THERMODYNAMICS OF FLUIDS. 



27 



c 

 3 







1 



a 







M 



Fig. 12. 



pared with the corresponding areas in the volume-entropy diagram. 

 Therefore, in the former diagram, either the isometrics, or the isen- 

 tropics, or both, will be crowded together in the vicinity of the line 

 LL, so that this part of the diagram will be necessarily indistinct. 



It may occur, however, in the volume-entropy diagram, that the 

 same point must represent two different states of the body. This 

 occurs in the case of liquids which can be vaporized. Let MM (fig. 12) 

 be the line representing the states of the liquid 

 bordering upon vaporization. This line will be * M 

 near to the axis of entropy, and nearly parallel 

 to it. If the body is in a state represented by 

 a point of the line MM, and is compressed 

 without addition or subtraction of heat, it will 

 remain of course liquid. Hence, the points of 

 the space immediately on the left of MM re- 

 present simple liquid. On the other hand, the 

 body being in the original state, if its volume 

 should be increased without addition or sub- 

 traction of heat, and if the conditions necessary 

 for vaporization are present (conditions relative 

 to the body enclosing the liquid in question, 

 etc.), the liquid will become partially vaporized, 

 but if these conditions are not present, it will continue liquid. Hence, 

 every point on the right of MM and sufficiently near to it represents 

 two different states of the body, in one of which it is partially 

 vaporized, and in the other it is entirely liquid. If we take the 

 points as representing the mixture of vapor and liquid, they form 

 one diagram, and if we take them as representing simple liquid, they 

 form a totally different diagram superposed on the first. There is 

 evidently no continuity between these diagrams except at the line 

 MM ; we may regard them as upon separate sheets united only along 

 MM. For the body cannot pass from the state of partial vaporization 

 to the state of liquid except at this line. The reverse process is 

 indeed possible; the body can pass from the state of superheated 

 liquid to that of partial vaporization, if the conditions of vaporization 

 alluded to above are supplied, or if the increase of volume is carried 

 beyond a certain limit, but not by gradual changes or reversible 

 processes. After such a change, the point representing the state of 

 the body will be found in a different position from that which it 

 occupied before, but the change of state cannot be properly repre- 

 sented by any path, as during the change the body does not satisfy 

 that condition of uniform temperature and pressure which has been 

 assumed throughout this article, and which is necessary for the 

 graphical methods under discussion. (See note on page 1.) 



