On Steani and Brines 183 



When the mixture has been completed, the amount of heat 

 lost by tJic hotter mass is equal to the amount of heat gained by 

 the colder mass. 



Taking the simplest case, namely that of the mixture of 

 masses of the same liquid, for example, water : 



Let WQ be the weight of one of the masses of water, and 

 let ( Q be its temperature. 



Let w be the weight of the other mass of water, and let T 

 be its temperature. 



When the two masses have been mixed, let W-^ = W + iv 

 be the weight of the mixture, and let /, be its temperature. 



Then, in terms of the above principle, we have 



W (t -t 1 ) = w(t 1 -T), .................. (i) 



whence W t = W^-wT. 



Let r=o, 



then W t = Wji ......................... (2) 



Equation (2) is the simplest expression of the law of 

 thermal mixture, and it also expresses Blagden's law of the 

 lowering of the freezing-point and that of the raising of the 

 boiling-point of water by the dissolution of salt in it. 



Therefore the three processes are identical. 



They are cases of simple thermal mixture. 



From equation (i) we obtain the temperature of the 

 mixture : 



In cases where masses of different liquids have been 

 mixed, unless they have the same specific heat, the above 

 equation will not give the observed temperature of the 

 mixture. 



Let s = the specific heat of the mass W Q referred to that 

 of w as unity. 



Then the temperature of the mixture will be 



