, originally equal, will remain always equal, whatever may be the variations of volume and of temperature, provided these variations are the same in both. This results obviously from the laws of Mariotte and MM. Gay-Lussac and Dalton—laws common to all elastic fluids, and in virtue of which the same relations exist for all these fluids between the volume, the expansive force, and the temperature.

Since two different gases at the same temperature and under the same pressure should behave alike under the same circumstances, if we subjected them both to the operations above described, they should give rise to equal quantities of motive power.

Now this implies, according to the fundamental proposition that we have established, the employment of two equal quantities of caloric; that is, it implies that the quantity of caloric transferred from the body A to the body B is the same, whichever gas is used.