Heat of Mixture of Substances. 543 



It should be observed that the functions H^ A 1? H 2 , A 2 , 

 have all the same form, namely </> 3 . The form of </> 3 depends 

 on that of </> 2 in the law of attraction between molecules, but 

 this is not exactly known. There is, however, some 

 evidence that (f> 3 \aries only slightly with the temperature 

 and distance of the molecules *. In the absence of further 

 information we may therefore take A 1} A 2 , H 1? H 2 equal to 

 the same constant for a given temperature. If the values 

 of A x and A 2 are available, it is best to take the mean of A : 

 and A 2 to represent the constants A A , A 2 , H 1? H 2 , as they 

 have the same value at corresponding temperatures. Other- 

 wise the value of this constant can be obtained from Table V. 

 p. 796, Phil. Mag. May 1910 ; at a temperature of 20° C. in 

 the case of ether it is equal to 3742. This will probably 

 give fairly accurate results. 



If the density of the mixture of saturated vapours is so 

 small that the constituent vapours obey Dalton's law of 

 partial pressures, we have p\=pi and p 2 =^ 2 '. The formula 

 for the heat of mixture then becomes 



{=-(^)}( T *- y .) + {s-(^)}( T *^) 



since 



P3 37 1 M 1 + ^^^M 2 = "7^ , 



When this is not the case there would be some difficulty in 

 practice in obtaining the values of the quantities p, p x ', p 2i p 2 '. 

 A special case of mixture which is of interest is a 

 saturated solution of a salt in a liquid. To obtain a formula 

 for the heat of mixture let the piston a in the figure be 

 removed and the semi-permeable piston b replaced by a 

 solid one. Let the piston c be moved away from the mixture 

 till n l grins, of liquid 1 have evaporated ; n 2 grms. of salt- 

 will then be deposited. From Clapeyron's equation we then 

 have 



Lp 4 \ P3 P2/J 



* Loo. cit. 



