188 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS 



method takes the following form: The properties of a quantity, In 12, are 

 considered in some detail, and it is shown that In 12 has the two fundamental 

 characteristics of thermodynamic entropy: (1) that In 12 for two or more in- 

 dependent systems is the sum of the In 12's for all the individual systems — 

 that is, that In 12 is an extensive property dependent upon quantity; and (2) 

 that In 12 increases for all spontaneous changes occurring in a system for 

 which the quantity of material and the energy are held constant. Both these 

 properties have been introduced earlier, although not in just this form. The 

 proportionality constant, R (cal/deg mole), then is introduced to relate S 

 and In 12: 



S = R In 12 



In this development 12 is a pure number, the number of ways in which the 

 particles or parts of the system can be arranged (organized or disorganized). 

 For one of a pair of playing dice the number is 6 (six sides). For a mole, 

 which contains 6 x 10 23 molecules, this number, 12, could be counted out, 

 if we were clever and patient enough! However, approximations can be 

 made through the methods of statistics which give closely enough the num- 

 ber of ways the particles can be arranged. Hence the expression above 

 means that the entropy, S, of a system increases as the number of ways in 

 which the system can be arranged increases. The greater the chaos or dis- 

 order, the greater the number of ways; and the greater the entropy of the 

 system. 



It has already been shown that all naturally occurring processes, which 

 occur irreversibly, make a positive contribution to the entropy and hence the 

 heat energy of the universe. If there are no violations of the Second Law 

 elsewhere in the universe, the available energy is decreasing all the time, 

 and the universe is approaching the ominous "heat death" or "entropic 

 death," in which the free energy will have reached zero and the entropy a 

 maximum or upper limit. We have then the two interesting possiblities: 

 a one-step creation during which the whole was wound up, from which condi- 

 tion it has been slowly running down ever since; or the continuous violation 

 of the Second Law is occurring somewhere in the universe. An interesting 

 question, then, is: Is continuous creation occurring within the living thing? 



Hence, one of the more important aspects of this study of entropy changes 

 centers on the fact that, although the net result of any physical process must 

 be (Second Law) a positive entropy contribution to the universe, there are 

 some processes in which the entropy definitely decreases within a limited 

 space; and it is not very obvious where the overriding increase, if any, occurs 

 to the universe. The process referred to is the creation of the living thing 

 (Figure 7-8), which, although very complex, is certainly not disordered. In 

 fact it is much more highly ordered than the components from which it is 



