FUNDAMENTAL EQUATIONS OF IDEAL GASES 375 



by G. van Lerberghe^^ which has as a basis the develop- 

 ment of the function p = f(ti, Vi, mj, W2, . . . ) by Taylor's theorem. 

 That it is possible to develop a consistent and rational system 

 for the discussion of the properties of solutions on such a basis 

 has, in fact, been pointed out by Planck ^^ The method is 

 equivalent in some respects to the system of treating solutions 

 developed by G. N. Lewis and systematically presented by 

 Lewis and Randall in their Thermodynamics. 



Methods of treating solutions along these lines have, however, 

 the limitations of procedures whose foundation is entirely 

 empirical. On the other hand any other procedure requires 

 much detailed knowledge pertaining to molecular interaction 

 and the surmounting of formidable mathematical difficulties*^. 

 Although the initial steps have been taken in acquiring the 

 requisite knowledge of the attractive and repulsive fields of 

 molecules, very much ground remains to be won before a 

 complete molecular statistical theory of solutions can be 

 achieved. The mathematical difficulties, forming an important 

 part of the problem, remain at the moment practically unsolved^^ 

 except for the case of infinitely dilute solutions*'^. The case 

 of electrolytes at infinite dilution has been treated by Debye 

 and Hiickel ^^- *^, and the accord of their theory with the facts is 

 astonishingly good in spite of important fundamental limitations. 



III. Considerations Relating to the Increase of Entropy Due 

 to the Mixture of Gases by Diffusion (Gihbs, I, 165-168) 



The entropy change on mixing gases has already been 

 mentioned with reference to the difference in entropy which 

 arises when pure gases mix at temperature, t, and constant 

 pressure, p. Thus we may imagine two perfect gases 1 and 2, 

 contained in the apparatus indicated in the diagram, Fig. 1. 



Suppose that the pistons are permeable to the gases as 

 indicated and the usual assumptions made with regard to the 

 absence of frictional effects. Each gas is assumed to occupy its 

 portion of the cylinder at the same pressure and temperature 

 when the pistons are in contact. As the pistons are slowly 

 moved out each gas passes through its respective semi-per- 



