Heat of Mixture of Substances. 



541. 



It is possible to develop formulae for the heat of mixture 

 of liquids which do not involve any knowledge of the relative 

 distribution of the molecules in the mixture. Let AB in 

 the figure be a cylinder containing four pistons c, a, b, d. 



Suppose the space C between the pistons a and b filled 

 with a mixture of molecules 1 and 2 in the proportion of n l 

 to n 2 . Suppose the piston a pervious to molecules 1 but not 

 to molecules 2, and the piston b pervious to molecules 2 but 

 not to molecules 1, so that the space between the pistons c 

 and a is filled with saturated vapour of molecules 1, and the 

 space between the pistons b and d filled with saturated vapour 

 of molecules 2. Suppose the pistons c and d be moved 

 towards the ends of the cylinder till the increase in the 

 masses of the vapours 1 and 2 be equal to n 1 and n 2 respec- 

 tively, and suppose that at the same time the pistons a and b 

 are moved so as to remain in contact with the mixture. 

 During the process the piston a has displaced a volume 



SV n, 



of the mixture, where V is the volume of a gram 



of the mixture and p z its density, and c-i is the concentration 



£V 1 £ V 

 of the molecules 1. The quantity p 3 -%- or i7 F~ ma 7 ^e 



called the volume a molecule 1 occupies in the mixture ; it is 

 a quantity which is of interest and importance and will be 

 discussed in the next ssction. Similarly, the piston b dis- 

 places a volume of the mixture equal to p^-K- .t/ • Let y> r 



OC 2 My 



denote the pressure per cm. 2 on the piston c and p 2 that on 

 d, and let the corresponding pressures on the pistons a and b 

 be p 2 an d pi respectively. Now according to Clapeyron's 

 thermodynamical equation we have 



T . SV n x , rpcfa, 5V n{T dp 2 



K+p^-^g- Wi p 2 = ni T M - P3 ^ w -^ 



av 71 



dp 2 8V n 2 T dpi 



I*+/W-ftj£ m 2 />i ="iT^, -^- 



M, dT 



where L», and L» a denote the internal heats of evaporation of ?ij 

 grms. of molecules 1 and n 2 grms. of molecules 2 respectively. 



