Entropy production and subsystems

Example 1.4 Entropy production and subsystems Equation (1.91) can be applied to various irreversible processes. Let us consider a system consisting of two closed subsystems of I and II, and maintained at uniform temperatures of Tl and 7 , respectively. The total entropy dS is expressed as 

Equation (1.101) shows that the rate of entropy production is the product of flow (heat flux) (8 qldt), and the thermodynamic force, (l/T1 —l/T11). 

Equation (1.90) is the total differential of the entropy as a function of the variables U and V only. To generalize this relation, we also consider the changes in the amounts of species. Using the mole amounts for the species, we have a general expression for the change of entropy from the Gibbs relation 

Equation (1.102) is one of the main relations for calculating entropy production. 

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