Part 13

1.290

for the motive power developed by 1000 units of heat acting upon the vapor of water between one degree and zero. This number approximates more closely than the first to

1.395.

It differs from it only ¹⁄₁₃, an error which does not exceed probable limits, considering the great number of data of different sorts of which we have been obliged to make use in order to arrive at this approximation. Thus is our fundamental law verified in a special case.

We will examine another case in which vapor of alcohol is acted upon by heat. The reasoning is precisely the same as for the vapor of water. The data alone are changed. Pure alcohol boils under ordinary pressure at 78°.7 Centigrade. One kilogram absorbs, according to MM. Delaroche and Bérard, 207 units of heat in undergoing transformation into vapor at this same temperature, 78°.7.

The tension of the vapor of alcohol at one degree below the boiling-point is found to be diminished ¹⁄₂₅. It is ¹⁄₂₅ less than the atmospheric pressure; at least, this is the result of the experiment of M. Bétancour reported in the second part of l’Architecture hydraulique of M. Prony, pp. 180, 195.

If we use these data, we find that, in acting upon one kilogram of alcohol at the temperatures of 78°.7 and 77°.7, the motive power developed will be 0.251 units.

This results from the employment of 207 units of heat. For 1000 units the proportion must be

(207)/(0.254) = (1000)/(x), whence x = 1.230.

This number is a little more than the 1.112 resulting from the use of the vapor of water at the temperatures 100° and 99°; but if we suppose the vapor of water used at the temperatures 78° and 77°, we find, according to the law of MM. Clement and Desorme, 1.212 for the motive power due to 1000 units of heat. This latter number approaches, as we see, very nearly to 1.230. There is a difference of only ¹⁄₅₀.

We should have liked to be able to make other approximations of this sort—to be able to calculate, for example, the motive power developed by the action of heat on solids and liquids, by the congelation of water, and so on; but Physics as yet refuses us the necessary data.

The fundamental law that we propose to confirm seems to us to require, however, in order to be placed beyond doubt, new verifications. It is based upon the theory of heat as it is understood to-day, and it should be said that this foundation does not appear to be of unquestionable solidity. New experiments alone can decide the question. Meanwhile we can apply the theoretical ideas expressed above, regarding them as exact, to the examination of the different methods proposed up to date, for the realization of the motive power of heat.

It has sometimes been proposed to develop motive power by the action of heat on solid bodies. The mode of procedure which naturally first occurs to the mind is to fasten immovably a solid body—a metallic bar, for example—by one of its extremities; to attach the other extremity to a movable part of the machine; then, by successive heating and cooling, to cause the length of the bar to vary, and so to produce motion. Let us try to decide whether this method of developing motive power can be advantageous. We have shown that the condition of the most effective employment of heat in the production of motion is, that all changes of temperature occurring in the bodies should be due to changes of volume. The nearer we come to fulfilling this condition the more fully will the heat be utilized. Now, working in the manner just described, we are very far from fulfilling this condition: change of temperature is not due here to change of volume; all the changes are due to contact of bodies differently heated—to the contact of the metallic bar, either with the body charged with furnishing heat to it, or with the body charged with carrying it off.

The only means of fulfilling the prescribed condition would be to act upon the solid body exactly as we did on the air in the operations described on page 92. But for this we must be able to produce, by a single change of volume of the solid body, considerable changes of temperature, that is, if we should want to utilize considerable falls of caloric. Now this appears impracticable. In short, many considerations lead to the conclusion that the changes produced in the temperature of solid or liquid bodies through the effect of compression and rarefaction would be but slight.

(1) We often observe in machines (particularly in steam-engines) solid pieces which endure considerable strain in one way or another, and although these efforts may be sometimes as great as the nature of the substances employed permits, the variations of temperature are scarcely perceptible.

