14 GRAPHICAL METHODS IN THE 



The equation of the isodynamics is of course the same as that of the 

 isothermals. None of these systems of lines have that property of 

 identity of form, which makes the systems of isometrics and isopiestics 

 so easy to draw in the entropy-temperature diagram. 



Case of condensable vapors. 



The case of bodies which 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, then, 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, these 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 vapor 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 determined by the temperature alone. In both the 

 diagrams 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 ex- 

 pressed by any simple equations. The following property, however, 

 renders it easy to construct equidifferent 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 graphically on the same scale on which 

 the volume 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 affected. 



