Irreversible processes in general

To treat an irreversible process of a closed system that is nonadiabatic, we proceed as follows. As in Sec. 4.4.1, we use a Carnot engine for heat transfer across the boundary of the experimental system. We move the boundary of the supersystem of Fig. 4.8 so that the supersystem now includes the experimental system, the Carnot engine, and a heat reservoir of constant temperature Tres, as depicted in Fig. 4.11. 

Thermodynamics and Chemistry, second eMion, version 3 20U by Howard DeVoe. Latest version www.chem.umd.edu/thermobook 

The entropy change of the supersystem is the sum of the entropy changes of its parts  

The process within the supersystem is adiabatic and includes an irreversible change within the experimental system, so according to the conclusions of Sec. 4.5.1, diSss is positive. Equation 4.5.2 then shows that AS, the infinitesimal entropy change during the irreversible change of the experimental system, must be greater than Aq/Tb  

This relation includes the case of an irreversible adiabatic change, because it shows that if Aq is zero, dS is greater than zero. 

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The derivation begins with irreversible processes that are adiabatic, and is then extended to irreversible processes in general. 

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