(2) In the action of striking medals, in that of the rolling-mill, of the draw-plate, the metals undergo the greatest compression to which we can submit them, employing the hardest and strongest tools. Nevertheless the elevation of temperature is not great. If it were, the pieces of steel used in these operations would soon lose their temper.

(3) We know that it would be necessary to exert on solids and liquids a very great strain in order to produce in them a reduction of volume comparable to that which they experience in cooling (cooling from 100° to zero, for example). Now the cooling requires a greater abstraction of caloric than would simple reduction of volume. If this reduction were produced by mechanical means, the heat set free would not then be able to make the temperature of the body vary as many degrees as the cooling makes it vary. It would, however, necessitate the employment of a force undoubtedly very considerable.

Since solid bodies are susceptible of little change of temperature through changes of volume, and since the condition of the most effective employment of heat for the development of motive power is precisely that all change of temperature should be due to a change of volume, solid bodies appear but ill fitted to realize this power.

The same remarks apply to liquids. The same reasons may be given for rejecting them.

We are not speaking now of practical difficulties. They will be numberless. The motion produced by the dilatation and compression of solid or liquid bodies would only be very slight. In order to give them sufficient amplitude we should be forced to make use of complicated mechanisms. It would be necessary to employ materials of the greatest strength to transmit enormous pressure; finally, the successive operations would be executed very slowly compared to those of the ordinary steam-engine, so that apparatus of large dimensions and heavy cost would produce but very ordinary results.

The elastic fluids, gases or vapors, are the means really adapted to the development of the motive power of heat. They combine all the conditions necessary to fulfil this office. They are easy to compress; they can be almost infinitely expanded; variations of volume occasion in them great changes of temperature; and, lastly, they are very mobile, easy to heat and to cool, easy to transport from one place to another, which enables them to produce rapidly the desired effects. We can easily conceive a multitude of machines fitted to develop the motive power of heat through the use of elastic fluids; but in whatever way we look at it, we should not lose sight of the following principles:

(1) The temperature of the fluid should be made as high as possible, in order to obtain a great fall of caloric, and consequently a large production of motive power.

(2) For the same reason the cooling should be carried as far as possible.

(3) It should be so arranged that the passage of the elastic fluid from the highest to the lowest temperature should be due to increase of volume; that is, it should be so arranged that the cooling of the gas should occur spontaneously as the effect of rarefaction. The limits of the temperature to which it is possible to bring the fluid primarily, are simply the limits of the temperature obtainable by combustion; they are very high.

The limits of cooling are found in the temperature of the coldest body of which we can easily and freely make use; this body is usually the water of the locality.

As to the third condition, it involves difficulties in the realization of the motive power of heat when the attempt is made to take advantage of great differences of temperature, to utilize great falls of heat. In short, it is necessary then that the gas, by reason of its rarefaction, should pass from a very high temperature to a very low one, which requires a great change of volume and of density, which requires also that the gas be first taken under a very heavy pressure, or that it acquire by its dilatation an enormous volume—conditions both difficult to fulfil. The first necessitates the employment of very strong vessels to contain the gas at a very high temperature and under very heavy pressure. The second necessitates the use of vessels of large dimensions. These are, in a word, the principal obstacles which prevent the utilization in steam-engines of a great part of the motive power of the heat. We are obliged to limit ourselves to the use of a slight fall of caloric, while the combustion of the coal furnishes the means of procuring a very great one.

It is seldom that in steam-engines the elastic fluid is produced under a higher pressure than six atmospheres—a pressure corresponding to about 160° Centigrade, and it is seldom that condensation takes place at a temperature much under 40°. The fall of caloric from 160° to 40° is 120°, while by combustion we can procure a fall of 1000° to 2000°.

In order to comprehend this more clearly, let us recall what we have termed the fall of caloric. This is the passage of the heat from one body, A, having an elevated temperature, to another, B, where it is lower. We say that the fall of the caloric is 100° or 1000° when the difference of temperature between the bodies A and B is 100° or 1000°.