Entropy generation driving forces

In this chapter, we show that it is not so much energy that is consumed but its quality, that is, the extent to which it is available for work. The quality of heat is the well-known thermal efficiency, the Carnot factor. If quality is lost, work has been consumed and lost. Lost work can be expressed in the products of flow rates and driving forces of a process. Its relation to entropy generation is established, which will allow us later to arrive at a universal relation between lost work and the driving forces in a process. 

At this point the need arises to become more explicit about the nature of entropy generation. In the case of the heat exchanger, entropy generation appears to be equal to the product of the heat flow and a factor that can be identified as the thermodynamic driving force, A(l/T). In the next chapter we turn to a branch of thermodynamics, better known as irreversible thermodynamics or nonequilibrium thermodynamics, to convey a much more universal message on entropy generation, flows, and driving forces. 

In Section 3.3, we have shown that the entropy generation rate in the case of heat transfer in a heat exchanger is simply the product of the thermodynamic driving force X = A(l/T), the natural cause, and its effect, the resultant flow / = Q, a velocity or rate. Selected monographs on irreversible thermodynamics, see, for example, [1], show how entropy generation also has roots in other driving forces such as chemical potential differences or affinities. 

Finally, we want to mention that Prigogine [1] has shown that for a coupled system of flows and associated driving forces, the rate of entropy generation is at a minimum when the system is in the nonequilibrium steady state all non-steady states are associated with higher rates of entropy generation. ... 

This chapter establishes a direct relation between lost work and the fluxes and driving forces of a process. The Carnot cycle is revisited to investigate how the Carnot efficiency is affected by the irreversibilities in the process. We show to what extent the constraints of finite size and finite time reduce the efficiency of the process, but we also show that these constraints still allow a most favorable operation mode, the thermodynamic optimum, where the entropy generation and thus the lost work are at a minimum. Attention is given to the equipartitioning principle, which seems to be a universal characteristic of optimal operation in both animate and inanimate dynamic systems. 

The ideal, unrealistic, but basic limit of the thermodynamic efficiency of a process is that of the reversible process where all work available and entering the process is still available after the process. Work has simply been transferred from one carrier to another. Driving forces are infinitesimally small and the process is "frictionless" no barriers have to be taken. As a result, there is neither entropy generation nor loss of available work. The work requirements of the process can be accurately calculated from the thermodynamic properties of the equilibrium states that the process passes through. 

For the establishment of the realistic limit, one has to take account of the rates of processes in which mass, heat, momentum, and chemical energy are transferred. In this so-called finite-time, finite-size thermodynamics, it is usually possible to establish optimal conditions for operating the process, namely, with a minimum, but nonzero, entropy generation and loss of work. Such optima seem to be characterized by a universal principle equiparti-tioning of the process s driving forces in time and space. The optima may eventually be shifted by including economic and environmental parameters such as fixed and variable costs and emissions. For this aspect, we refer to Chapter 13. 

The above equation implies that the extremum is a minimum. Thus, with a constant transfer coefficient, the distribution of the driving force that minimizes the entropy generation under the constraint of a specified duty is a uniform distribution. The minimal dissipation for a specified duty implies the equipartition of the driving force and entropy generation along the time and space variables of the process. 

Basic Idea Already in the nineteenth century it was assumed that the energy Wf released in a chemical transformation as well as the heat generated by it were a measure of the driving force of such a process. Energy was considered to he free when, for given conditions, it could be used for some other purpose, especially generation of entropy. W( increases proportionally to the conversion A, so Wf itself is not the correct measure, but Wf, relative to the conversion, is or, more... 

The entropy of the system is assumed to be exclusively generated by the heat conduction from the hot to the cold fluids. The entropy production rate, at microscopic level, can be estimated as the product of thermal driving force and heat flux. From a macroscopic stand-point the measurable heat flow is used for this computation. A better approximation can be obtained by introducing phenomenological coefficients (Hasse, 1969 Koeijer, 2002 Meeuse, 2003). For our analysis, however, we adopt an alternative approach. The overall steady state entropy equation of change is applied and the production term is related to the net change of entropy. 

Extended Stefan-Maxwell constitutive laws for diffusion Eq. 4 resolve a number of fundamental problems presented by the Nemst-Planck transport formulation Eq. 1. A thermodynamically proper pair of fluxes and driving forces is used, guaranteeing that all the entropy generated by transport is taken into account. The symmetric formulation of Eq. 4 makes it unnecessary to identify a particular species as a solvent - every species in a solution is a solute on equal footing. Use of velocity differences reflects the physical criterion that the forces driving diffusion of species i relative to species j be invariant with respect to the convective velocity. Finally, all possible binary solute/solute interactions are quantified by distinct transport coefficients each species i in the solution has a diffusivity or mobility relative to every other species j, Djj or up, respectively. 

As mentioned before, nonequilibrium thermodynamics could be used to study the entropy generated by an irreversible process (Prigogine, 1945, 1947). The concept ofhnear nonequilibrium thermodynamics is that when the system is close to equilibrium, the hnear relationship can be obtained between the flux and the driving force (Demirel and Sandler, 2004 Lu et al, 2011). Based on our previous linear nonequihbrium thermodynamic studies on the dissolution and crystallization kinetics of potassium inorganic compounds (Ji et al, 2010 Liu et al, 2009 Lu et al, 2011), the nonequihbrium thermodynamic model of CO2 absorption and desorption kinetics by ILs could be studied. Figure 17 shows the schematic diagram of CO2 absorption kinetic process by ILs. In our work, the surface reaction mass transport rate and diffusion mass transport rate were described using the Hnear nonequihbrium thermodynamic theory. 

The driving force for this exergonic reaction is the generation of the carbonyl bond. The metabolic reaction is catalyzed by chorismate mutase. The enzyme increases the rate by a factor of a million. The enzyme mechanism has been extensively studied, and it appears that the enzyme stabilizes the transition state in the conformation required for catalysis. Thus, it might well be that the enzyme increases the reaction rate mostly by an entropy effect. 

Equation (2.3.10) shows that in closed systems, entropy can be generated in two general ways. First, as already discussed in 2.1.2, the lost work 5Wiogt is the energy needed to overcome dissipative forces that act to oppose a mechanical process. Second, the heat-transfer term in (2.3.10) contributes when a finite temperature difference irreversibly drives heat across system boundaries. This second term is zero in two important special cases (a) for adiabatic processes, = 0, and (b) for processes in which heat is driven by a differential temperature difference, Tg t = T dT. In both of these special cases, (2.3.10) reduces to... 

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