ENTROPY 63 



There are substances able to exist in two or more crystalline phases: tin 

 and sulphur are probably the best-known examples. For some of these 

 it is possible to start with one phase at a temperature extremely low: 

 warm the substance up to a temperature of "transition," at which it changes 

 reversibly into the other phase; and cool the new phase down to the tempera- 

 ture at which the experimenter started. Let me denote by Si the entropy 

 at the commencement of this process; by ^2 the entropy at its finish; by 

 Cpi and Cp2 the specific heats of the two phases; by Tt the temperature of 

 transition, by Lt the heat absorbed during the transition. We have: 



S2- Si= ( ' {CJT) dT + Lt/Tt - I ' {Cp,/T) dT (16) 



According to Nernst's Theorem, S2 and ^i and consequently their difference 

 should vanish if the extremely low temperature at start and finish were 

 the absolute zero. We should therefore expect the right-hand member 

 of this equation to be at any rate extremely small, if the temperature in 

 question is at the bottom of the accessible range. Such is indeed the case. 



It is very evident that the argument just given proves at the very most 

 that the entropies of the two phases are equal at the absolute zero — not that 

 either of them has the particular value zero. The like is true for the other 

 arguments thus far cited; and indeed in the earliest phrasings of the "Third 

 Law," no value was Assigned to the entropy at the absolute zero — neither 

 the value zero, nor any other. Why then are we to adopt, and presently 

 seek to justify, the particular value zero? One part of the answer will be 

 the climax of this paper. The other derives from the speculations as to 

 the nature of entropy, which for half a century have been among the most 

 deeply perpended, the most difficult and the most fruitful of the divisions 

 of theoretical physics. 



There are two words which dominate these speculations: "probability" 

 on the one hand, "disorder" on the other. Both of these are very familiar 

 words with very familiar meanings, and some tinge of the familiar meaning 

 is in each case carried over into the technical meaning. The technical 

 meanings, are, however, abstruse; and cynical though it may sound, there 

 is no exaggeration in saying that a large part of the speculation consists in 

 trying to find meanings for the one and the other, which can be fruitfully 

 used in the study of entropy. "Disorder" is the word which we shall 

 examine first. 



The familiar meaning of the word "disorder" leads straight to one useful 

 consequence. Of all the possible or conceivable states of matter, the one 

 which anybody would choose as the least disorderly is the crystalline state. 

 But moreover, most people would deem the thermal agitation of the atoms 

 in a crystal as a departure from order; therefore the colder the crystal, the 



