62 BELL SYSTEM TECHNICAL JOURNAL 



This is often incorporated into (15), and alters its aspect; but until page 71 

 I will pass over this detail. If the point (P, T) lies beside the liquid-gas 

 divide, the isobar to which (14) refers will cut both this and the solid-liquid 

 divide, and traverse the liquid region. Extra terms will then appear in 

 (14) and in (15), but I leave it to the student to divine them. 



The Theory of the Constant ^o 



The theory of the constant ^o is easy to state, provided that no objection 

 is raised to having it stated in a manner rather too drastic at first, and 

 waiting for the necessary reservations to be added later. 



The constant Sq — the entropy at the absolute zero — is taken to be zero for 

 euery substance of a single kind. 



This is a way of putting, and the strongest possible way of putting, what 

 is known as "Nernst's Law" or "Nernst's Heat Theorem" or even "the 

 Third Law of thermodynamics." Originally expressed in a much milder 

 form nearly forty years ago, it rapidly progressed to the stringent form 

 embodied in these words. As I have suggested already, it is a form too 

 stringent; but the truth lies nearer to it than to the milder phrasings earlier 

 used, and therefore it is justifiable as a commencement. 



Notice to begin with that, in the statement as just given, there is no 

 allusion to the pressure or the volume. It is therefore asserted that, at the 

 absolute zero, the entropy of a substance (of a single kind) does not depend 

 on either. This I implied already in the caption to this section, by dis- 

 carding the symbol S{P, 0) which had previously served for the additive 

 constant in (14), and replacing it by ^o. From the general thermodynamic 

 equations based on First and Second Laws, it can be shown that if this is 

 true for any substance in particular, then certain measurable features of that 

 substance — notably the coefficient of thermal expansion — must be zero at 

 the absolute zero. Now it does appear to be a general rule that this co- 

 efficient, and the other features in question, are trending rapidly to zero at 

 the lower end of the accessible range of temperatures; so this, the mildest 

 form of the "Third Law," is well attested. 



Notice then that in the statement as given there is no allusion to phase. 

 Thus, if any substance can exist in both the solid and the liquid phase at the 

 absolute zero, its entropy must be the same in both (if the theorem is true). 

 If we insist on fluidity as a quality of a liquid, there is evidently just one 

 such substance — helium, of course. It appears that for this case the 

 theorem is true.^ 



* At the lowest accessible temperatures, the divide between the "Hquid" area and the 

 "solid" area of the phase-diagram is running nearly parallel to the temperature axis, 

 and heading for the ordinate 25 (in atmospheres) on the pressure-axis. Strict parallehsm 

 of the divide to the temperature-axis, which is probably reahzed just before the absolute 

 zero, would imply equality of entropy in the two phases (by one of the thermodynamic 

 equations hinted at above). Another item of evidence is cited on p. 72. 



