The third law—preliminary

Now quantum theory assigns definite values to the P s and also to Cl. Therefore, for any system, 8 and 8 have perfectly definite values which are positive or zero. (They cannot be negative because the probabilities Pi are all fractions and the number of complexions Cl of the system cannot be less than one.) 

It was shown subsequently that 8 and 8 possess all of the properties of entropy and the primes were therefore deleted. On the other hand, since thermodynamics deals only with changes of entropy, it is clear that the statistical analogues would have been equally satisfactory if they had contained an additive constant. Let us write such a constant in the form —i( ln Then the entropy analogue 

In Chapter 12 we discussed randomization over translational and configurational states and also, to some extent, over rotational, vibrational and electronic states. Two other factors which are known to contribute small amounts to the entropy are (a) the number of possible orientations of the nuclear spins and (6) the entropy of isotope mixing. (The latter factor arises if the substance in question contains two or more isotopes.). However, this leaves quite untouched the possibility of randomness within the nncUus about which nothing whatever is known. It is evident that even when we have allowed for all the known factors our computed entropy may still be incomplete. 

In brief, it is not possible to calculate absolute entropies. Instead it is necessary to adopt some convention concerning what factors are to be included in Q, in view of the present state of knowledge. The convention which is usually adopted in physical chemistry is that the entropy is taken as zero when the substance is in a physical state such that translational, configurational, rotational, vibrational and electronic contributions to the entropy are all zero. Contributions due to the nucleus, including its spin, are ignored and also the effect of isotope mixing. The justification for omitting these factors lies in the fact that nuclei are conserved in chemical processes and also because the isotopic composition usually remains almost constant. 

Effects of this kind therefore cancel when we consider changes of entropy. 

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