The Laws for Closed Nonreacting Systems

Careful observation teaches us that, left undisturbed, every material system tends to evolve to a unique equilibrium state that is consistent with any imposed constraints. The rates of such evolutions cannot be determined from thermodynamics, but thermodynamics does provide quantitative criteria both for identifying the directions of such evolutions and for identifying equilibrium once it is reached. Those criteria are obtained by combining the first and second laws. 

In Chapter 3 we combined the first and second laws to obtain the fundamental equations for closed systems one example is (3.2.4), which we now write as 

But in writing such equations, we assumed that our system is homogeneous—that its values for intensive properties are uniform throughout. Here we want to generalize the development so we can identify equilibrium in heterogeneous systems, especially those in which the heterogeneity results from the presence of more than one part, such as multiple phases. For such systems, the fundamental equation (7.1.1) takes the form 

We now consider the term in (7.1.4) that applies to the surroundings. The first law for the surroundings takes the form 

Next we replace the path functions in (7.1.7) with state functions. To eliminate the heat, we appeal to the second law (2.3.8), which for this situation takes the form 

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In this section we obtain the combined first and second laws for reacting systems. The development parallels that presented in 7.1 for nonreacting systems. However, the development here is more elaborate than the earlier one because our analysis must account for the fact that, during reactions, chemical species are not conserved. This problem is addressed in 7.4.1 and examples are offered in 7.4.2 and 7.4.3 then in 7.4.4 we derive the combined laws for reactions in closed systems. 

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