Transport of entropy

Likewise, we can relate the heat of transport and entropy of transport by using the relation... 

The thermal diffusion potential, td> arises if an electrochemical system is nonisothermal. This phenomenon is due to the heat transport of ionic species and can be taken into account if the individual ion entropy of transport, conductivity, and activity coefficients of the species of interest are known. Therefore, the thermal diffusion potential depends on the temperature, pressure, and composition of the electrolyte liquid junction. Also, td is a function of the temperature gradient and can be a substantial value from tens to hundreds of millivolts [19]. 

The thermal diffusion potential arises when there is a temperature gradient within an electrolyte bridge and is due to heat transport by ionic species. The magnitude of Etd can be estimated from the entropy of transport, conductivity and activity coefficients of the individual ions. Therefore, the magnitude of Etd depends on the temperature, pressure and composition of the electrolyte liquid junction. The value of Ejd can be as high as tens to hundreds of mV. 

The paradox involved here ean be made more understandable by introdueing the eoneept of entropy ereation. Unlike the energy, the volume or the number of moles, the entropy is not eonserved. The entropy of a system (in the example, subsystems a or P) may ehange in two ways first, by the transport of entropy aeross the boundary (in this ease, from a to P or vice versa) when energy is transferred in the fomi of heat, and seeond. 

This completes the heuristic derivation of the Boltzmann transport equation. Now we trim to Boltzmaim s argument that his equation implies the Clausius fonn of the second law of thennodynamics, namely, that the entropy of an isolated system will increase as the result of any irreversible process taking place in the system. This result is referred to as Boltzmann s H-theorem. 

To close this chapter we emphasize that Hie statistical mechanical definition of macroscopic parameters such as temperature and entropy are well designed to describe isentropic equilibrium systems, but are not immediately applicable to the discussion of transport processes where irreversible entropy increase is an essential feature. A macroscopic system through which heat is flowing does not possess a single tempera-... 

Production of Entropy, the Driving Forces of Transport Phenomena... 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

Irreversible thermodynamics thus accomplishes two things. Firstly, the entropy production rate EE t allows the appropriate thermodynamic forces X, to be deduced if we start with well defined fluxes (eg., T-VijifT) for the isobaric transport of species i, or (IZT)- VT for heat flow). Secondly, through the Onsager relations, the number of transport coefficients can be reduced in a system of n fluxes to l/2-( - 1 )-n. Finally, it should be pointed out that reacting solids are (due to the... 

Since the entropy production is positive, the transport coefficients Lik must satisfy the relation TAA-Lhh>LhA-TAh [S.R. de Groot, P. Mazur (1962)]. This restricts the range for the charges of transport to aA-Oh< 1, see Eq. (8.56) ff. We should also add that whereas the Ly are phenomenological coefficients appropriate for the description of the experiments on transport, the ly relate directly to the SE s (Eqn. (8.28)) and can be derived from lattice dynamics based theoretical calculations. 

The heat flux consists of two parts. The first is the heat flux due to the flux of entropy, which is carried along by the mass flux in the form of the partial atomic entropy, si. Because si = dS/dN, a flux of atoms will transport a flux of heat given by Jq = TJs — Ts J. The second part is a "cross effect" proportional to the flux of mass, with the proportionality factor being the heat of transport. 

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