Final statement of the second law

As a result of the last two propositions, the second law can now be expressed as follows  

This second result must apply to each infinitesimal stage of a process, sts may be seen by applying the last proposition to an infinitesimal change of an adiabatic system, instead of to a finite change. We can therefore writef dg 0, 

For many purposes it is convenient to convert this relation into an equality by defining a quantity cr  

As a corollary to the above, consider a thermodynamic system contained within a heat bath. The two together are an adiabatically isolated system, and therefore from (1 15) we have 

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