Page:Scientific Memoirs, Vol. 1 (1837).djvu/365

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M. CLAPEYRON ON THE MOTIVE POWER OF HEAT.
353

drawn and the dilatation continued. A fresh quantity of liquid will then pass into the gaseous state, and a part of the sensible caloric becoming latent, the temperature of the mixture will diminish as well as

Fig. 2

the pressure. Suppose the dilatation to be continued until the temperature diminishing gradually becomes equal to the temperature of the body ; let be the volume and the pressure corresponding to it. The law of the variation of the pressure will be given by a curve , which will pass through the points and .

During this first part of the operation which we are describing, a quantity of action will be developed represented by the surface of the rectangle , and that of the mixtilinear trapezium .

We will now bring forward the body , put it in contact with the mixture of liquid and vapour, and successively reduce its volume; a part of the vapour will pass into the liquid state, and as the latent heat disengaged in its condensation will be absorbed by the body , the temperature will remain constant and equal to . We shall thus continue to reduce the volume until all the heat furnished by the body in the first part of the operation has been conveyed to the body .

Let then be the volume occupied by the mixture of vapour and liquid; the corresponding pressure will be equal to : the temperature remaining equal to , during the reduction of the volume from to , the law of the pressure between these two limits will be represented by the line parallel to the axis of the abscisses.

Arrived at this point, the mixture of vapour and liquid upon which we are operating, which occupies the volume under a pressure ,