Properties of the Equation of State. 393 



the substance at the distance they are separated, and that 

 the internal energy of a molecule is independent of the 

 vicinity of* other molecules. Equation (1) now becomes 

 p — 7J]l. This formula is only realized in the case of a gas, 

 showing that at the distance the molecules are then separated 

 from one another these conditions are approximately fulfilled. 

 When deviations from the formula occur, one or both of 

 these conditions are not satisfied. 



Conditions satisfied by a Liquid and its Saturated Vapour. 



In general the state of a substance is defined if the magni- 

 tude of two of the variables p, H, and v are known, except 

 in the case of a liquid in contact with its saturated vapour, 

 when it is necessary to know only the magnitude of one of 

 the variables. Since in the latter case two variables take 

 the place of one, namely, the volume of a gram of liquid 

 and that of a gram of saturated vapour, there must exist 

 another equation besides the equation of state by the help of 

 which the variables can be determined if one of them is 

 known. This is the well-known equation 



I 



2 



p .Sv = p(v 2 — v 1 ) (2) 



obtained by means of the theory of continuity of state, and 

 the thermodynamical principle that in an isothermal trans- 

 formation the external work done is independent of the 

 nature of the path described. The suffixes 1 and 2 refer to 

 the liquid and its saturated vapour respectively. 



The equations from which the variables T, p, v^ and v 2 can 

 be determined in terms of one of them are therefore 



_ T C/dTJA ST T f (du{\ ST T r/ /Q , 



T C/dJJ 2 \ ST T C { du 2 \ ST T „ ,. 



.... (5) 



Therefore if the form of each of the functions U, u, and Z 

 were known, the equations could be completely set down. 

 It will be recognized that J] 1 is the work done per molecule 

 against the molecular attraction on separating the molecules 



