Irreversible chemical reaction, entropy production

For a closed system, if the change of mole numbers dNk is due to irreversible chemical reactions, the entropy production is... 

Another Way of Looking at Entropy, by Daniel Hershey in Chemical Engineering Education (1989, summer, p. 154), discusses entropy and aging. Write an expression for entropy production in the hnman body that is consistent with the following statement by Hershey The internal entropy production in living systems is a consequence of several irreversible chemical reactions which constitute the chemistry of life. ... 

Though Gibbs did not consider irreversible chemical reactions, equation (4.1.1) that he introduced included all that was needed for the consideration of irreversibility and entropy production in chemical processes. By making the important distinction between the entropy change S due to exchange of matter and energy with the exterior, and the irreversible increase of entropy djS due to chemical reactions [2, 3], De Bonder formulated the thermodynamics of irreversible chemical transformations. And we can now show he took the uncompensated heat of Clausius and gave it a clear expression for chemical reactions. 

Let us look at equation (4.1.2) from the viewpoint of entropy flow d S and entropy production diS, that was introduced in the previous chapter. To make a distinction between irreversible chemical reactions and reversible exchange with the exterior, we express the change in the mole numbers dN as a sum of two parts ... 

Further development of this theory relates the chemical potential to measurable state variables such as p, T and iV. Thus, the pioneering work of De Donder established a clear connection between entropy production and irreversible chemical reactions. In a closed system, if initially the system is not in chemical equilibrium, chemical reactions will take place that irreversibly drive the system towards equilibrium. And, according to the Second Law of thermodynamics, this will happen in such a way that (4.1.10) is satisfied. 

An example of the minimization of F is a reaction, such as 2H2(g)+ 02(g) 2H20(g), that takes place at a fixed value of T and V (Fig. 5.2(a)X To keep T constant, the heat generated by the reaction has to be removed. In this case, following De Bonder s identification of the entropy production in an irreversible chemical reaction (4.1.6), we have Td S = —Y i. i d Nk = —dF. Another example is the natural evolution in the shape of a liquid drop (Fig. 5.2(b)). In the absence of gravity (or if the liquid drop is small enough that the change... 

As an example of entropy production due to an irreversible chemical reaction, consider the simple reaction... 

That is, the entropy production in the volume consists of three terms, each of which is due to an irreversible process. The first term is the heat conduction term, the second is the mass diffusion term, and the third is the chemical reaction term. The above equation is known as the entropy production equation. 

Irreversible processes correspond to the time evolution in which the past and the future play different roles. In processes such as heat conduction, diffusion, and chemical reaction there is an arrow of time. As we have seen, the second law postulates the existence of entropy 5, whose time change can be written as a sum of two parts One is the flow of entropy deS and the other is the entropy production dtS, what Clausius called uncompensated heat, ... 

Technical combustion processes are highly irreversible. Theoretical considerations show that the irreversible entropy production of combustion can be decreased if immediate contact of fuel with oxygen is prevented and intermediate chemical reactions are supported. Therefore, the potential for mechanical work output can be increased. Metal oxides can be used as reactants for these intermediate reactions. 

The irreversible entropy production for isothermal, isobaric chemical reactions is plotted in each diagram for an isothermal irreversible process at 1200K, but can be evaluated as easily for any other temperature. 

In order to clarify these ideas, we need to compare the irreversible entropy productions (or the exergy destruction) in cycles that utilize regenerative heating of compressed air, thermal recuperation in the form of evaporation and superheating of the methanol fuel, and chemical recuperation through either reforming or cracking reaction with methanol. The next section presents such a comparison in a simplified form to illustrate the utility of thermodynamic analyses. 

Theophile De Donder showed that this paradox could be resolved elegantly by the explicit calculation of the uncompensated heat, or better of the entropy production, resulting from a chemical reaction. To do this it is necessary to introduce a new function of state, the affinity, characteristic of the reaction and closely related to its irreversibility. In a series of papers since 1920, De Donder has developed a new formulation of chemical thermodynamics by combining the fundamental features of both the Gibbs method and those of the vanT Hoff-Nernst school. 

The method developed here is in many ways analogous to that employed by Schottky, Ulich and Wagner. Both methods emphasize the criterion for establishing the irreversibility of a chemical reaction and for deciding whether the reaction will proceed spontaneously in a particular direction. In De Bonder s method this criterion appears immediately the production of entropy must be positive. On the other hand Schottky, Ulich and Wagner employ as the criterion of irreversibility the loss of useful work associated with the real process when compared with a hypothetical reversible process. As is shown in chap. V, these criteria are equivalent for isothermal changes. For non-isothermal changes, however, the concept of loss of useful work... 

The entropy production S for irreversible processes is defined as positive. If we consider one chemical reaction, the flux j and the affinity A have opposite signs, so that we get... 

In this problem we explore classical irreversible thermodynamics for a multicomponent system, entropy generation, linear laws, and the molecnlar flux of thermal energy for a ternary system. Consider an N-component system (1 < j < Af) in the presence of external force fields and mnltiple chemical reactions (1 < y < / ). g, is the external force per unit mass that acts specifically on component i in the mixture, and r, is the overall rate of production of the mass of component i per unit volume, which is defined by... 

The product of thermodynamic forces and fiows yields the rate of entropy production in an irreversible process. The Gouy-Stodola theorem states that the lost available energy (work) is directly proportional to the entropy production in a nonequilibrium phenomenon. Transport phenomena and chemical reactions are nonequilibrium phenomena and are irreversible processes. Thermodynamics, fiuid mechanics, heat and mass transfer, kinetics, material properties, constraints, and geometry are required to establish the relationships... 

A chemical reaction is an irreversible process that produces entropy. The changes in thermodynamic potentials for chemical reactions yield the affinity A. All four potentials U, H, A, and G decrease as a chemical reaction proceeds. The rate of reaction, which is the change of the extent of the reaction with time, has the same sign as the affinity. The reaction system is in equilibrium state when the affinity is zero. This chapter, after introducing the equilibrium constant, discusses briefly the rate of entropy production in chemical reactions and coupling aspects of multiple reactions. Enzyme kinetics is also summarized. 

The change of total entropy is dS = dgS + diS. The term deS is the entropy exchange through the boundary, which can be positive, zero, or negative, while the term diS is the rate of entropy production, which is always positive for irreversible processes and zero for reversible ones. The rate of entropy production is diS/dt = JkXk. A near-equilibrium system is stable to fluctuations if the change of entropy production is negative, i.e. Ai5 < 0. For isolated systems, dS/dt > 0 shows the tendency toward disorder as d S/dt = 0 and dS = diS > 0. For nonisolated systems, diS/dt > 0 shows irreversible processes, such as chemical reactions, heat conduction, diffusion, or viscous dissipation. For states near global equilibrium, d S is a bilinear form of flows and forces that are related in linear form. 

Figure 5.2 Minimization of Helmholtz free energy F. (a) If V and T are kept at a fixed value, a chemical reaction will progress to state of minimum F. In this case the irreversible production of entropy Td S — — 0- Similarly, for a liquid drop,...

The balance equation for entropy can be derived using the conservation of energy and the balance equation for the concentrations. This gives us an explicit expression for entropy production or— which can be related to irreversible processes such as heat conduction, diffusion and chemical reactions—and the entropy current is- The formal entropy balance equation is... 

Also, the entropy production due to chemical reactions in each phase should be separately positive.) Thus, the symmetry principle provides constraints for the coupling of, and the entropy production due to, irreversible processes. 

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