Reversible process, maximum electrical work

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 ... 

Maximum Electrical Work for a Reversible Process Consider a generic reversible system with mechanical and electrical work and heat transfer at constant temperature. From the first law of thermodynamics for a simple compressible system... 

An electrical potential difference between the electrodes of an electrochemical cell (called the cell potential) causes a flow of electrons in the circuit that connects those electrodes and therefore produces electrical work. If the cell operates under reversible conditions and at constant composition, the work produced reaches a maximum value and, at constant temperature and pressure, can be identified with the Gibbs energy change of the net chemical process that occurs at the electrodes [180,316]. This is only achieved when the cell potential is balanced by the potential of an external source, so that the net current is zero. The value of this potential is known as the zero-current cell potential or the electromotive force (emf) of the cell, and it is represented by E. The relationship between E and the reaction Gibbs energy is given by... 

If there are no dissipative effects, that is, friction, viscosity, inelasticity, electrical resistance, and so on, during a quasi-static process, the process is termed reversible. Only an infinitesimal change is required to reverse the process, a concept that leads to the name reversible. Most industrial processes exhibit heat transfer over finite temperature differenees, mixing of dissimilar substances, sudden changes in phase, mass transport under finite concentration differences, free expansion, pipe friction, and other mechanical, chemical, and thermal nonidealities, and consequently are deemed irreversible. An irreversible process always involves a degradation of the potential of the process to do work, that is, will not produce the maximum amount of work that would be possible via a reversible process (if such a process could occur). 

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. 

That is, when non-pV work is performed, AG represents a limit. Again, because work performed by a system is negative, AG represents the maximum amount of non-p V work a system can perform on the surroundings. For a reversible process, the change in the Gibbs energy is equal to the non-pV work of the process. Equation 4.11 will become important to us in Chapter 8, when we discuss electrochemistry and electrical work. 

Because work is done when changing the area of a surface, we should be able to correlate this work to one of the thermodynamic state functions. Recall that we found in an earlier chapter that the Gibbs energy is equal to the maximum amount of non-pV work that a process could do. Because changing the area of a surface is not pressure-volume work (just like electrical work isn t pressure-volume work), then surface-tension-area work must be related to the Gibbs energy. For a reversible change in surface area that occurs at constant temperature and pressure, we have... 

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 ... 

The quantity PAV is the work of expansion done against the external pressure, and so — AF represents the maximum work at constant temperature and pressure, other than that due to volume change. The quantity iv — PAV is called the net work and so the decrease —AF in the free energy of a system is equal to the net work obtainable (at constant temperature and pressure) from the system under reversible conditions. An important form of net work, since it does not involve external work due to a volume change, is electrical work consequently, a valuable method for determining the free energy change of a process is to carry it out electrically, in a reversible manner, at constant temperature and pressure. 

For a given amount of chemical reaction, the electrical work refers to a reversible process, and it has its maximum value, which corresponds to the absolute value of the change of the free enthalpy of the chemical cell reaction A G = = max = U It. For a not negligibly small... 

If the E.M.F. of a voltaic cell is E int. volts, and the process taking place within it is accompanied by the passage of N faradays of electricity, i.e., NF coulombs, where F represents 96,600 int. coulombs, the work done by the cell is NFE int. volt-coulombs, or int. joules (cf. 3b). If the cell is a reversible one, as described above, and E is its reversible, i.e., maximum, E.M.F., at a given temperature and pressure, usually atmospheric, it follows from the arguments presented earlier that... 

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