THERMODYNAMICS OF FLUIDS. 



This case can be but very imperfectly represented in the volume- 

 pressure, or in the entropy-temperature diagram. For all points in 

 the same vertical line in the triangle VLS will, in the volume-pressure 

 diagram, be represented by a single point, as having the same volume 

 and pressure. And all the points in the same horizontal line will be 

 represented in the entropy-temperature diagram by a single point, as 

 having the same entropy and temperature. In either diagram, the 

 whole triangle reduces to a straight line. It must reduce to a line 

 in any diagram whatever of constant scale, as its area must become 

 in such a diagram. This must be regarded as a defect in these 

 diagrams, as essentially different states are represented by the same 

 point. In consequence, any circuit within the triangle VLS will be 

 represented in any diagram of constant scale by two paths of opposite 

 directions superposed, the appearance being as if a body should change 

 its state and then return to its original state by inverse processes, so 

 as to repass through the same series of states. It is true that the 

 circuit in question is like this combination of processes in one important 

 particular, viz : that W= H=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 



i.e., -f 

 dq 



is 



positive and in another negative. 

 These parts of the diagram may 

 be separated by a line, in which 



dp . , i dp 



-TT- = 0, or by one in which - 

 dr\ dij 



changes abruptly from a positive to 

 a negative value.* (In part, also, 

 they may be separated by an area in 



which -jt- = 0.) In the representa- 

 tion of such cases in any diagram 

 of constant scale, we meet with a O 

 difficulty of the following nature. 



Let us suppose that on the right of the line LL (fig. 10) in a volume- 

 entropy diagram, -J: is positive, and t>n the left negative. Then, if 

 we draw any circuit ABCD on the right side of LL, the direction 



Fig. 10. 



* 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. 



