Reversible process concept

This is one of the most useful aspects of the concepts of a reversible process. 

Considering the concepts of reversible processes, a reversible cycle can be carried out for given thermal reservoirs at temperatures and Tl. The Carnot heat engine cycle on a p-V diagram and a T-S diagram, as shown in Fig. 1.4 is composed of the following four reversible processes ... 

However, the reverse process, in going from speed to distance, involves integration of the rate equation (6.2). In chemistry, the concept of rate is central to an understanding of chemical kinetics, in which we have to deal with analogous rate equations which typically involve the rate of change of concentration, rather than the rate of change of distance. For example, in a first-order chemical reaction, where the rate of loss of the reactant is proportional to the concentration of the reactant, the rate equation takes the form ... 

The concentration profiles are very sensitive to the kinetics of the electrode reaction. In this context, the determination of the diffusion layer thickness is of great importance in the study of non-reversible charge transfer processes. This magnitude can be defined as the thickness of the region adjacent to the electrode surface where the concentration of electro-active species differs from its bulk value, and it can be accurately calculated from the concentration profiles. In the previous chapter, the extensively used concept of Nemst diffusion layer (8), defined as the distance at which the linear concentration profile (obtained from the straight line tangent to the concentration profile curve at the electrode surface) takes its bulk value, has been explained. In this chapter, we will refer to it as linear diffusion layer since the term Nemst can be misunderstood when non-reversible processes... 

Equation 6.33 provides the definition of exergy if state 1 is chosen as the state at ambient condition, namely, P, = P0 and = T0 the minimum amount of work required to transfer the system from environmental conditions to those at P2 and T2. At these conditions, this is the maximum amount of work available for the reverse process. That is the valuable idea behind the exergy concept to be able to assign to any process stream a value, its exergy, that expresses the confined work available in the stream. For the general change in state from P0r T0 to P, T, we can write the net energy input as... 

The sand analogy made above makes one appreciate that this reversible process cannot feasibly be carried out in practice -it would be infinitely slow since in order to truly achieve a smooth transition between the individual snapshot equilibrium states it would be necessary to make the sand grains infinitesimally small in size and so their number would approach infinity and the whole process would take an infinite amount of time to achieve The concept of reversibility is therefore a theoretical concept rather than a practical one. Despite this the concept of reversibility is extremely useful in thermodynamics and will arise in later discussions. 

Nature s concept of hydrogen conversion - or the reverse process of hydrogen generation - at these highly optimized catalytic centers is based on a heterolytic mechanism ... 

Reversibility — This concept is used in several ways. We may speak of chemical reversibility when the same reaction (e.g., -> cell reaction) can take place in both directions. Thermodynamic reversibility means that an infinitesimal reversal of a driving force causes the process to reverse its direction. The reaction proceeds through a series of equilibrium states, however, such a path would require an infinite length of time. The electrochemical reversibility is a practical concept. In short, it means that the -> Nernst equation can be applied also when the actual electrode potential (E) is higher (anodic reaction) or lower (cathodic reaction) than the - equilibrium potential (Ee), E > Ee. Therefore, such a process is called a reversible or nernstian reaction (reversible or nerns-tian system, behavior). It is the case when the - activation energy is small, consequently the -> standard rate constants (ks) and the -> exchange current density (jo) are high. 

Now let us assume that after some time - obviously in infinite time for a reversible process - the balloon is in fully-inflated state and is being ever so slowly being inflated further. How quiet and orderly this process is Suddenly disaster strikes. Some mischief monger pricks the balloon with a pin - or the balloon otherwise gives way. The changes are spontaneous - far removed from the concept of thermodynamic reversibility. 

Entrojiy and probability. The recognition of the universal applicability of the law of the conservation of energy is partly based on the mechanical conception of heat as motion of the ultimate particles of matter. If heat, energy, and kinetic energy of the molecules are essentially of the same nature, and are differentiated from one another only by the units in which we measure them, the validity of the law of the equivalence of heat and work is explained. At first sight, however, it is not easy to understand why heat cannot be converted completely into work, or, in other words, why the conversion of heat into work is an irreversible process (second law of thermodynamics). In pure mechanics we deal only with perfectly reversible processes. By the principles of mechanics the complete conversion of heat into work should be just as possible as the conversion... 

