( 202 ) 



Now tlie question rises iiow under certain condijions the two tber- 

 niodjnaniic functions U and A (vai-iation of tlie total and the free 

 energy) behave al low temperatures, and in the discussion of this 

 (|uestion I pointed out that when gases are present in the considered 

 system, we cannot reach the absolute zero of temperature wiliiout 

 discontinuities making theii- a|)j)earance, bid that when only solid and 

 li(piid substances occur, the following equation holds: 



dA dU 



Urn -— = Ivtn — =r 0, for 7' = C2). 



dT dT '' ^^ 



The (juestion what is the relationshii) between U ami A for very low 

 temperatures, has, moreover, already been ti-eated by different authors'); 

 hence it seemed superlluous to me to give further explanation about 

 this problem itself. 



In the strange way in which they treat the problem the two 

 authors write that "it may be assumed" that the meaning is that 

 the limit is approached with constant volume, because otherwise 

 the whole [)roblem would be indefinite. 



It appears fi-om this remark that the authors do not quite under- 

 stand the meaning of equation (2), and though it seems hardly 

 necessary, I shall illustrate the question of the way in which 

 the limit is reached by an example. Let us consider the reaction 



S (rhomb) —^ S {mon) ; 



independently of the pressure under which the two modiücations 

 of the sul|)hur are, A possesses definite values, of course variable 

 with the pressure. As equation (2) if it is correct, must also hold 

 for the case of compression — and we come here to the conclusion 

 that for low temperatures the heat of compression A — U becomes 

 equal to 0'^) — we need not impose any restriction on equation (2): 

 only the differential quotient of A must of course in each special 

 case be formed in the way that classical thermodynamics requires for 

 equation (1). I can, however, not be expected to set this forth more 

 fully here. 



The authors now come to the conclusion in a rather circumstantial 

 way, some points of which are by no means indisputable that when 

 we consider van der Waals' formula to hold for tluids down to 

 any temperature however low, equation (2j cannot hold. 



This result, which, of course, ] had known for a long time, may 

 be arrived at in the following direct and exact way. 



1) Van 't Hoff, Boltzmann Festschrift 1904 S. 238; Brönsted, Zeitschr. phys. 

 Ghem. 56 645 (1906). 



•) Nernst, Journ. de Ghim. Phys. 8 236 (1910). 



