Order and the Third Law of Thermodynamics

To make a proportionality an equality, a proportionality constant is necessary  

There are several important ramifications of equation 3.26. First, it introduces the concept that an absolute entropy can be determined. Entropy thus stands alone among state functions as the only one whose absolute values can be determined. Therefore, in large thermodynamic tables of At/ and AH values, parallel entries for entropy are for S, not AS. It also implies that the entropies found in tables are not zero for elements under standard conditions, because we are now tabulating absolute entropies, not entropies for formation reactions. We can determine changes in entropies, AS s, for processes up to now we have dealt exclusively with changes in entropy. But Boltzmann s equation 3.26 means that we can determine absolute values for entropy. 

Second, equation 3.26 brings up an intriguing notion. Consider a system where all species (atoms or molecules) of the component are in the same state. One way of illustrating this is to assume that it is in the form of a perfect crystal, implying perfect order. If this was the case, then ft (the number of possible combinations of conditions that would have this arrangement) would be 1, the logarithm of ft would be zero, and thus S would be zero. 

O equals 6 in this case. Chapter 17 gives more details on this and other concepts relating to Boltzmann s interpretation of entropy. 

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