078 PROCEEDINGS OF THE AMERICAN ACADEMY. 



An Indirect Method of Measuring the Specific Heats op 

 MORE Dilute Solutions. 



Having once determined accurately the specific heat of a given solu- 

 tion, it is easy without much more labor to determine that of any more 

 dilute solution of the same substance. The method for accomplishing 

 this purpose, depending upon the change of the heat of dilution with 

 temperature, was first suggested by Berthelot,* but seems never to have 

 been used in actual practice. Probably the reason for this neglect was 

 the difficulty of determining accurately with any ordinary apparatus the 

 very small heats of dilution involved — but this difficulty is now removed 

 by the very simple and convenient divided beaker-calorimeter, described 

 above. Therefore it seems worth while to explain the method and re- 

 port a few experiments demonstrating its value. 



In principle, this method depends upon the well-known thermodynamic 

 relation usually known as Kirchhoff's law, namely 



where A' and K^ represent heat capacities of factors and products respec- 

 tively, and Uj. and U^j^t heats of reaction (in this case of dilution) at the 

 temperatures T'and T -\- t. Having measured f/j, and U^^t by means of 

 our apparatus, the change of heat capacity of the system during the reac- 

 tion is very simply obtained ; and if the heat capacity of the concentrated 

 solution and the water are both known at first, the heat capacity of the 

 more dilute solution is at once found. The dilute solution can then be 

 once more diluted, and so on indefinitely. 



This is a very accurate process, the error being divided instead of 

 being multiplied in the operation. 



The heat of dilution of the solutions at 16° or 17° had already been 

 determined. Lack of time and the high temperature of summer weather 

 (June, 1904) prevented us from carrying out the dilution of one of the 

 previous solutions at 0° as would have been desirable, — for t° should 

 cover the range over which the specific heats iiave been studied. Never- 

 theless, a few determinations of the heat of dilution of the argentic nitrate 

 made at 24° will show the mode of applying the problem and afford a 

 fairly accurate result. In four experiments, the temperature-changes on 

 the dilution of the argentic nitrate solution, with an equal bulk of water 



* Mecli. Chim., I, p. 278 (1879). 



