20 GRAPHICAL METHODS IN THE 



The properties of the part of the entropy-temperature diagram 

 representing a mixture of vapor and liquid, which are given on 

 page 14, will evidently not be altered if the ordinates are made 

 proportional to the logarithms of the temperatures instead of the 

 temperatures simply. 



The representation of specific heat in the diagram under discussion 

 is peculiarly simple. The specific heat of any substance at constant 

 volume or under constant pressure may be defined as the value of 



(dH\ fdH\ . ( drj \ 

 \dt) v GC \dt) p ' * e *' \d log t) v 



for a certain quantity of the substance. Therefore, if we draw a dia- 

 gram, in which x = r\ and y log t, for that quantity of the substance 

 which is used for the determination of the specific heat, the tangents 

 of the angles made by the isometrics and the isopiestics with the 

 ordinates in the diagram will be equal to the specific heat of the 

 substance determined for constant volume and for constant pressure 

 respectively. Sometimes, instead of the condition of constant volume 

 or constant pressure, some other condition is used in the determination 

 of specific heat. In all cases, the condition will be represented by a 

 line in the diagram, and the tangent of the angle made by this line 

 with an ordinate will be equal to the specific heat as thus defined. If 

 the diagram be drawn for any other quantity of the substance, the 

 specific heat for constant volume or constant pressure, or for any other 

 condition, will be equal to the tangent of the proper angle in the 

 diagram, multiplied by the ratio of the quantity of the substance for 

 which the specific heat is determined to the quantity for which the 

 diagram is drawn.* 



The Volume-entropy Diagram. 



The method of representation, in which the co-ordinates of the point 

 in the diagram are made equal to the volume and entropy of the 

 body, presents certain characteristics which entitle it to a somewhat 

 detailed consideration, and for some purposes give it substantial 

 advantages over any other method. We might anticipate some of 

 these advantages from the simple and symmetrical form of the general 

 equations of thermodynamics, when volume and entropy are chosen 

 as independent variables, viz : t 



*From this general property of the diagram, its character in the case of a perfect 

 gas might be immediately deduced. 



t See page 2, equations (2), (3) and (4). 



In general, in this article, where differential coefficients are used, the quantity which 

 is constant in the differentiation is indicated by a subscript letter. In this discussion 

 of the volume-entropy diagram, however, v and 77 are uniformly regarded as the inde- 

 pendent variables, and the subscript letter is omitted. 



