Thermodynamics of Fluids. 



337 



Fig. li 

 M 



M 



It may occur, liowcver, in the volunie-oiitropy diagram, that the 

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

 occurs in the case of liquids wliich can be va- 

 porized. Let MM (tig. 12) be the line repre- 

 senting the states of the liquid bordering upon 

 va2)orization. This line will be 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 ad- 

 dition or subtraction of heat, it will remain of 

 course liquid. Hence, the points of the space 

 immediately on the left of MM represent sim- 

 ple liquid. On the other hand, the body being 

 in the original state, if its volume should be 

 increased without addition or subtraction of 

 heat, and if the conditions necessary for vapor- 

 ization 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 con- 

 tinue 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 caimot be properly represented by any path, 

 as during the change the body does not satisfy that condition of uni- 

 form temperature and pressure which has been assumed throughout 

 this article, and which is necessary for the gi-aphical methods under 

 discussion. (See note on page 309.) 



Of the two superposed diagrams, that which represents simple 

 liquid is a continuation of the diagram on the left of MM. The iso- 



