THE APPLICATION OF THE EQUATION OF HELMHOLTZ. S7 



THE APPLICATION OF THE EQUATION OF HELMHOLTZ. 



According to the equation of Helmholtz, 60 



ttvF U = vFT %L 



the sum of the heat of reaction and the product of the absolute temperature 

 and the temperature-coefficient of the change of free energy should equal 

 the change of free energy itself. 



In the case of the cadmium cell it is possible to prove the rigorous applica- 

 tion of this equation, because all the quantities are known. 



For example, taking the cell 2-4 (which gives about the average tempera- 

 ture coefficient), we have 



tt = 0.030826 volt 

 Att = 0.001719 volt 

 AT= 15.20 

 T = 273.09 

 v= 2 



F = 96,580 

 U = 0.001 



Therefore, for the left-hand number we have 



5.95 0.001 = 5.95 kilojoules 

 and for the right-hand = 5.95 kilojoules 



showing a difference of .00 



The difference between the two members of the equation is thus certainly 

 less than the probable magnitude of the experimental error. No more satis- 

 factory verification of this equation has ever been offered ; and the case is of 

 especial interest because of the extremely small value of the heat of reaction. 



The Helmholtz equation can not be supported in the same way by the 

 results with zinc, because lack of time prevented us from determining its 

 temperature-coefficient with sufficient accuracy. On the other hand, know- 

 ing the heat of dilution on doubling the volume of a 0.91 per cent zinc amal- 

 gam to be 0.052 kilojoules (see page 55), the temperature-coefficient of a 

 cell of this kind can easily be calculated with the help of the Helmholtz equa- 

 tion. Transposed for this purpose 61 the equation becomes 



AT~ T^ 2 X 96,580 X T 



60 In this case ^ and A T can be substituted for the infinitesimals, as the heat 

 capacity does not change on dilution. 



61 See Richards and Lewis, Proc. Am. Acad., 34, 88 (1898). 



