Heat of Mixture of Substances. 549 



are again put into their place is the above expression 

 multiplied bv — — 1 — 2 , and substituting x c . 2 and T c for 



(V%) 



certain of the quantities xc x and Tc x occurring in Wi and u l . 

 This will at once be evident if we consider that this expression 

 is suuposed to be derived by a direct application o( the law 

 of attraction between two molecules 1 and 2, viz. 



But since Wj and W 2 are each of the form </> 3 , and therefore 

 do not depend much on the magnitude of the variables they 

 contain, we may suppose both these quantities equal to a 

 constant. The work done when a molecule 1 is removed 

 from a mixture against the attraction of the remaining mole- 

 cules 1 and 2 is therefore 



W-&J" - ••«)"> "=. * ' -■ + -(if « «'-)■• 



where W 1 = ?/ 1 = constant approximately. If the density 

 of the molecules 1 in the mixture is expressed in terms 



of that of the mixture we have p 7 = —^ * . Similarly the 



work done when a molecule 2 is removed is 



where W 2 =w 2 = Wi = Wi= a constant approximately, and 



p 3 M 2 

 ^"Mi + M/ 



This constant at 20° C. is equal to 3742, and the heat of 

 mixture of ri\ gram of molecules 1 with n 2 grams of mole- 

 cules 2 so that -~- = -=— , is at that temperature therefore 

 given by x 2 



mi S \/m 2 



the molecular weights of Mj and M 2 being expressed relative 

 to that of hydrogen. 



