204 M. A. Hitter's Contributions to the Study 



§ 2. Isothermals of Water-vapour. 



The temperature-surface of the so-called perfect gases is, as 

 was shown in the preceding paragraph with reference to atmo- 

 spheric air, a surface continuously curved in all its parts. The 

 temperature-surface of steam is, on the contrary, a curved sur- 

 face with edges. 



As its temperature falls, steam passes into the liquid and 

 solid states of aggregation. To these changes correspond 

 changes in the law of curvature of the temperature-surface, 

 which will accordingly appear as a curved surface made up of 

 several surfaces of continuous curvature. 



We get a clear conception of the difference between vapours 

 and perfect gases by likening their temperature-surfaces to 

 mountain-faces as before. In the higher regions the forms of 

 both mountains would most probably be approximately the 

 same, since we may assume that at very high temperatures 

 steam behaves like a perfect gas. Considerable differences 

 between the two forms, however, will make an appearance 

 lower down, since, in the mountain which represents the beha- 

 viour of water in its three states of aggregation, the uniformity 

 of the continuously curved slope is broken by sharp-edged 

 cliffs and steep walls of rock that stand out and project cor- 

 nice-like, wholly changing the character of the landscape in 

 the lower regions. Consequently also the horizontal paths, 

 that run along the mountain-slope and represent the isother- 

 mals, will in the lower regions differ very considerably in form 

 from the isothermals of perfect gases. 



If superheated steam undergoes isothermal compression, and 

 the law of alteration of its pressure p with the volume v during 

 the motion of the piston is represented geometrically by a line, 

 then this line runs on at first just as in the case of atmospheric 

 air. At the point M, however, that corresponds to the pas- 

 sage of the vapour into the saturated state, the line will form 

 an angle (fig, 3). Condensation begins at this position of 

 the piston, and the pressure p remains constant when the 

 piston is pushed further in. The following part of the iso- 

 thermal will therefore be a straight line parallel to the volume- 

 axis Y. This straight line M N extends to the point N cor- 

 responding to the condensation of the last particle of steam. 

 Here the isothermal forms another angle ; for the pressure of 

 water increases with extraordinary rapidity when its volume 

 is diminished. This last piece of the isothermal will there- 

 fore be a curve that rises up very steeply from the axis of 

 abscissae. 



In passing from the isothermal T to the isothermal T + dT 