The method developed here is in many ways analogous to that employed by Schottky, Ulich and Wagner. Both methods emphasize the criterion for establishing the irreversibility of a chemical reaction and for deciding whether the reaction will proceed spontaneously in a particular direction. In De Bonder s method this criterion appears immediately the production of entropy must be positive. On the other hand Schottky, Ulich and Wagner employ as the criterion of irreversibility the loss of useful work associated with the real process when compared with a hypothetical reversible process. As is shown in chap. V, these criteria are equivalent for isothermal changes. For non-isothermal changes, however, the concept of loss of useful work... 

Ylide formation by capture of electrophilic carbenes with tertiary phosphines has been shown to be a symmetry-breaking allowed pathway. The reverse process, dissociation of a phosphonium ylide into carbene and phosphine, is in agreement with the concept of phosphonium ylides as phosphine-carbene complexes."... 

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). 

Given the concept of an ideal (reversible process) and knowing the work in an actual process, two ways in which we can define mechanical efficiency are... 

The concept that the removal of an undesired reaction product by selective adsorption from the reaction zone of an equilibrium-controlled reaction increases the conversion and the rate of formation of the desired component (based on Le Chatelier s principle) was used to develop a novel PSA process concept called SERP for direct production of fuel cell-grade hydrogen by steam reforming of methane (CH4 + 2H20 44 C02 + 4H2).57 61 The concept uses a physical admixture of a reforming (noble metal on alumina) catalyst and a chemisorbent (K2C03 promoted hydrotalcite), which selectively and reversibly chemisorbs C02 from a gas at a temperature of -450 °C in the presence of steam. The cyclic SERP steps consisted of the following ... 

Adsorption is a surface phenomenon. When a multi-component fluid mixture is contacted with a solid adsorbent, certain components of the mixture (adsorbates) are preferentially concentrated (selectively adsorbed) near the solid surface creating an adsorbed phase. This is because of the differences in the fluid-solid molecular forces of attraction between the components of the mixture. The difference in the compositions of the adsorbed and the bulk fluid phases forms the basis of separation by adsorption. It is a thermodynamically spontaneous process, which is exothermic in nature. The reverse process by which the adsorbed molecules are removed from the solid surface to the bulk fluid phase is called desorption. Energy must be supplied to carry out the endothermic desorption process. Both adsorption and desorption form two vital and integral steps of a practical adsorptive separation process where the adsorbent is repeatedly used. This concept of regenerative use of the adsorbent is key to the commercial and economic viability of this technology. 

The presence of both synthesizing and degrading enzymes in cells, together with the established rapid turnover of many of the ADP-ribose residues, supports the concept that ADP-ribosylation is, indeed, a reversible process which plays a regulatory role in cell metabolism. 

A process is said to be ideal if there is no destruction of this capacity to affect other systems that is, if there is no destruction of availability. Not every ideal process is reversible for example, if a given state is not an equilibrium state (internally) it cannot be a state of a reversible process. However, it can be a state of an ideal process. In particular, it is the initial state of any process which would furnish its availability (i.e., any process which goes from the given state to one in equilibrium with the reference, and does indeed have the maximum effect on another system). Thus, the concept of ideality can be used to replace the concept of reversibility as a more general criterion for the perfection of processes. 

So, we can assign temperatures consistently with our experience of hotness. Now it s time to move on and prove both the existence of entropy as a state function and the Clausius inequality. This requires employing the concept of the reversible process. A reversible process is one each step of which may be exactly reversed by an infinitesimal change in the external conditions prevailing at the time of that step. The two requirements needed for a real process to approximate reversibility are (1) the process proceeds slowly compared to all internal... 

The familiar notion [37,38] of a close to equilibrium process differs from our concept of a nearly reversible process. For close to equilibrium processes, the initial and final equilibrium states E and Ep must have nearly identical A values. Thus, for such processes ot is always small, and Eq. (A.36) is guaranteed to be valid. In contrast for nearly reversible processes, the A values for states T and Tp need not be close. Instead, for such processes the actual system states Tp- (r) during the process must differ only slightly from the equilibrium states Tp- with the same A values. Thus for nearly reversible processes a does not have to be small, and Eq. (A.36) may or may not be valid.)... 

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