II. 



A METHOD OF GEOMETRICAL REPRESENTATION OF THE 

 THERMODYNAMIC PROPERTIES OF SUBSTANCES BY 

 MEANS OF SURFACES. 



[Transactions of the Connecticut Academy, II. pp. 382-404, Dec. 1873.] 



THE leading thermodynamic properties of a fluid are determined 

 by the relations which exist between the volume, pressure, tempera- 

 ture, energy, and entropy of a given mass of the fluid in a state of 

 thermodynamic equilibrium. The same is true of a solid in regard 

 to those properties which it exhibits in processes in which the 

 pressure is the same in every direction about any point of the solid. 

 But all the relations existing between these five quantities for any 

 substance (three independent relations) may be deduced from the 

 single relation existing for that substance between the volume, energy, 

 and entropy. This may be done by means of the general equation, 



de tdripdv, (1)* 



that is, *--l) (2) 



where v, p, t, e, and 77 denote severally the volume, pressure, absolute 

 temperature, energy, and entropy of the body considered. The sub- 

 script letter after the differential coefficient indicates the quantity 

 which is supposed constant in the differentiation. 



Representation of Volume, Entropy, Energy, Pressure, and 



Temperature. 



Now the relation between the volume, entropy, and energy may 

 be represented by a surface, most simply if the rectangular co- 

 ordinates of the various points of the surface are made equal to the 

 volume, entropy, and energy of the body in its various states. It 

 may be interesting to examine the properties of such a surface, which 



*For the demonstration of this equation, and in regard to the units used in the 

 measurement of the quantities, the reader is referred to page 2. 

 G. I. C 



