LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 65 



P{dv -dv) + Udv'-U dv ' + dnRTln — = 



tda+ P(dv -dr). 

 Now from equation (2), II d vj = II d v', 



U^ if/ 



and, as on page 55, 

 Therefore 



RTlu^ = t^ = ts. (26) 



This is the general equation connecting fugacity and surface tension at 

 constant temperature and pressure. If t is variable we may differentiate, 

 \p and s being constant, obtaining 



dR Tlnif/ = sdt, 



or expressing the constancy of T and P, 



fdRT\xxxb\ 



C-srf )„...=* (27) 



This equation completely confirms the validity of equation (19) as 

 applied to surface energy and corresponds to equations (20) and (21). 

 An important form of energy which we have not yet discussed is 

 electrical energy, whose dimensions are potential, and quantity of elec- 

 tricity. If these be represented by i? and e, respectively, in any case 

 where the fugacity is influenced by the electrical potential, we should 

 have the equation, 



(-^L.=* (28) 



There are in fact a number of cases in which the potential may be 

 shown to have an effect upon the escaping tendency, the most important 

 being that in which the potential influences the fugacity of the ions. The 

 following equation has been amply proved experimentally, and thermo- 

 dynamically is shown to be rigorously exact on the assumption that the 

 ions form an ideal solution. 



e 77 = R T In n + K, 



in which tt is the potential at which equilibrium is established between 

 an electrode and its ions at the osmotic pressure II, if e is the charge of 

 one gram-ion and K is at constant temperature and pressure a character- 

 istic constant of the electrode. In other words, II is the osmotic pressure 

 of the ions which will be in equilibrium with the electrode when the 



VOL. XXXVII. — 5 



