By Alexander N. Gorban, Boris M. Kaganovich, Sergey P. Filippov, Alexandre V. Keiko, Vitaly A. Shamansky, Igor A. Shirkalin

This e-book discusses mathematical types which are in response to the options of classical equilibrium thermodynamics. they're meant for the research of attainable result of various typical and creation methods. in contrast to the normal versions, those let one to view the achieveable set of partial equilibria on the subject of constraints on kinetics, power and mass alternate and to figure out states of the studied platforms of curiosity for the researcher. software of the recommended types in chemical expertise, power and ecology is illustrated within the examples.

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**Additional info for Thermodynamic Equilibria and Extrema: Analysis of Attainability Regions and Partial Equilibrium**

**Sample text**

Being closed, the models applied should also possess an aggregate of valuable qualitative characteristics. In principle we can construct the formal thermodynamics by building on ﬁve variables only: pressure P, volume V , temperature T , internal energy U and entropy S, as well as by two more quantities: heat q and work l, which can be expressed via these variables. However, the vocabulary – at a minimum it contains only the listed terms—does not make it possible to see all the qualitative diversity of thermodynamic systems and processes, nor does it give clear explanations of their speciﬁc features or unfold clear and efﬁcient theoretical principles.

Examples of these techniques were mentioned above. Decrease in the number of phases when modeling a heterogeneous system can be illustrated in the example of studying atmospheric processes; in that discussion, formation of harmful substances on the surface of aerosols is described by their emergence in the homogeneous medium. Equilibrium Thermodynamics [81] presents examples of real systems descriptions by ideal models: a real gas by an ideal gas; real solutions by ideal solutions; the mixture of adsorbed substance on the surface of solid phase by ideal surface gas.

The above differentiation of mathematical models was carried out in accordance with the probable composition of real systems to be modeled. The systems may contain: ideal gas phase; real gases; plasma consisting of neutral active particles (radicals), ions, and electron gas; pure condensed substances; ideal solutions of neutral substances and solutions of electrolytes; surface gas (two-dimensional gas of adsorbed substances on the surface of adsorbent); substances in colloidal (dispersed) state, with the surfaces of their particles subject to the surface tension forces, and other components.