ENTROPY 65 



known as "the order-disorder transition." The entropy goes down as the 

 transition is made from disorder into order. 



The conclusion then is, that we may accept entropy as a measure of 

 disorder and disorder as a way of visualizing entropy, provided that we are 

 prepared to define "disorder" in ways which at least in certain striking 

 cases do not depart impossibly far from its traditional meaning. A conse- 

 quence of this attitude is, that it is plausible and sensible to attach the 

 value zero to the constant here called So, the entropy of any substance of a 

 single kind in a crystalline phase at the absolute zero. The words "in a 

 crystalline phase" are a reservation to the original statement. If further 

 reservations become necessary, they will of course have to be made. 



The Theory of the Constant /. 



To give even an inkling of the theory of the constant /, it is desirable to 

 take "probability" as the word for which meanings must be found, not too 

 distant from the popular meaning and yet fruitful for the study of entropy. 

 Those who began this process were Gibbs and Boltzmann, working in the 

 closing years of the nineteenth century. Their ideas have since undergone 

 many a transformation, usually in the direction of greater adequacy but 

 also (alas!) in that of greater difficulty. I will follow a route beginning as 

 Boltzmann's did, but carried onward in a manner which became possible 

 about thirty-five years ago, at the time when Nernst's Heat Theorem was 

 oeing established. It does not lead us quite the whole way to the accepted 

 . .Aue of /, so that at the end I shall have to make an extra step without 

 doing more than to indicate whence its justification comes. 



We begin by considering a gas in a container of volume V, in equilibrium 

 with itself and with the outer world at a temperature T. "In equilibrium 

 with itself" implies first of all that it is evenly spread throughout the 

 volume of the container — surely one of the earliest of all inbred ideas con- 

 cerning the behavior of gases. To give a quantitative meaning to this 

 notion of the gas being evenly spread throughout the container, we imagine 

 the volume divided into little compartments or cells of equal volume Fo. 

 The statement then is that the number of atoms in every cell is the same. 

 Putting N for the total number of atoms and Nfi for the number in the ith 

 compartment, 



fi = constant = Vo/V (17) 



The quantity /i is called the "probability" that an atom chosen at random 

 shall be in the zth cell — the first occurrence of the word "probability" with 

 a definite meaning in this discourse. 



The next step is to define the entropy in the manner which follows: 



