ENTROPY 73 



to be carried over all values of £,. There is less of a mental obstacle now 

 than there was in the "translatory" terms, for the doctrine of discrete per- 

 mitted energy-values in rotation is among the oldest, while that of discrete 

 energy-states in vibration is quite the oldest, of the whole of quantum- 

 theory. To get the energy-values £«-, the spectra are consulted. Spectrum 

 analysis is the most highly-developed of the branches of physics, and the 

 knowledge of the values of £, which it affords for the better-known of the 

 diatomic molecules — and even for some few of the triatomic — may be 

 described as complete, daring as it may sound. 



Values of entropy figured by the statistical way which I have been 

 describing, with additions duly made to the partition-function to allow 

 for rotation and vibration, are called "spectroscopic" entropy-values by 

 Giauque and his colleagues of the Berkeley school. As a rule they are 

 computed for a standard pressure and temperature, often for one atmosphere 

 and 25°C.; let us call these Pq and To. Now as a rule the point (Po, Tq) 

 does not lie just off the divide which on the phase-diagram separates solid 

 (or liquid) from gas. One may, however, use (11) for getting the entropy- 

 difference between (Po, T'e) and any such point {P, T) lying along the 

 divide on the side corresponding to gas. At the point (P, T) the entropy 

 may be evaluated by the right-hand member of (14), and to it may then be 

 added the entropy-difference just mentioned. The sum, computed with the 

 assumption that So is zero, is what Giauque and his school name a "calori- 

 metric" entropy-value. If the two agree, there is a verification of the 

 conjoined assumptions that the statistical theory is sound, and that the 

 crystalline solid at zero absolute has none of that disorder which is the 

 source of entropy. 



I take the following data from Eastman^ of the Berkeley school. Of his 

 two tables, one comprising gases for which the data are definitely better 

 known than they are for the rest, I quote this one only. The accuracy of 

 the calorimetric value "is in all cases high, errors being of the order of 0.1 

 throughout." The supposed accuracy of the spectroscopic values is in- 

 dicated by the number of significant figures to which they are carried. 



^ Chem. Rev. 18, 257 (1936). 



