Abstract
We reexamine the basic equation from which Clausius deduced the existence of entropy for a reversible cycle. By endowing the uncompensated heat and the compensated heat (d Q/T) in the equation with the status of physically independent entities, we show that there exists an entropy for an irreversible cycle consisting of a reversible and an irreversible process. The differential d S for entropy change over an irreversible process has the form of an extended Gibbs relation which reduces to the equilibrium Gibbs relation if the process is reversible. From the differential form follows a local entropy balance equation with a positive source term as a representation of the second law of thermodynamics.
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