Uniform Reacting Mixture in Closed System

Balance of energy (2.1) and entropy inequality (2.2) may be applied also for more complicated models [59, 67], namely mixtures and multiphase systems. Similarly classical thermodynamics balances (2.1), (2.2) have given the equilibrium result (namely model A of Sect. 2.2) and we can then obtain classical results for chemical and phase equilibria we show them on simple examples in Sects. 2.4,2.5. 

In this Sect. 2.4 we discuss the uniform fluid (i.e., gas or liquid) mixture composed of two constituents (components of mixture) 1, 2 which (possibly) chemically react by a simple chemical reaction 

However, these models are closed (not exchanging mass with surroundings). In their opposite-open systems (the whole mass of which is not constant)-it is not clear how to formulate heat when mass passes through the boundary simultaneously [12, 43]. Plausible formulation seems to be known in continua, cf. Sects. 3.1,4.4 and Rems. 23 in Chap. 3,11 in Chap. 4. 

The whole mass m of the system is constant and this closed system, exchanging only heat and volume work with its surroundings, is supposed to be described again by fields (time function) (2.3) and (2.4) added with fields of (positive) masses /ni(t), m2(t) of both constituents 1, 2 respectively. For closed systems (cf. Sects. 1.2, 2.1) the balance of energy (2.1) and entropy inequality (2.2) are valid but now together with the balance of mass 

Using free energy (2.12), we can also use the reduced inequality (2.13) joining energy balance and entfopy inequality. 

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