Processes irreversible

Also very important of course are processes leading from a metastable equilibrium state to a stable equilibrium state. These are irreversible, because when the (extra) constraint is released, even momentarily, the system is not in balance and proceeds in one direction, towards equilibrium. However, this inexorable progress towards equilibrium can be performed in one jump or can be halted in a succession of (metastable) equilibrium states called a quasistatic process. 

In many presentations of thermodynamics, quasistatic processes are either not mentioned or are said to be the same as reversible processes. In our usage, however, quasistatic processes are similar to reversible ones in that they are a continuous succession of equilibrium states, but these states are metastable equilibrium states, not stable equilibrium states. A quasistatic process is most easily imagined as resulting when one of the constraints on a metastable equilibrium state is released for an extremely short time, then re-imposed. While the constraint is released, the system changes slightly but irreversibly towards equilibrium, then settles down in its new metastable equilibrium state when the constraint is re-applied. This succession of events is repeated until the final state is reached. 

If the rate of the electron transfer is lower than that of the mass transport, or in the case of irreversible processes (see Chapter 1, Section 4.3), the potential at which the reduction reaction Ox + neT— Red takes place can be much more cathodic than the formal electrode potential of the couple Ox/Red. In addition, commonly the separation between the forward peak and the reverse peak is so large that the reverse peak is undetected. 

Also in this case the shape of the voltammogram can be mathematically accounted for by solving Fick s second law for the two species Ox and Red. 

The initial conditions and those at semi-infinite distance are the same as for the reversible case. The conditions at the electrode surface differ. In this case they are  

The numeric solution of the relative differential equations gives that, 

As anticipated, for an irreversible process the forward peak is located at potentials more negative than if it were reversible (i.e. compared to its standard thermodynamic potential). Moreover, since the above relationship shows that the peak current depends on the square root of the transfer coefficient a, under equivalent conditions the height of the irreversible peak equals 78.6% of the reversible peak given that, as often happens, ot = 0.5 

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. 

Isothermal reversible Reversible adiabatic Isothermal reversible expansion at 7 expansion compression at T  

The transfer of heat q from a hot reservoir at temperature Tj, to a cooler one at temperature T  

The entropy changes that occur in the two reservoirs and in the gas are shown in the figure. We, see that the two reservoirs have experienced a net entropy change of 

This is a positive quantity, since % %. The gas has experienced an exactly equal and opposite entropy change  

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A2.1.4.7 IRREVERSIBLE PROCESSES WORK, HEAT AND ENTROPY CREATION... 

In an irreversible process the temperature and pressure of the system (and other properties such as the chemical potentials to be defined later) are not necessarily definable at some intemiediate time between the equilibrium initial state and the equilibrium final state they may vary greatly from one point to another. One can usually define T and p for each small volume element. (These volume elements must not be too small e.g. for gases, it is impossible to define T, p, S, etc for volume elements smaller than the cube of the mean free... 

Essentially this requirement means that, during die irreversible process, innnediately inside die boundary, i.e. on the system side, the pressure and/or the temperature are only infinitesimally different from that outside, although substantial pressure or temperature gradients may be found outside the vicinity of the boundary. Thus an infinitesimal change in p or T would instantly reverse the direction of the energy flow, i.e. the... 

One may note, in concluding this discussion of the second law, that in a sense the zeroth law (thennal equilibrium) presupposes the second. Were there no irreversible processes, no tendency to move toward equilibrium rather than away from it, the concepts of thennal equilibrium and of temperature would be meaningless. 

For an irreversible process, invoking the notion of entropy transfer and entropy creation, one can write... 

Now, as has been shown, q = TASior an isothennal reversible process only for an isothennal irreversible process AS = A S + Aj.S, and q = TA S. Since Aj.S is positive for irreversible changes and zero only for reversible processes, one concludes... 

This completes the heuristic derivation of the Boltzmann transport equation. Now we trim to Boltzmaim s argument that his equation implies the Clausius fonn of the second law of thennodynamics, namely, that the entropy of an isolated system will increase as the result of any irreversible process taking place in the system. This result is referred to as Boltzmann s H-theorem. 

Onsager postulates [4, 5] the phenomenological equations for irreversible processes given by... 

Onsager L 1931 Reciprocal relations in irreversible processes. I Rhys. Rev. 37 405... 

Onsager L and Machlup S 1953 Fluctuations and irreversible processes Rhys. Rev. 91 1505... 

Green M S 1954 Markov random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids J. Chem. Phys. 22 398... 

Kubo R, Yokota M and Nakajima S 1957 Statistical-mechanical theory of irreversible processes. Response to thermal disturbance J. Phys. Soc. Japan 12 1203... 

