330 J. W. Gihhs on Graphical Methods hi the 



THE VOLUME-ENTROPY DIAGRAM. 



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

 in the diagram are made eqnal to tlie vohime and entropy of the 

 body, presents certain characteristics whicli 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 symmetical form of the general 

 equations of thermodynamics, when volume and entropy are chosen 

 as independent variables, viz : — * 



d^ , , 



dE , ^ 



t = ^, (1-2) 



d W= p dti, 



dll = t dij. 



Eliminating p and t we have also 



d F 

 dW= - ~dv, (13) 



dv 



dH = %^dn. (H) 



The geometrical relations corresponding to these equations are iu 

 the volume-entropy diagram extremely simple. To fix our ideas, let 

 the axes of volume and enti'opy be horizontal and vertical respec- 

 tively, volume increasing toward the right and entropy upward. 

 Then the pressure taken negatively will equal the ratio of the differ- 

 ence of energy to the difference of volume of two adjacent points in 

 the same horizontal line, and the temperature will equal the ratio of 

 the difference of energy to the difference of entropy of two adjacent 

 points in the same vertical line. Or, if a series of isodynamics be 

 drawn for equal infinitessimal differences of energy, any series of hori- 

 zontal lines will be divided into segments inversely proportional to 

 the pressure, and any series of vertical lines into segments inversely 

 proportional to the temperature. We see by equations (13) and (14), 

 that for a motion parallel to the axis of volume, the heat received is 

 0, and the work done is equal to the decrease of the energy, while for 



* See page 310, equations (2), (3) and (4). 



In general, in this article, where differential co-efficients 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 j? are uniformly regarded as the inde 

 pendent variables, and the subscript letter is omitted. 



