Therm odyncmiics of Fluids. 323 



Case of condensable vapors. 



The case of bodies w^hich pass from the liquid to the gaseous condi- 

 tion is next to be considered. It is usual to assume of such a body, 

 that when sufficiently superheated it approaches the condition of a 

 perfect gas. If, tlien, in the entropy-temperature diagram of such a 

 body we draw systems of isometrics, isopiestics and isodynamics, as if 

 for a perfect gas, for proper values of the constants a and c, tliese will 

 be asymptotes to the true isometrics, etc., of the vapor, and in many 

 cases will not vary from them greatly in the part of the diagram which 

 represents va])or unmixed with liquid, except in the vicinity of the 

 line of saturation. In the volume-pressure diagram of the same body, 

 the isothermals, isentropics and isodynamics, drawn for a perfect gas 

 for the same values of a and c', will have the same relations to the true 

 isothermals, etc. 



In that part of any diagram which represents a mixture of vapor 

 and liquid, the isopiestics and isothermals will be identical, as the 

 pressure is detei-mined by the temperature alone. In both the dia- 

 grams which we are now comparing, they will be straight and parallel 

 to the axis of abscissas. The form of the isometrics and isodynamics 

 in the entropy-temperature diagram, or that of the isentropics and 

 isodynamics in the volume-pressure diagram, will depend upon the 

 nature of the fluid, and probably cannot be expressed by any simple 

 equations. The following property, however, renders it easy to con- 

 struct equidifterent systems of these lines, viz : any such system will 

 divide any isothermal (isopiestic) into equal segments. 



It remains to consider that part of the diagram which represents 

 the body when entirely in the condition of liquid. The fundamental 

 characteristic of this condition of matter is that the volume is very 

 nearly constant, so that variations of volume are generally entirely in- 

 appreciable when represented gra])hically on the same scale on which 

 the vohinie of the body in the state of vapor is represented, and both 

 the variations of volume and the connected variations of the connected 

 quantities may be, and generally are, neglected by the side of the 

 variations of the same quantities which occur when the body passes 

 to the state of vapor. 



Let us make, then, the usual assumption that v is constant, and see 

 how the general equations (1), (2), (3) and (4) are thereby aftected. 



We have first, 



dv =1 0, 

 then d [V=z 0, 



and ds z=.t dj]. 



If we add dH ■=l t di). 



Trans. Connecticut Acad., Vol. II. 25 April, 187.S. 



