Entropy, Reversible and Irreversible Processes

The usefulness of the concept of entropy and the Second Law depends on our ability to define entropy of a physical system in a calculable way. Using (3.3.3), if the entropy So of a reference or standard state is defined, then the entropy of an arbitrary state S% can be obtained through a reversible process that transforms the state 0 to the state X (Fig. 3.6). 

A process is reversible only in the limit of infinite slowness as perfect reversibility is approached, the speed of the process tends to zero. As Max Planck notes in his treatise [5, p. 86], Whether reversible processes exist in nature or not, is not a priori evident or demonstrable . But irreversibility, if it exists, has to be universal because a spontaneous decrease of entropy in one system could be utilized to decrease the entropy of any other system through appropriate interaction a spontaneous decrease of entropy of one system implies a spontaneous decrease of entropy of all systems. Hence, either all systems are irreversible, or none are. 

in most texts on thermodynamics, an irreversible transformation is usually identified by the Clausius inequality 

Clausius also stated the Second Law like this Uncompensated transformations can only be positive. [4, p.-247]. 

Perhaps Clausius hoped to, but did not, provide a way of computing N associated with irreversible processes. Nineteenth-century thermodynamics remained in the restricted domain of idealized reversible transformation and without a theory that related entropy explicitly to irreversible processes. Some expressed the view that entropy is a physical quantity that is spatially distributed and transported (e.g. Bertrand [7] in his 1887 text), but still no theory relating irreversible processes to entropy was formulated in the nineteenth century. 

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