INVESTIGATION OF THE SPECIFIC HEATS OF ELASTIC FLUIDS. 



134 



mechanical work, and that, reciprocal!)', mechanical work may be 

 transformed into heat. In the theory of Carnot, the quantity of 

 heat possessed by the elastic fluid at its entrance into the engine 

 is found entirely in the elastic fluid which issues from it, or in the 

 "condenser ; the work is done merely by the passage of the heat 

 from the boiler into the condenser, while it traverses the engine. 

 In the new theory, this quantity of heat is not entirely preserved 

 in the form of heat; a portion disappears during its passage 

 through the machine, and the work done is in every case propor- 

 tional to the quantity of heat lost. Thus, in a steam engine with 

 or without condensation, with or without cut-off, the work done by 

 the machine is proportional to the difference between the quantity 

 of heat which the vapour has at its entrance into the machine, and 

 that which it keeps at the moment of its exit or condensation. In 

 this theory, to obtain the maximum mechanical effect from a 

 given quantity of heat, we must make this loss of heat the greatest 

 possible ; that is to say, the elastic force which the expanded steam 

 keeps at the moment of its entrance into the condenser must be 

 as small as possible. But in every case, in the steam engine, the 

 quantity of heat utilised in mechanical work will be but a very 

 small portion of that which we have been obliged to give to the 

 boiler. 



In a steam engine in which the steam is expanded, but not 

 condensed, the steam entering under a pressure of five atmos- 

 pheres, and discharged at atmospheric, pressure, the quantity of 

 heat which the steam has, when it enters the machine, is, accord- 

 ing to my experiments, about 653 units; that which it retains at 

 its discharge, 637. According to the theory of which I am 

 speaking, the quantity of heat utilised in mechanical work is 

 653 — 637=16 units; that is, only i,th of the quantity of heat 

 given to the boiler. In a condensing engine, receiving its steam 

 at five atmospheres, and the condenser keeping, constantly, an 

 elastic force of 55 min. of mercury, the quantity of heat in the 

 entering steam will be 653 units, and that which it has at the 

 moment of its condensation 619; the heat utilised will be 34 

 units, or a little more than /„ th of the heat given to the boiler. 



A larger portion of the heat may be utilised in mechanical 

 work, either by overheating the steam before its entrance into the 

 machine, or by lowering as much as possible the temperature of 

 the condenser. But this latter means is hard to realise in practice ; 

 it would, moreover, require a considerable increase in the quantity 

 of cold water necessary for effecting the condensation, which 

 wastes power, and the boiler can only be fed by water which is 

 but little heated. We shall attain the same end more easily by 

 expanding the steam to a less degree in the machine, and con- 

 densing the steam by the injection of a very volatile liquid, such 

 as chloroform or ether. The heat which the steam has at the 

 moment of this condensation, and of which but a very small part 

 would have been transformed into mechanical work, passes into 

 the more volatile liquid, which it transforms into vapour of high 

 pressure. By passing this vapour into a second machine, where 

 it expands to the elastic force to which the injection water can 

 practically reduce the condenser, a part of the heat is transformed 

 into mechanical work ; and a calculation founded on the numeri- 

 cal data of my experiments, shows that this quantity is much 

 greater than could have been obtained by the further expansion 

 of steam in the first machine. In this way can be perfectly 

 explained the economical result obtained from two connected 

 machines, the one working with water, the other with ether or 

 chloroform, on which experiments have been recently made. 



In the air engines, where the motive force is produced by the 

 dilatation which heat produces upon the gas in the machine, or 

 by the increase which it produces in its elastic-force, the work 

 done at each stroke of the piston will always be proportional to 

 t-h<s difference of the quantities of heat in the sir entering end 



[1854 



leaving; that is, to the less of heat by the air in traversing the 

 machine! But as, in the Ericsson system, the heat which the 

 air gives out is given up to bodies from which the entering air 

 takes it again, and brings it back to the machine, we see that, 

 theoretically, all the heat expended is utilised for mechanical work ; 

 whilst, in the best steam engine, the heat utilised in mechanical 

 work is not the J-„th part of the heat expended. Be it observed 

 here, that I neglect all the extraneous., sources of loss, as well as 

 the mechanical or practical obstacles which may present them- 

 selves in the application of the principle. 



MM. Joule, Thomson, and Rankine, in England, and MM. 

 Mayer and Clausius, in Germany, starting frequently from differ- 

 ent points of view, have developed analytically this mechanical 

 theory of heat, and have sought to deduce from it the laws of all 

 the phenomena relative to elastic fluids. For my part, I have 

 for a long time expressed, in my courses of lectures, analogous 

 ideas, to which I have been led by my experimental labours upon 

 elastic fluids. In these researches I, in fact, met anomalies which 

 appeared to me inexplicable in the theories before admitted. To 

 give an idea of them, I will cite some of the most simple 

 examples. 



First example. — 1st, A mass of gas, under a pressure of ten 

 atmospheres, enclosed in a space the capacity of wdiich is suddenly 

 doubled, the pressure descends to five atmospheres. 



2nd. Two reservoirs of equal capacity are placed in the same 

 calorimeter ; the one is filled with a gas under ten atmospheres, 

 the second has a complete vacuum ; the communication between 

 the two reservoirs is suddenly opened ; the gas expands into 

 double its volume, and the pressure is al.o reduced to five 

 atmospheres. 



Thus, in the two experiments, the initial and final conditions 

 of the gas are the same; but this identity of conditions is accom- 

 panied by very different caloric results ; for, whilst in the first 

 case a considerable cooling is observed, in the second the calori- 

 meter shows not the least change of temperature. 



Second example. — 1st. A mass of gas traverses, under 

 atmospheric pressure, a worm, in which it is heated to 100° cent; 

 then, a calorimeter, whose initial temperature is 0°. It raises the 

 temperature of the calorimeter 1°. 



2nd. The same mass of gas traverses, under the pressure of 

 ten atmospheres, the worm, in which it is heated to 100°, then 

 the calorimeter at 0° under the same pressure ; it raises the tem- 

 perature of the calorimeter t'°, and experiment shows that t and 

 t' are but slightly different. 



3rd. The same mass of gas, under the pressure of ten atmos- 

 pheres, traverses the worm, in which it is heated to 100°; but 

 when it arrives at the orifice of the calorimeter at 0°, or to any 

 point of its course, the gas dilates, and descends to the pressure 

 of the atmosphere; so that it issues from the calorimeter in 

 equilibrium of temperature with it, and in equilibrium of pressure 

 with the surrounding atmosphere. An elevation of temperature, 

 I", is observed in the calorimeter. 



According to the theories formerly admitted, the quantity of 

 heat abandoned by the gas in experiment No. 3, ought to be 

 equal to that of No. 2, diminished by the quantity of heat which 

 has been absorbed by the gas during the enormous dilatation 

 which it has undergone. On the contrary, experiment shows a 

 higher value for t" than for t' and t. I might multiply these 

 citations, but I should anticipate what I have hereafter to say. I 

 reserve the farther elucidation until I shall publish together the 

 experiments which I have made on the compression and dilata- 

 tion of gases. 



However, tlin examples which T hnvc just ciM suffice fo show 



