Reversible and Irreversible Processes A Summary

As we demonstrated in the analysis of the isothermal expansion-compression of an ideal gas in Section 10.2, the amount of work we actually obtain from a spontaneous process is always less than the maximum possible amount. 

However, if the battery is discharged to run the starter motor and then recharged by using a finite current flow, as is actually the case, more work will always be required to recharge the battery than the battery produces as 

A battery can do work by sending current to a starter motor. The battery can then be recharged by forcing current through it. If the current flow in both processes is infinitesimally small, wn [ = w21. This is a reversible process. But if the current flow is finite, as it would be in any real case, 

1 w21 w,. This is an irreversible process (the universe is different after the cyclic process occurs). All real processes are irreversible. 

When energy is used to do work, it becomes less organized and less concentrated and thus less useful. 

Thus we have shown that at constant temperatnre and pressure the change in free energy for a process gives the maximnm nsefnl work available from that process. 

Let s consider a few more points in connection with these relationships. If a process is carried out so that it usefui = 0, then the expression 

This relationship between AH and qp is used frequently in thermochemical studies. We bring it up again to emphasize that AH = qp only at constant pressure and when no useful work is done (only PV work is allowed). This last condition is often neglected. 

If a process is carried out so that M usefui is at a maximum (the hypothetical reversible pathway where AG = u usefui), then from the expression 

Thus qp, which is pathway-dependent, varies between AH (when tt usefui = 0) and TAS (when li usefui = ttCSii)- The quantity TAS represents the minimum heat flow that must accompany the process under consideration. That is, TAS represents the minimum energy that must be wasted through heat flow as the process occurs. 

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For an irreversible adiabatic expansion in which some work is performed, the work performed is less in magnimde than that in the reversible process because the external pressure is less than the pressure of the gas by a finite amount. Thus, if the final volume is the same as in the reversible process, the final temperature will not be as low in the irreversible process, because, according to Equation (5.47), the temperature drop depends directly on the work performed by the expanding gas. Similarly, from Equations (5.42) and (5.44), AC7 and A//, respectively, also must be numerically smaller in the intermediate expansion than in the reversible expansion. In the adiabatic expansion, from a common set of initial conditions to the same final volume, the values of Af7 and A//, as well as the values of the work performed, seem to depend on the path (see summary in Table 5.2). At first glance, such behavior seems to contradict the assumption that U and H are state functions. Careful consideration shows that the difference occurs because the endpoints of the three paths are different. Even though the final volume can be made the same, the final temperature depends on whether the expansion is free, reversible, or intermediate (Table 5.2). 

The plan of this chapter is the following. Section II gives a summary of the phenomenology of irreversible processes and set up the stage for the results of nonequilibrium statistical mechanics to follow. In Section III, it is explained that time asymmetry is compatible with microreversibility. In Section IV, the concept of Pollicott-Ruelle resonance is presented and shown to break the time-reversal symmetry in the statistical description of the time evolution of nonequilibrium relaxation toward the state of thermodynamic equilibrium. This concept is applied in Section V to the construction of the hydrodynamic modes of diffusion at the microscopic level of description in the phase space of Newton s equations. This framework allows us to derive ab initio entropy production as shown in Section VI. In Section VII, the concept of Pollicott-Ruelle resonance is also used to obtain the different transport coefficients, as well as the rates of various kinetic processes in the framework of the escape-rate theory. The time asymmetry in the dynamical randomness of nonequilibrium systems and the fluctuation theorem for the currents are presented in Section VIII. Conclusions and perspectives in biology are discussed in Section IX. 

This is known as the Clausius inequality and has important applications in irreversible processes. For example, dS > (dQ/T) for an irreversible chemical reaction or material exchange in a closed heterogeneous system, because of the extra disorder created in the system. In summary, when we consider a closed system and its surroundings together, if the process is reversible and if any entropy decrease takes place in either the system or in its surroundings, this decrease in entropy should be compensated by an entropy increase in the other part, and the total entropy change is thus zero. However, if the process is irreversible and thus spontaneous, we should apply Clausius inequality and can state that there is a net increase in total entropy. Total entropy change approaches zero when the process approaches reversibility. 

The mechanism depicted in Scheme 18.3 which involves the disproportionation of HO2 radicals was the more accepted one at that time [3]. Posteriorly, the role of a proton source in the oxygen reduction reaction was evaluated in a similar ionic liquid, [C2mim][BF4] (Scheme 18.2), in the presence of2.1 mM and 2.64Mof water [11]. The increase in water concentration modified the electrochemistry of the oxygen reduction reaction from a reversible reduction process corresponding to the 02/02 redox couple to an irreversible cathodic process. In summary, the main features observed upon addition of water were (1) an increase of the current density due to more favourable mass transport condition (increased fluidity and conductivity in the medium), (2) shift in potential for the reduction process to more positive values caused by changes to the protonation equilibria and the solvation of the electrogenerated species [13], and (3) loss of reversibility for the reduction process. 

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