488 SESSION V. DISCUSSION 



where Tn represents the temperature of the surrounding medium, d^/dr the rate of the 

 reaction and A the 'affinity' of the system. If 7^ is low di^/df will be practically equal to 

 zero and the entropy of a 'frozen' system does not increase even though A ; > o. 



In actually existing systems there must be catalysts which enable the chemical reactions 

 to occur at Ta- Let us suppose that in the open systems there are catalysts under the 

 influence of which 



- const, -a. 



.at/ cat., 



Then, if we consider the 'affinity' A as being of constant magnitude, we obtain : 



A = aA =Ci 



éS\ /d^\ 



^dr / irrcv. cat., \df/cat.i 



and 



r^A^COirrev. cat., = CiAf + Ca (3) 



From equation (i) the magnitude raA5(r)irrcv. cat., is equal to the whole amount of 

 'uncompensated heat'. Hence: 



TaASCOirrev. cat., = A?(f) = CiAl (4) 



As for the sum CiAr + C2 this is equal to the total amount of potential energy AFIcat., 

 which is dissipated during the course of the irreversible process : 



Ancat.. = r„A5(r)irrcv. cat., + Ca (5) 



Furthermore, equation (5) shows that the process must necessarily take place in one 

 direction, from left to right, in that the term denoting the entropy is a function of time. 

 Ag(r) represents the flow of heat. According to Fourier's law 



q --^ grad T. 



The temperature of the open system, Teat. 5 must therefore be higher than the tem- 

 perature of the surrounding medium. Under stationary conditions the flow of heat out- 

 wards from the open system is [2] : 



^q{t) = ß^crcat., - r„)Af (6) 



where ß is a form factor and Ti is the mean conductivity of the material concerned for the 

 particular temperature difference. Before the beginning of the flow of heat the internal 

 energy of the open system must have increased to a value of CXTcar.. — Ta) where d is 

 the mean thermal capacity of the open system. Hence 



Ca = C„(rcat. - Ta) (7) 



From equations (4), (5), (6) and (7) we obtain an equation for the motion of the whole 

 system : 



AHcat., = Bh{Tc^l. - Ta)^t + C,{Tcal. - Ta) (8) 



Let us suppose that there are, within the open system, catalysts (cat.2) under the influence 

 of which the rate of the chemical reactions is a function of time : 



^') =-- a + q>{t) (9) 



dt/cat.. 



If the state of the whole system is sharply displaced in relation to the thermodynamic 

 equihbrium, then the rate of the chemical reaction will be exponential in nature [3] : 



<p{t) = f(r)e*' (ic 



where f(r) is a function of time and ^ is a constant. 

 From (9), (10) and (2) we obtain 



T„ [^^\ = [a + f(r)e^'] A 



\dr / irrcv. cat.« 



and 



7'„A5(0irrcv. cat., = ^ J f(r)e^'df + Bk{Tcz,. - Ta)àt 



