Thermodynamically reversible processes

If the chronopotentiometric reaction involves a thermodynamically reversible process without complications, Eq. (4.17) may be used to relate concentrations to transition times in the Nemst expression. For a system where both reactant and product are soluble species (such as in Figure 4.11), the chronopotentio-gram is described by the relations... 

For a thermodynamically reversible process under the same conditions, TAS = qrev so that ... 

Even though thermodynamically reversible processes cannot be real processes, they have an important significance as they indicate a limit to which real processes may attempt to reach. We may say that thermodynamically reversible processes replicate the real processes in an ideal mode . 

It is not very difficult to visualise a thermodynamically reversible process. Suppose we want to inflate a balloon, which we want later to climb up into atmosphere. We connect the balloon to a cylinder containing compressed hydrogen gas. And we allow the gas to pass very slowly from the cylinder to the balloon. The slower this is done, the closer is the inflation process to a thermodynamically reversible process. 

This is a thermodynamically reversible process that often serves as a standard reference electrode, known as the reversible hydrogen electrode (RHE), for all other electrochemical processes. 

So-called underpotential deposited species arise when an electrochemical reaction produces first, on a suitable substrate adsorbent metal, a two-dimensional array or in some cases two-dimensional domain structures (cf. Ref 100) at potentials lower than that for the thermodynamically reversible process of bulk crystal or gas formation of the same element. The latter often requires an overpotential for initial nucleation of the bulk phase. The thermodynamic condition for underpotential deposition is that the Gibbs energy for two-dimensional adatom chemisorption on an appropriate substrate must be more negative than that for the corresponding three-dimensional bulk-phase formation. Underpotential electrochemisorption processes commonly involve deposition of adatoms of metals, adatoms of H, and adspecies of OH and O. 

If the e ansion were carried out rapidly, e.g., by suddenly relearing the pressure on the piston, or the compression were rapid, e.g., by a sudden and large increase of the external pressure, the processes would not be reversible. The changes would not involve a continuous succession of equilibrium states of the system, and hence they could not be reversible. There would be both temperature and pressure gradients which would be different in the expanrion and compression the conditions for a thermodynamically reversible process would thus not be applicable. 

This paper is concerned with the amount of work needed to separate air into an oxygen-rich fraction containing 90 mole percent oxygen and a nitrogen-rich fraction containing 99 mole percent nitrogen. The minimum work required in a thermodynamically reversible process conducted in an environment at one atmosphere and 77°F with feed and product gases at these conditions is 421 Btu per pound mole of air fed. 

This expression gives a lower bound for the equilibrium time, which can be attained only if mixing of streams of different composition can be prevented during the entire start-up period. It provides a lower bound for the equilibrium time in somewhat the same way that consideration of a thermodynamically reversible process provides a lower bound for the amount of work needed to carry out a given change of state. 

Explain clearly what is meant by a thermodynamically reversible process. Why is the reversible work done by a system the maximum work ... 

The treatment of thermodynamically reversible processes is of great importance in connection with the second law. However, in practice we are concerned with thermodynamically irreversible processes, since these are the processes that occur in nature. Therefore it is important to consider the relationships which apply to irreversible processes. 

A thermodynamically reversible process is defined as one in which the system changes infinitesimally slowly from one equilibrium state to the next. According to the second law of thermodynamics, the heat added to a system during a reversible process dQKV is given by... 

The jacketed reactor process also illustrates the principle. The big reactor has a lot of heat transfer area, so only a fraction of the available temperature difference between the inlet cooling water and the reactor is used. A thermodynamically reversible process has no temperature difference between the source (the reactor) and the sink (the inlet cooling water). So the big reactor is thermodynamically inefficient, but it gives better control. 

As discussed, ORR equations listed in Table 4.1 and the description above are all the cases for thermodynamically reversible processes. In reality, all reactions have limited reaction rates, which are either slower or faster, depending on the natures of the reactions. Furthermore, the ORR processes are actually not as simple as expressed by those reactions listed in Table 4.1. For each reaction, there should be a reaction mechanisms associated with it. This reaction mechanism may include several elementary reaction steps. Particularly, for ORR elec-trocatalyzed hy a catalyst, the reaction mechanism may be even more complicated. Therefore, when ORR is discussed, both its reaction mechanism and kinetics must be explored in order to obtain fundamental understanding and full pictures. 

Since it is simple to keep reversible conditions in an electrochemical experiment, thermodynamic information can easily be obtained. According to the first and second laws of thermodynamics, reversible processes must satisfy... 

Although the thermodynamically reversible process of distillation is unrealizable, it is of great practical interest for the following reasons (1) it shows in which direction real processes should be developed in order to achieve the greatest economy, and (2) the analysis of this mode is the important stage in the creation of a general theory of multicomponent azeotropic mixtures distillation. 

First investigations of thermodynamically reversible process concerned binary distillation of ideal mixtures (Hausen, 1932 Benedict, 1947). Later works concerned multicomponent ideal mixtures (Grunberg, 1960 Scofield, 1960 Petlyuk Platonov, 1964 Petlyuk, Platonov, Girsanov, 1964). 

The analysis of the thermodynamically reversible process of distillation for multicomponent azeotropic mixtures was made considerably later. Restrictions at sharp reversible distillation were revealed (Petlyuk, 1978), and trajectory bundles at sharp and nonsharp reversible distillation of three-component azeotropic mixtures were investigated (Petlyuk, Serafimov, Avet yan, Vinogradova, 1981a, 1981b). 

Equation (4.1) concerns not only reversible distillation process, but also any thermodynamically reversible process. For the distillation. 

Total change of entropy in the incoming and outgoing flows of the column and in the sources and receivers of heat should be equal to zero [Eq. (4.3)] in the case of the thermodynamically reversible process of distillation. 

Physically, the proton should overcome the voltage barrier — g, which separates the potentials of the membrane and carbon phases. Here is the cathode half-cell open-circuit voltage. However, the irreversible dissipation of energy occurs only when the proton acquires the voltage g required to reach the potential Further transport of the proton with the potential to the Pt particle is a thermodynamically reversible process. 

A thermodynamically reversible process is very efficient from a steady-state point of view. No entropy is created, so energy requirements are minimized. However, this reversibility is achieved by having negligibly small driving forces in temperature, pressure, concentrations, etc. Thus this very efficient process has little muscle to use to reject disturbances or to move the process to a different desired steady state. 

One possible implementation of a chemical reaction as a thermodynamically reversible process was proposed by van t Hoflf. This method involves applying semi-permeable membranes that allow only one of the reactants involved in the reaction to pass. The van t Hoflf chamber, the device in which there is a thermodynamically reversible reaction, is presented in Fig. 2.1. It will be considered in the example that hydrogen combustion occurs in the gas phase reaction given by Eq. 2.2. 

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