Page:Scientific Memoirs, Vol. 1 (1837).djvu/364

tion in the same envelope,—but after having introduced the body $B$, which is at the same temperature,—and carry on the operation until the body $B$ has restored to the gas the heat which it had received in the preceding operation. We next remove the body $B$, and condense the gas in an inclosure impermeable to heat until its temperature again becomes equal to $T$. We then introduce the body $A$, which possesses the same temperature, and continue the reduction of volume until all the heat taken from the body $B$ is transferred to the body $A$. The gas will then be found to have the same temperature and to contain the same absolute quantity of heat as at the beginning of the operation, whence we may conclude that it occupies the same volume and is subjected to the same pressure.

Here the gas passes successively, but in an inverse order, through all the states of temperature and pressure through which it had passed in the first series of operations; consequently the dilatations become compressions, and reciprocally, but they follow the same law. Further, the quantities of action developed in the first case are absorbed in the second, and reciprocally; but they retain the same numerical values, for the elements of the integrals which compose them are the same.

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.

We may arrive at a similar result by converting any liquid into vapour. We take the liquid and bring it into contact with the body $A$ in an extensible envelope impermeable to heat, and suppose the temperature of the liquid to be equal to the temperature $T$ of the body $A$. Upon the axis of the abscisses $A\;X$ (fig. 2.) we describe a quantity $A\;B$ equal to the volume of the liquid, and upon a line parallel to the axis of the ordinates $A\;Y$, a quantity $B\;C$ equal to the pressure of the vapour of the liquid, which corresponds to the temperature $T$.

If we increase the volume of the liquid, a portion of it will pass into the state of vapour; and as the source of heat $A$ furnishes the latent caloric necessary to its formation, the temperature will remain constant and equal to $T$. Then if quantities representing the successive volumes occupied by the mixture of liquid and vapour are described upon the axis of the abscisses, and the corresponding values of the pressures are taken for ordinates, as the pressure remains constant, the curve of the pressures will here be reduced to a right line $C\;E$ parallel to the axis of the abscisses.

When a certain quantity of vapour has been formed, and the mixture of liquid and vapour occupies a volume $A\;D$, the body $A$ may be with-