Electrical work irreversible

It suffices to carry out one such experiment, such as the expansion or compression of a gas, to establish that there are states inaccessible by adiabatic reversible paths, indeed even by any adiabatic irreversible path. For example, if one takes one mole of N2 gas in a volume of 24 litres at a pressure of 1.00 atm (i.e. at 25 °C), there is no combination of adiabatic reversible paths that can bring the system to a final state with the same volume and a different temperature. A higher temperature (on the ideal-gas scale Oj ) can be reached by an adiabatic irreversible path, e.g. by doing electrical work on the system, but a state with the same volume and a lower temperature Oj is inaccessible by any adiabatic path. 

The equals sign is valid for a reversible i —> 0) conversion the greater than sign is valid for an irreversible conversion (finite i). Hence, an electrochemical cell delivers electric work equal to the free energy ehange only at infinitesimal current flow under these eonditions the cell potential is the OCV and the electric work delivered is the maximum ITei max = nPVoc = -AG (n is the number of moles of transferred electrons and Fthe Faraday constant). 

By the principles of thermodynamics discussed in Chapter V., a galvanic cell will yield the maximum amount of work when the production of electricity takes place reversibly, that is to say, when the changes which take place both inside and outside the cell are completely reversed when an equally strong current is sent in the opposite direction through the cell. This can only occur when the current flowing through the cell is infinitely small, so that the irreversible production of Joule heat inside the cell is avoided. The electrode potential of the cell on open circuit (measured by the compensation method, for example) is therefore a measure of the maximum electrical work which the cell can do. It is also a measure of the chemical affinity of the reaction as defined on p. 318, Chapter IX. 

From what has been said in Chapter VI., it is clear that it is by no means always possible to convert the whole of the heat set free in an irreversible process into mechanical or electrical work by causing the process to take place reversibly and isother-mally. By doing so we obtain only the change in the thermodynamic potential, while the determination of the heat of reaction gives us the change in the heat content H. By p. 320, we have... 

In the same cell operated irreversibly (i.e., with a large current permitted to flow), less electrical work is accomplished. The maximum electrical work is done by the galvanic cell when it is operated reversibly. 

In general, the work that can be obtained in an isothermal change is a maximum when the process is performed in a reversible manner. This is true, for example, in the production of electrical work by means of a voltaic cell. Cells of this type can be made to operate isothermally and reversibly by withdrawing current extremely slowly ( 331) the e.m.f. of a given cell then has virtually its maximum value. On the other hand, if large currents are taken from the cell, so that it functions in an irreversible manner, the E.M.F. is less. Since the electrical work done by the cell is equal to the product of the e.m.f. and the quantity of electricity passing, it is clear that the same extent of chemical reaction in the cell will yield more work in the reversible than in the irreversible operation. 

If the process is irreversible, q m spontaneous change, weieo will be less than the best available, which is AG. We will see later that the maximum electrical work available from an electrical cell will be obtained under reversible conditions, where the cell e.m.f. is opposed by an infinitesimally smaller potential. The electrons are made to work their passage around the external circuit to the maximum of their ability. Under these conditions, the electrical work depends on the equilibrium voltage, E, and on the number of electrons made to go through the circuit, corresponding to nF coulombs F is a unit of charge, the Faraday=96 485 coulombs/mol of electrons and / =numbcr of moles of electrons or equivalents . This is expressed as ... 

In Example 17.3, we computed the AH° for the cell reaction from the cell potential and its temperature coefficient. If the reaction were carried out irreversibly by simply mixing the reactants together, AH° is the heat that flows into the system in the transformation by the usual relation, AH = Qp. However, if the reaction is brought about reversibly in the cell, electrical work in the amount is produced. Then, by Eq. (9.4), the definition of AS,... 

Hence, at least for fast irreversible reactions, by (6.2.113) the loss of exergy is enormous whatever be the arrangement of the process. Classical thermodynamics knows still another hypothetical device in addition to the reversibly-working Camot cycles, viz. the reversible galvanic (electrochemical) cell. In this device, with constant volume the electric work (say) equals the affinity of the reaction, per unit integral reaction rate. Thus considering the cell working at temperature Tq with pure species, we have... 

A cell that is operated infinitesimally close to electrochemical equilibrium (or open circuit conditions) will not produce any useful power output. To produce a significant power output, sufficient to propel a vehicle, for instance, the cell must be operated at a current density on the order of 1 A cm . Under load, the value of the current density jo of fuel cell operation determines the power output. The current density is directly related to reaction rates at catalyst layers, as well as flows of electrons, protons, reactants, and product species in the cell components. Each of these processes contributes to irreversible heat losses in the cell. These losses diminish the amount of electrical work that the cell could perform. 

FIGURE 1.4 Illustration of basic fuel ceU processes and their relation to the thermodynamic properties of a cell. The electrical work performed by the cell, corresponds to the reaction enthalpy, — A//, minus the reversible heat due to entropy production, —TAS, and minus the sum of irreversible heat losses at finite load, Qi. These losses are caused by kinetic processes at electrochemical interfaces as well as by transport processes in diffusion and conduction media. 

W does not include the work of displacement. W is the useful work. It can be, for example, an electrical work. This is the maximum work obtained from a galvanic cell (see Sect. 2.8). The preceding relationship holds only in the case of a reversible process. Let s examine the concept of reversibility in some depth. The reversibility conditions are approached when the process takes place very slowly. In practice, a galvanic cell is an interesting device to obtain quasi-reversibility. When the process is irreversible, the following inequality holds ... 

Since the maximum possible electrical work is equivalent to the change in Gibbs free energy (Agf) considering no losses or irreversibilities, the maximum theoretical limit for the efficiency is 100% in an ideal fuel cell. 

A solid oxide fuel cell (SOFC) is an electrochemical device that converts chemical energy of a fuel and an oxidant gas (air) directly into electricity without irreversible oxidation. It can be treated thermodynamically in terms of the free enthalpy of the reaction of the fuel with oxidant. Hydrogen and oxygen are used to illustrate the simplest case in the early part (Section 3.2) of this chapter. This treatment allows the calculation of the reversible work at equilibrium for the reversible reaction. Heat must also be transferred reversibly to the surrounding environment in this instance. 

It can be noted that other approaches, based on irreversible continuum mechanics, have also been used to study diffusion in polymers [61,224]. This work involves development of the species momentum and continuity equations for the polymer matrix as well as for the solvent and solute of interest. The major difficulty with this approach lies in the determination of the proper constitutive equations for the mixture. Electric-field-induced transport has not been considered within this context. 

Here, an electrochemical cell working under irreversible conditions is considered. Its emf invariably moves away from the equilibrium value, and if the cell is serving as a battery or source of electricity, then its voltage drops below the equilibrium value. If, on the other hand, the cell is in a place where electrolysis is occurring, then the voltage to be applied must exceed the equilibrium value. 

Useful work (electrical energy) is obtained from a fuel cell only when a reasonable current is drawn, but the actual cell potential is decreased from its equilibrium potential because of irreversible losses as shown in Figure 2-2". Several sources contribute to irreversible losses in a practical fuel cell. The losses, which are often called polarization, overpotential, or overvoltage (ri), originate primarily from three sources (1) activation polarization (r act), (2) ohmic polarization (rjohm), and (3) concentration polarization (ricoiic)- These losses result in a cell voltage (V) for a fuel cell that is less than its ideal potential, E (V = E - Losses). 

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