GIBBS' PAPERS I AND II 27 



Consider the function x = e + py and dx = tdr] + vdp. Then 



\dr]/p ' \dp/,, ' dr]dp \dp/^ \dr]/p 



Consider ^ = e — trj -{- pv and d^ = — rjdt + vdp. Then 



(^\ = - (^\ = -^ = - ('h\ = (^\ 



Kdt/p ''' \dpJt ^' dtdp \dp)t KdtJp 



The four Maxwell relations. For perfect gases 



7] = Cvlogp -{- {Cv + a) log y — C„ log a = (7„ log i + a log y, 



\p = Cvt — Cvt log t — at log V, 



with similar expressions in f and x- The fundamental forms 

 imply that e is a function of t?, y; that ;^ is a function oi t, v; that 

 X is a function of 77, p; and that f is a function of t, p. 



Lecture XV. Avogadro's law. This differs from the laws 

 thus far considered in that it relates to the invisible, molecular, 

 properties of a gas instead of to the observable properties. The 

 equation of a gas becomes pv = A{m/M)t where m is the mass 

 of the gas and M is the molecular weight. 



Lecture XVI. A gas mixture has the equation 



\Mi Mi Mj 



The translational kinetic energy of the molecules is proportional 

 to the pressure and therefore to the temperature. 



Lecture XVII. The geometric interpretation of p and t on 

 the thermodynamic surface €(17, v). The use of the surface is to 

 aid in thermodynamic investigations. The equation of the sur- 

 face is known for a perfect gas, but the idea of it is equally 

 applicable to any substance which need not be in a homogeneous 

 state. Discussion of a substance in a liquid and vapor phase; 

 ruhngs on the surface; the py-diagram. 



