RICHARDS. CHANGING HEAT CAPACITY. 303 



ments are necessary to attain a precise knowledge of this relationship of 

 the temperature coefficients ; and moreover it probably differs with dif- 

 ferent cells. The foregoing calculations are merely for the purpose of 

 orientation. 



Qualitatively all the results correspond with the theory at first proposed. 

 In every case where the heat capacity diminishes, the heat evolved is 

 greater than the free-energy change. But in some cases tlie difference 

 is very great ; and the suspicion arises that perhaps the free-energy 

 chantre is at least as much smaller than the sum of the attracting energies 

 as the heat of reaction is greater than this sum. Is there any method of 

 determining quantitatively the heat which has been displaced by the 

 change of heat capacity in order to test this question ? If the free- 

 energy change could be proved to be equal to the total-energy change 

 after correction for change of heat capacity, it would lie fairly safe to 

 assume that this two-fold result really represented the attracting energies. 

 If, on the other hand, the heat evolved is still the larger, even after correc- 

 tion for the change of heat capacity, there would be valid reason to suspect 

 that the free-energy change is less than the sum of the affinities. 



Thus the question is a very fundamental one; but unfortunately the 

 exact computation of how much of the heat energy which has been 

 needed to raise the system from the absolute zero is still present as heat 

 vibration, and how much has been expended in separating the atoms, and 

 thus stored as potential energy, is impossible.* Nevertheless, the heat 

 still present as vibrational activity obviously cannot exceed the total heat 

 which has been put into the system, and this total may be calculated with 

 considerable exactness when the specific heat of ice at very low temper- 

 atures is known with accuracy. 



For the present, as usual, an approximate calculation must suffice. 

 Making allowance for every circumstance, it is hardly conceivable that 

 more than 2o00 kilojoules of heat energy have thus been introduced into 

 the system Mg -f CU.SO4 -|- 2OOII2O, in order to raise it from absolute 

 zero to 20°C. But in this system as given in the table on p. 2i)7 the 

 beat capacity changed 106 mayers during its subsequent reaction, or 

 0.71 per cent of the whole. This change, entirely apart from any heat 

 which might be evolved from the affinities concerned, might cause an 

 isothermal displacement of 0.71 per cent of the heat energy present,! 



* Boltzmann has calculated tliat about half of the enerfjy is used for each pur- 

 pose, but tlie result is doubtful. Sitz. ber. Wien. Akad., 63, II. 1871. 



t This assumption is uncertain, but lack of data forbids greater accuracy 

 (p. .293). The result given is probably a maxiinum, whicii is ail tiiat is desired. 



