Irreversible mixing

During the operation of a SOFC, two effects are identified to reduce the electrical power available from an ideal cell the first is the ohmic resistance which generates heat, and the second is the irreversible mixing of gases which causes a voltage drop. Generally, this means that an SOFC is not able to convert the complete fuel. 

Irreversible losses result in the difference of the efficiency between the reversible and the real processes. These losses can be described by the irreversible entropy production within the components however the system structure itself might be reversible. The consideration of the ohmic losses shows that the irreversible entropy production at a high temperature is smaller than at a low temperature. The effects of the irreversible mixing of reactants and products lead to an irreversible entropy production as well that reduce the cell voltage. 

In Figure A.4 the fuels are consumed in separate CO and H2 cells to avoid mixed potential irreversibility. The alternative irreversible mixed process, using one fuel cell, involves ... 

This effect that flow speeds up the irreversible mixing is one mechanism active when stirring a... 

By using Stirling s statistical approximation, Botzmann reached the equation for the isothermal, isobaric, irreversible mixing of two perfect gases having equal volumes ... 

Figure 3.28. Sequence showing the evolution of a tongue of nitrous oxide extending from the tropics into mid-latitude regions and subsequent irreversible mixing. Nitrous oxide mixing ratio (ppbv) is shown on the 1100 K isentropic surface (near 38 km altitude or a pressure surface of 5 hPa) for 6-10 September, 1992, based on the measurements of UARS/CLAES. From Randel et al. (1993).

An accurate representation of wave drag is essential for chemical modeling because chemical species are advected by the mean meridional circulation and are also transported by the irreversible mixing which accompanies wave drag. Modeling studies (e.g., Schoeberl and Strobel, 1978 Holton and Wehrbein, 1980) sometimes use a Rayleigh coefficient to crudely parameterize the effects of wave dissipation. In this case, a deceleration is assumed to act linearly on u, and is substituted for the wave drag term Gu as follows ... 

Plate 4. Ozone volume mixing ratio on the 417 K isentropic surface (approximately 16 km altitude) on 31 December 1991. Filaments of ozone-rich air pulled from the polar region are irreversibly mixed into the mid-latitude surf zone. The net effect is to weaken the latitudinal ozone gradient created by the Brewer-Dobon circulation. From NASA. 

Lesher C (1994) Kinetics of Sr and Nd exchange in silicate liquids Theory, experiments and applications to uphill diffusion, isotopic equilibration, and irreversible mixing of magmas. J Geophys Res B... 

Therefore, similarity is not a continuous process as Gibbs believed. A more recent attempt to explain Gibbs paradox stresses the reversible and irreversible mixing [2], The chapter also reviews previous views. 

In Eq. (2.50) s° is the entropy at standard conditions, nj is the number of moles of the substance i and n the total number of moles. Since important contributions to the entropy are only made by the gaseous reaction products, the pressures pj = nj/n are the partial pressures of product i in the mixture. The sum term in Eq. (2.50) constitutes the entropy increase caused by the irreversible mixing process (vid. [5]). Obviously it is only relevant if the mole numbers before and after the reaction differ substantially. 

One of the main differences between radiochemical analytical procedures and classical analytical methods is that the element (and particularly its radioisotope) to be determined is present in the sample in minor to trace amounts. Separation of radionuclides is performed with the aid of a suitable carrier. Generally, the carrier is a stable isotope (or a suitable compound) that is added to the radioactive compound in a small but detectable amount and has identical chemical properties. An isotopic carrier, i.e., a stable isotope of the element in question, is most frequently used. Both the radioactive isotope and the carrier must be in the same chemical form. The isotopic carrier is irreversibly mixed with the radioactive compound and cannot be separated from it again by chemical means. Such a carrier can therefore be used only when a lower specific activity is sufficient for the subsequent operations. For example, barium or lead can serve as carriers when... 

In his usual elegant style, Jaynes uses this situation to clarify not only the macroscopic nature of thermodynamics, but the role of information, reversible and irreversible mixing and the work available. Particularly interesting is his use of this example to emphasize the importance of defining the constraints (which he calls macrovariables) defining a system. When we know about Arl and Ar2 and are able to separate them by doing work on the system, we have an extra constraint in the sense of 4.9.2. 

In this instance the changes in O and S due to the irreversible mixing process may be said to be exactly cancelled by equal and opposite effects due to the reduction in volume of the system, which is necessary if Pi pi= 1 for all components. 

Fig. 18. Magnetic phase diagram for the SK model (EA model for Ising spins with infinite-range couplings). J and / denote the width and mean of the exchange distribution. P = paramagnet FM = ferromagnet SG = spin glass. F is a ferromagnetic phase viith replica symmetry breaking, i.e. irreversibility ( mixed phase ) and is separated from FM by an AT line.

Application of LDHs is mostly based on their use after thermal treatment and mixed oxide formation. If the calcination is performed at temperatures below 550 °C, mixed oxides also have, besides the aforementioned properties, the memory effect. This very specific property of mixed oxides derived from thermal degradation of LDHs allows the reconstruction of the layered structure in mild conditions when mixed oxides are in contact with aqueous solution or air. If calcination is carried out at temperatures above 827 °C, irreversible mixed spinels are formed and the memory effect is disabled [48]. The main application of the memory effect is for the synthesis of LDHs with different interlayer anions than CO ". Taking to consideration that carbonate anions have the highest affinity toward the incorporation in the LDH interlayer, during the classical synthesis methods the contamination with carbon dioxide from the air always occurs. If, for example, the synthesis LDH with OH" ions in the interlayer is required, the reconstruction of mixed oxides can be performed by steam or contact with decarbonized water. Similarly, if synthesis of LDHs with other anions in the interlayer is anticipated, reconstruction is carried out in an aqueous solution containing the desired anions. Catalytic properties of mixed oxides obtained by reconstruc-tion/recrystallization procedure depend mainly on the conditions of each activation step. 

Figure 3.4 shows the Nernst voltage as a function of the fuel utilisation Uf in a SOFC with H2 fuel and with the system pressure p as a parameter. The excess air and the SOFC temperature are fixed. The interesting area between Uf= 0.1 and Uf= 0.9 can be well approximated with the model of the ideal gas. The dotted line shows the adoption of the model. The irreversible mixing within the SOFC reduces between Uf - 0.1 and Uf = 0.9 by about more than 200 mV. An increase of the system pressure from 1 to 10 bar increases V,v by about 70 mV. An increasing SOFC temperature decreases V. as shown by Eqs. (2 7) and (50). 

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