Thermodynamics of Fluids. 



335 



VLS will be represented in any diagram of constant scale by two 

 paths of opposite directions superposed, the appearance being as if a 

 body shonld change its state and then i-etnrn to its original state by 

 inverse processes, so as to repass throiigh the same series of states. 

 It is true that the circuit in question is like tliis combination of pro- 

 cesses in one important particular, viz : that IF =://= 0, i. e., there 

 is no transformation of heat into work. But this very fact, that a 

 circuit without transformation of heat into work is possible, is worthy 

 of distinct representation. 



A body may have such properties that in one part of the volume- 



entropy diagram 



\ . dp . . . , . , 



— , 1. e., -^ IS positive and m another negative. 



These parts of the diagram may l)e separated by a line, in which 



-J- =■ 0, or by one in which -^ changes abruptly from a positive to a 



negative value.* (In part, also, they may be separated by an area in 



which -— :=.0.) In the representation of such cases in any diagram 



of constant scale, we meet with 

 a difficulty of the following na- v 

 ture. 



Let us suppose that on the 

 right of the line LL (fig. 10) in 



dp 



a volume-entroi)y diagram. 



di/ 



is positive, and on the left nega- 

 tive. Then, if we draw any cir- 

 cuit ABCD on the right side of 

 LL, the direction being that of 

 the hands of a watch, the work 

 and heat of the circuit will be 

 positive. But if we draw any 

 circuit EFGH in the same direc- 

 tion on the other side of the line 

 LL, the work and heat will be negative. For 



Yv, V ^'^ 







Tr= 11= :^ 



* The line which represents the various states of water at its maximum density for 

 various constant pressures is an example of the first case. A substance which as a 

 liquid has no proper maximum density for constant pressure, but which expands in 

 solidifying, affords an example of the second case. 



