Entropy as a function of state

It will be noticed that the proof depends on the existence of entropy as a function of state. The experimental verification of (2 91) is thus, in a certain sense, a confirmation of the second law, and the same may be said of any of the other quantitative relations based on this law. For practical purposes the value of equations such as (2 91) is the calculation of one quantity, say from known values of the others. 

On account of the second law— the existence of entropy as a function of state—the Joule-Thomson coefficient can be related to other measurable properties of the gas. Thus from (2 95)... 

Only the third equality is conditional on the temperature being measured on an absolute scale. The proof of the first two equalities depends only on the definitions of Cj, andC in terms of H and U, and is no dependent on the second law (i.e. on the existence of entropy as a function of state). On the other hand, the proof of the third equality requires the second law. 

Entropy, as formulated here and in the previous chapter, encompasses all aspects of matter transformations changes in energy, volume and composition. Thus, every system in Nature, be it a gas, an aqueous solution or a living cell, is associated with a certain entropy. We shall obtain explicit expressions for entropies of various systems in the following chapters and study how entropy production is related to irreversible processes. At this stage, however, we shall note some general properties of entropy as a function of state. 

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