Entropy generation coefficients

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. 

In other words, the matrix giving the phenomenological coefficients for the system is symmetric. Another important part of this theory is that one can estimate the entropy generated in an irreversible process. Onsager showed that the local rate of entropy production per unit volume is... 

Lee and Kesler (reference cited) found an accurate representation for compressibility of both gases and liquids by combining BWR-EOS with corresponding states law. They generated departure functions for enthalpy, entropy, fugacity coefficient and heat capacity. Tables are given in Reid et al. (1987), whereas illustrative graphs are presented in Perry (1997). The method is similar to that developed for compressibility. As an example, the enthalpy departure function may be calculated with the relation ... 

The quantity Ss TcTe)IQe in the denominator is positive, which implies that entropy generation decreases the coefficient of performance. The maximum value of the coefficient of performance is obtained under reversible operation. Setting Sgen = o we find... 

The general equations of change given in the previous chapter show that the property flux vectors P, q, and s depend on the nonequi-lihrium behavior of the lower-order distribution functions g(r, R, t), f2(r, rf, p, p, t), and fi(r, P, t). These functions are, in turn, obtained from solutions to the reduced Liouville equation (RLE) given in Chap. 3. Unfortunately, this equation is difficult to solve without a significant number of approximations. On the other hand, these approximate solutions have led to the theoretical basis of the so-called phenomenological laws, such as Newton s law of viscosity, Fourier s law of heat conduction, and Boltzmann s entropy generation, and have consequently provided a firm molecular, theoretical basis for such well-known equations as the Navier-Stokes equation in fluid mechanics, Laplace s equation in heat transfer, and the second law of thermodynamics, respectively. Furthermore, theoretical expressions to quantitatively predict fluid transport properties, such as the coefficient of viscosity and thermal... 

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. 

Thompson [8]). Pure A and B are assumed to melt at 800 and 1000 K with the entropy of fusion of both compounds set to 10 J K-1 mol-1 (this is the typical entropy of fusion for metals, while semi-metals like Ga, In and Sb may take quite different values - in these three specific cases 18.4, 7.6 and 21.9 J K-1 mol-1, respectively). The interaction coefficients of the two solutions have been varied systematically in order to generate the nine different phase diagrams given in Figure 4.10. 

The molar volume change in ionization reactions at higher temperatures and pressures cannot be calculated for most of the aqueous complexes because of a lack of data on isobaric expansion and isothermal compressibility coefficients. Entropy and heat capacity correlations have recently been used to generate equation of state parameters for estimating molal volumes of aqueous complexes at elevated temperatures and pressures (Sverjensky, 12). These coefficients are available for aqueous complexes only of univalent anions and, therefore, the pressure dependence of ionization constants at elevated temperatures cannot be estimated using Equation 4. 

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. 

NIST/ASME Steam Properties Database versiou 2.21 http //www.nist.gov/srd/nistlO.cfm (accessed November 10, 2010) (purchase required). Thermophysical properties include in the STEAM Database temperature, Helmholtz energy, thermodynamic derivatives, pressure, Gibbs energy, density, fugacity, thermal conductivity, volume, isothermal compressibility, viscosity, dielectric constant, enthalpy, volume expansivity, dielectric derivatives, internal energy, speed of sound, Debye-Hlickel slopes, entropy, Joule-Thomson coefficient, refractive index, heat capacity, surface tension. The STEAM database generates tables and plots of property values. Vapor-liquid-solid saturation calculations with either temperature or pressure specified are available. 

AIST can calculate the values of density, compressibility, enthalpy, entropy, isochoric and isobaric heat capacity, speed of sound, adiabatic Joule-Thomson coefficient, thermal pressure coefficient, samrated vapor pressure, enthalpy of vaporization, heat capacities on the saturation and solidification lines, viscosity and thermal conductivity. Values of properties can be determined at temperatures from the triple point up to 1500 K and pressures up to 100 MPa. The system generates the following databases with appropriate algorithms and programs for their calculation ... 

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