Density, entropy current

This definition suggests a reasonable formulation of entropy current density as... 

The entropy is given in terms of the specific entropy shy S = J pscPr so that the entropy flux out of the system is related to the entropy current density by... 

In the above, Ps(r, t) is the entropy density, Osir, t) the entropy source strength, and Jsip, t) the entropy current density. The volmne integrations in Eqs. (293) (294b) are over the spatial domain V occupied by the system. The surface integration in Eq. (295) is over the boundary surface S separating the system from its surroundings. The unit vector h is normal to S and directed outward. 

The thermoelectric effect is due to the gradient in electrochemical potential caused by a temperature gradient in a conducting material. The Seebeck coefficient a is the constant of proportionality between the voltage and the temperature gradient which causes it when there is no current flow, and is defined as (A F/A7) as AT- 0 where A Fis the thermo-emf caused by the temperature gradient AT it is related to the entropy transported per charge carrier (a = — S /e). The Peltier coefficient n is the proportionality constant between the heat flux transported by electrons and the current density a and n are related as a = Tr/T. 

The phenomenological equations (6.9.1) have thus been reexpressed in (6.9.9) solely in terms of the measurable transport coefficients a, k, and o. The Seebeck coefficient may be interpreted as the entropy carried per electronic charge. Equation (6.9.9a) represents a further generalization of Ohm s Law, showing how the current density behaves in the presence of a temperature gradient see also Exercise 6.9.3. Equation (6.9.9b) specifies the entropy flux under the joint action of a gradient in electrochemical potential and in temperature this represents a generalization of Fourier s Law. 

S area entropy probability current density Poynting... 

S area, entropy, probability current density, Poynting... 

The electrical current density and the thermal entropy flux q /T are linked to the driving forces, the potential gradient A17 and the temperature gradient AT with linear coefficients Cei as the electrical conductivity, Lq for the heat transfer, Ls for the Seebeck effect, and Lp for the Peltier effect. 

The kinetic parameters required to characterize an electrode reaction are reaction order, rate constant or exchange current density, symmetry factor, stoichiometric coefficient. and the standard heat and entropy of activation. These basic parameters can be measured using electrochemical techniques, some of which are discussed in this chapter. The interested reader is referred to refs. [ 1-12] for a detailed discussion of the various electrochemical and physicochemical techniques available at present to charaeterize the electrode surfaces and the electrochemical reactions. 

The decrease in the current also results in the decrease in the polarisation losses and the decrease in the reaction entropy flow rate (5r) (due to reduced mass flow rates) and thereby results in the fall of the system temperature. The reverse phenomena are observed (at time 2000 s in Fig. 10.8) when the load current density is increased. 

Here AS is the entropy change in the half-cell reaction, rj is the half-cell polarization voltage, j is the mean current density in the cell, I is the thickness of the respective catalyst layer, at is the proton conductivity of the catalyst layer, am is the proton conductivity of the bulk membrane, and A and Am are the thermal conductivities of the catalyst layers and membrane, respectively. Note that the thermal conductivities of the ACL and CCL are assumed to be the same. 

The last term on the right side of (3.71) describes the effect of the reaction (3.67). Here A5 is the entropy change in (3.67) and jcross is the equivalent current density of the methanol crossover given by Eq. (3.23). Discussion of the other terms is given in Section 3.4.2. 

Here AS is the entropy change in the overall reaction, j is the local current density in the cell, and r] is the sum of half-cell polarization voltages r) = q° +... 

Determine the thermodynamic reaction forces for a membrane having multiple transports of chemical components forced by a current density from outside source. Determine the OM-function of the process. What is the entropy production resulted by the reaction forces in this case ... 

Prescribe the coordinate of the current density in direction of outer normal vector on Qj part of the boundary Q = Qj u Q(o and the electric potential on Q.

vector-scalar ordered pair is the unique solution of the equations (126), which are identical(126), and uniform with the (127) transport equation. The entropy production of the system could be calculated by the Joule-law, [19],... 

Integrate the OM-function on the volume V of the system, while the entropy production is transformed by the surface integral taking into account the continuity equation of the electric current density. Take into account also the boundary conditions prescribing the values of the electric potential and current densities on the boundaries of the system. Than we get the following form of the OM-functional... 

The current density of an HR suspension should be a direct indicator on how temperature alTects the ER performance, as it closely relates to the conductivity of the dispersed particle and the temperature. The conductivity of the insulating oil is usually very low and can be neglected. Since tlie order is increased when an ER fluid fibrillate under an electric field, and the entropy of whole suspension thereby reduces, and an excessive work must be spent to maintain this state. The magnitude of the current density likely scales the power demand, and the minimum current density demanded in an ER fluid is an important parameter. The current density versus temperature was found to fit to the power law at an electric field [117], increasing exponentially with the elevated temperature. However, any increase of the current density would result in excessive power demands with possible serious implications in terms of power supply and energy dissipation in ER... 

A5h2 ASco are the entropy changes for the electrochemical reactions associated with H2 fuel and CO fuel. and refer to the total overpotentials for H2 fuel and CO fuel. Rdir and Rwgsr are the reaction rates (molm s ) for DIR and WGSR, while //dir and Hwgsr are the corresponding reaction heat (Jmol ). F is the Faraday constant (96485 Cmol ). L is the thickness of the electrolyte (m). 7h2 and Jqo are the current densities produced from electrochemical oxidation of H2 and CO, respectively. 

Ji is the electron flux vector, C is the electrochemical potential acting on the electron flux, and Js represents the total entropy density flux vector. We choose this expression, rather than a version based on Eq. (6.1.29), because we wish to treat separately the effects of temperature and of electrochemical potential. The latter involves aU the contributions associated with temperature gradients, electron density gradients, and the externally imposed electrostatic field. It is expedient to introduce a current density vector as = e Ti- Then, along one dimension, we adopt i) = T 3s T + -V( /e) as our dissipation function. For this unidirectional flow pattern, the... 

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