1854] 



INVESTIGATION OF THE SPECIFIC HEATS OF ELASTIC FLUIDS. 



135 



how careful we must be in the conclusions to be drawn from the 

 experiments in which elastic fluids that are in motion, undergo 

 changes of elasticity, and perform mechanical work often difficult 

 to appreciate ; for the calorific effects produced depend, in great 

 part, upon the order and manner in which these changes have 

 taken place. 



Unhappily, if it is easy to announce vagu'ly a physical theory, 

 it is very difficult to specify it with precision, so as not only to 

 connect with it all the facts known to science, but also to deduce 

 from it those which have heretofore escaped observation. The 

 theory of luminous undulations, as it was established heretofore 

 by Fresnel, presents the only example heretofore known in 

 physics. The expression in equations of the problems of heat,- 

 looked upon in a mechanical point of view, leads, like all anala- 

 gous problems, to an equation of partial differences of the second 

 order, between several variables which are unknown functions of 

 each other. These functions represent the true elementary 

 physical laws, which must be known, in order to have the com- 

 plete solution of the problem. The integration of the equation 

 introduces arbitrary functions, thu nature of which we must seek 

 to discover by preparing the results given by the equation with 

 those which direct experiments give, and with the laws derived 

 from those experiments. Unhappily, in experiments on heat, 

 direct experiments are rarely applicable to simple phenomena ; 

 genera \y, they attack complex questions, which depend on several 

 of these laws at a time, and most frequently it is difficult to assign 

 the part which belongs to each of them. The experimenter must 

 then endeavour to modify the circumstances under which he 

 operates, so as to vary as far as possible, in the respective experi- 

 ments, the parts which belong to each of the elementary 

 phenomena, and to the law which expresses it. He will thus 

 obtain equations of condition which may be of great aid for the 

 discovery of a general theory ; for this, whatever it may be, must 

 always satisfy these equations. 



This is the manner in which I have directed my researches ; 

 and I have always endeavored to define, in the most precise way, 

 the conditions under which I was working, so that my experi- 

 ments might be of service, whatever theory might finally prevail. 



I published, in 1847, the first part of my researches; they 

 compose the second volume of the Memoirs of the Academy (of 

 Sciences of Paris). Since that date I have not ceased to pursue 

 them ; but the experiments which they required were so numer- 

 ous, the numerical calculations so long and troublesome, that it 

 would have been impossible for me to have executed them, if I 

 had been left to my own individual efforts. I have been power- 

 fully seconded by M. Izarn, who had already lent me his 

 assistance for the first part of my work, and by a young engineer 

 of mines, M. Descos, whom the minister of public works has 

 kindly appointed my assistant for the last two years, in order to 

 hasten the conclusion of my work. Let me be permitted thus 

 publicly to express my thanks for the indefatigable zeal with 

 which they have seconded me. 



The subjects. to which my new experiments have been directed 

 are the following : — 



1st. The relations which exist between the temperatures and 

 the elastic forces of a great number of saturated vapours, from 

 the feeblest pressures up to twelve atmospheres. 



2nd. The elastic forces of these same vapours, saturated or 

 not, in the gases. 



3rd. The elastic forces, at saturation, of the vapours produced 

 by mixed liquids. 



4th. The latent heat of these vapours, under different pressures, 

 from the. feeblest up to those of eight or ten atmosphere*. 



5th. The latent heats of vaporization of the same substances, 

 in gases. 



6 th. The specific heats of permanent gases and vapours, 

 under different pressures. 



7th. The quantities of heat absorbed and disengaged by the 

 compression and dilitation of gases, whether this dilatation takes 

 place hi a space whose capacity is augmented, or whether it 

 takes place through a capillary opening in a thin wall, or by a 

 long capillary tube. 



8th. The quantities of heat absorbed by the gas, when it 

 produces, during its expansion, a motive force which is altogether 

 consumed in the interior of the calorimeter, or is principally 

 utilised elsewhere. 



9th. And, finally, the densities of saturated vapours under 

 different pressures. 



The experiments which have reference to these different 

 questions, with the exception of the last one, are now nearly 

 finished. But, as much time will still be required to put them 

 in order, and discuss them with the proper care, I propose to 

 present the general results, successively, to the academy, while 

 awaiting the time when I can publish them together. 



I will present at present my researches on the calorific 

 capacities of elastic fluids. 



The capacities for heat of elastic fluids. — The specific heat 

 of elastic fluids may be defined in two different ways ; in the 

 first, the specific heat of an elastic fluid is the quantity of heat 

 which must be given to a gas to raise its temperature from 0° to 

 1° cent., allowing it to dilate freely, so as to preserve a constant 

 elasticity ; in the second, it is the quantity of heat which must 

 be given to it, to raise its temperature from 0° to 1°, forcing it 

 to keep its volume, its elastic force increasing. 



The first of these has been called the specific heat of a gas under 

 constant pressure. The second, specific heat of a gas under 

 constant volume. The first definition only, coincides with 

 that which has been admitted for the capacity for heat of solid 

 and liquid bodies ; it is also the only one which has heretofore, 

 lent itself to direct experimental demonstration. 



A great number of physicists have employed themselves 

 during the last century, in the examination of the specific heats 

 of elastic fluids; Crawford, Lavoisier and Laplace, Dalton, 

 Clement and Desormes, De la Eoche and Berard, Haycrafft, 

 Gay-Lussac, Dulong, De la Rive, and Marcet, have successively 

 published researches on this subject. The greater part of these 

 physicists have sought to demonstrate experimentally certain laws 

 to which they had been led by the ideas which they had formed 

 a priori as to the constitution of elastic fluids. They have 

 applied themselves to determine the numerical values of the 

 caloric capacities of the different gases in relation to that of 

 liquid water generally taken as unity, than to look for the simple 

 relations which they supposed must exist among themselves. 

 The conclusions to which they have come are generally very 

 erroneous. 



The work of De la Roche and Berard, which was crowned 

 by the Academy in 1813, is still the most complete on this 

 subject, and the one whose results differ the least from the truth. 

 This superiority is caused not only by the extreme care which 

 these skilful experimenters exercised in their experiments, but also 

 by the direct method which they followed ; whilst the greater 

 part of the other physicists had recourse to indirect methods, in 

 which the element they sought exercised frequently but a very 

 feeble influence. 



The general conclusions which De la Roche and Berard drew 

 from their labours were as follows: — 



1. The specific heats of the ga*es are not the same for all. 



