THERMODYNAMICS OF FLUIDS. 



17 



the distances of the isometrics being proportional to the differences 

 of the logarithms of the volumes, the distances of the isopiestics being 

 proportional to the differences of the logarithms of the pressures, and 

 so with the isothermals and the isodynamics, the distances of the 

 isentropics, however, being proportional to the differences of entropy 

 simply. 



The scale of work and heat in such a diagram will vary inversely 

 as the temperature. For if we imagine systems of isentropics and 

 isothermals drawn throughout the diagram for equal small differences 

 of entropy and temperature, the isentropics will be equidistant, but 

 the distances of the isothermals will vary inversely as the temperature, 

 and the small quadrilaterals into which the diagram is divided will 

 vary in the same ratio: /. y * l+t. (See p. 5.) 



So far, however, the form of the diagram has not been completely 

 defined. This may be done in various ways : e.g., if x and y be the 

 rectangular co-ordinates, we may make 



or 



' etc. 



Or we may set the condition that the logarithms of volume, of pressure 

 and of temperature, shall be represented 

 in the diagram on the same scale. (The 

 logarithms of energy are necessarily re- 

 presented on the same scale as those of 

 temperature.) This will require that the 

 isometrics, isopiestics and isothermals cut 

 one another at angles of 60. 



The general character of all these dia- 

 grams, which may be derived from one 

 another by projection by parallel lines, may 

 be illustrated by the case in which x = log v , 

 and y = \ogp. 



Through any point A (fig. 6) of such a 

 diagram let there be drawn the isometric 

 vv', the isopiestic pp', the isothermal tt' and the isentropic i\r{. The 

 lines pp' and vv' are of course parallel to the axes. Also by equation (H) 



P' 



Fig. 6. 



\dlog v 



and by (a) 



J 



c + a 



TJ vw *^> "' 1J 



Therefore, if we draw another isometric, cutting TJJJ', tt', and pp' in 

 B, C and D, 



CD_c 



"' CD~c BC~~a' 



G.I. B 



