and Entropy-Temperature Diagrams of Fluids. 035 



others have supplied data by help of which one may draw a 

 first approximation to the entropy-temperature diagram. 



l^rom that diagram it is easy, by inspection, to see how 

 the sign and magnitude of K* are affected by changes of 

 temperature. The diagram exhibits the entropy of the 

 liquid, <£„., at saturation pressure, and also the entropy of 

 the saturated vapour, <p Sf in relation to the temperature, by 

 means of a continuous curve whose summit is at the critical 

 point. The outer limb of this curve, from the critical point 

 onwards, is the saturation line, relating to saturated vapour, 

 and is the part with which we are immediately concerned. 

 Let the state of the substance change by a small step along 

 the saturation line, with the result that the entropy changes 

 by d(j} 8 and the temperature by dT. The heat taken in is 

 K s dT, by definition of K s . It is also equal to Td<j> 8 , since 

 -the step is reversible. Hence 



K =T-^ 



and is negative under all conditions that make the entropy 

 of the vapour increase with decreasing temperature. In 

 other words, it is negative so long as the entropy-temperature 

 line for saturated vapour slopes down to the right, as in 

 fio;. 1 or fio-. 2.. This is what may be called the normal 

 form of the curve, such as is found in steam, carbon dioxide, 

 or ammonia. 



To make K s positive would require that a part of the line 

 ■for saturated vapour should slope the other way, as in fig. 3, 

 •where positive values of K s would be found at any temper- 

 ature between A and B, with negative' values at any tem- 

 perature above A or below B. The point B corresponds to 

 the reVersal of the sign of K s which was, in certain sub- 

 stances, predicted from Regnault's data and verified by the 

 experiments of Hirn * and C;izin f on the effects of adiabatic 

 expansion and compression. 



It is obvious that, however strongly positive K 5 . may be at 

 :an intermediate temperature, it necessarily becomes negative, 

 in all substances, as the critical point is approached ; for the 

 saturation line must then bend over to the left to become 

 continuous with the liquid line which forms the other limb 

 of the diagram. At the critical point the value of K s is — go . 



In any fluid the entropy increases during vaporization- at 

 •constant temperature bv the amount L T. Thus 



* Hirn, Cosmos, vol. xxii. p. 413 (1863). 



t Cazin, Ann. de Chim. et de Phys. (4) vol. xiv. p. 874 (1868 ). 



2 T2 



