Benoît Paul Émile Clapeyron

“ Variation is produced in the volume of all the substances of nature by changes in the temperature and pressure to which they are subjected; liquids and solids are amenable to this law, and serve equally to develop the motive power of heat; it has been proposed to substitute them for the vapour of water, in order to render this motive force available; they have even occasionally been advantageously employed, particularly when it was necessary to develop a very considerable momentaneous effort, exerted within narrow limits. ”

“ We shall not insist upon the consequences which result from the equation We shall simply remark that if, as everything leads us to believe, and do not become infinite for any value of the temperature, will become null when we have , that is, that when the pressure is strong enough, and the temperature sufficiently elevated to render the density of the vapour equal to that of the liquid, the latent caloric is reduced to zero. ”

“ I will finally quote among the works which have appeared on the theory of heat, one by M. S. Carnot, published in 1824, under the title of Reflexions sur la Puissance Motrice du Feu. The idea taken for the basis of his researches appears to me fertile and incontestible: his demonstrations are founded on the absurdity which arises from admitting the possibility of producing absolutely either the motive force or the heat. ”

“ We thus see that by causing heat to pass, in the manner first indicated, from a body retained at a determinate temperature, into a body retained at an inferior temperature, we develop a certain quantity of mechanical action, which is equal to the quantity which must be consumed in order to cause the same quantity of heat to pass from a cold to a hot body, by the inverse process we have subsequently described. ”

“ Now a volume of of iron weighs kilogrammes; the heat disengaged by one kilogramme will therefore be ; for the pressure of an atmosphere it will be times more considerable, or equal to ; the division of this number by the specific caloric of the iron referred to that of water gives the quantity of the elevation of the temperature of the iron by the pressure of an atmosphere; it is, we see, too feeble to be appreciated by our thermometrical instruments. ”

“ Knowing the quantity of heat disengaged from gases by compression, to ascertain that which a similar pressure would disengage from any substance whatever, from iron for example, we write the proportion: of heat disengaged by a volume of air equal to of a cubic metre, subjected to an increase of pressure equal to of an atmosphere, is to that disengaged from the same volume of iron under the same circumstances as , the cubic dilatability of the air, is to , the cubic dilatability of iron. ”

“ Now that the gas is brought to the temperature of the body , let us bring them together: if we compress the gas in an inclosure impermeable to heat, but in contact with the body , the temperature of the gas will tend to rise by the evolution of latent heat rendered sensible by compression, but will be absorbed in proportion by the body , so that the temperature of the gas will remain equal to . ”

“ Still, however, the entire quantity of heat furnished by the body to the gas during its dilatation by contact with it, passes into the body during the condensation of the gas, which takes place by contact with it. ”

“ When a gas varies in volume without change of temperature, the quantities of heat absorbed or disengaged by that gas are in arithmetical progression, if the increments or diminutions of volume are in geometrical progression. ”

“ To render useful all the motive force at our disposal, the detent should be continued until the temperature of the vapour be reduced to that of the condenser; but practical considerations, suggested by the manner in which the motive force of fire is employed in the arts, prevent the attainment of this limit. ”

“ The integral of the general equation is, as we have seen, is an arbitrary function of the temperature , varying from one body to another; is a function of the temperature which is the same for all the substances of nature, and is a particular function of , and of satisfying the equation This function may be determined in the following manner. ”