Under compression or shear most polymers show qualitatively similar behaviour. However, under the application of tensile stress, two different defonnation processes after the yield point are known. Ductile polymers elongate in an irreversible process similar to flow, while brittle systems whiten due the fonnation of microvoids. These voids rapidly grow and lead to sample failure [50, 51]- The reason for these conspicuously different defonnation mechanisms are thought to be related to the local dynamics of the polymer chains and to the entanglement network density. 

Wylation under neutral conditions. Reactions which proceed under neutral conditions are highly desirable, Allylation with allylic acetates and phosphates is carried out under basic conditions. Almost no reaction of these allylic Compounds takes place in the absence of bases. The useful allylation under neutral conditions is possible with some allylic compounds. Among them, allylic carbonates 218 are the most reactive and their reactions proceed under neutral conditions[13,14,134], In the mechanism shown, the oxidative addition of the allyl carbonates 218 is followed by decarboxylation as an irreversible process to afford the 7r-allylpalladium alkoxide 219. and the generated alkoxide is sufficiently basic to pick up a proton from active methylene compounds, yielding 220. This in situ formation of the alkoxide. which is a... 

Kelvin showed the interdependence of these phenomena by thermodynamic analysis, assuming that the irreversible processes were independent of the reversible ones. This approach was later proved theoretically sound using Onsager s concepts of irreversible thermodynamics (9). 

The more negative the value of AG, the more energy or useful work can be obtained from the reaction. Reversible processes yield the maximum output. In irreversible processes, a portion of the useful work or energy is used to help carry out the reaction. The cell voltage or emf also has a sign and direction. Spontaneous processes have a positive emf the reaction, written in a reversible fashion, goes in the forward direction. 

Overcharge Reactions. Water electrolysis during overcharge is an irreversible process. Oxygen forms at the positive electrode ... 

Irreversible Processes. Irreversible processes are among the most expensive continuous processes. These are used only in special situations, such as when the separation factors of more efficient processes (that is, processes that are theoretically more efficient from an energy point of view) are found to be uneconomicaHy small. Except for pressure diffusion, the diffusion methods discussed herein are essentially irreversible processes. Thus,... 

Irreversible processes are mainly appHed for the separation of heavy stable isotopes, where the separation factors of the more reversible methods, eg, distillation, absorption, or chemical exchange, are so low that the diffusion separation methods become economically more attractive. Although appHcation of these processes is presented in terms of isotope separation, the results are equally vaUd for the description of separation processes for any ideal mixture of very similar constituents such as close-cut petroleum fractions, members of a homologous series of organic compounds, isomeric chemical compounds, or biological materials. 

Various constraints may be put on this expression to produce alternative criteria for the directions of irreversible processes and for the condition of equilibrium. For example, it follows immediately that... 

Real irreversible processes can be subjected to thermodynamic analysis. The goal is to calciilate the efficiency of energy use or production and to show how energy loss is apportioned among the steps of a process. The treatment here is limited to steady-state, steady-flow processes, because of their predominance in chemical technology. 

When a process is completely reversible, the equahty holds, and the lost work is zero. For irreversible processes the inequality holds, and the lost work, that is, the energy that becomes unavailable for work, is positive. The engineering significance of this result is clear The greater the irreversibility of a process, the greater the rate of entropy production and the greater the amount of energy that becomes unavailable for work. Thus, every irreversibility carries with it a price. 

Nature of current of additional peak was determined. It s multiple depending on the rate of polarizing tension. The absence of anodic peaks on the voltamperograms of calces testifies that the reduction of the compound is an irreversible process. 

The main problem of elementary chemical reaction dynamics is to find the rate constant of the transition in the reaction complex interacting with its environment. This problem, in principle, is close to the general problem of statistical mechanics of irreversible processes (see, e.g., Blum [1981], Kubo et al. [1985]) about the relaxation of initially nonequilibrium state of a particle in the presence of a reservoir (heat bath). If the particle is coupled to the reservoir weakly enough, then the properties of the latter are fully determined by the spectral characteristics of its susceptibility coefficients. 

Enzymatic reactions frequently undergo a phenomenon referred to as substrate inhibition. Here, the reaction rate reaches a maximum and subsequently falls as shown in Eigure 11-lb. Enzymatic reactions can also exhibit substrate activation as depicted by the sigmoidal type rate dependence in Eigure 11-lc. Biochemical reactions are limited by mass transfer where a substrate has to cross cell walls. Enzymatic reactions that depend on temperature are modeled with the Arrhenius equation. Most enzymes deactivate rapidly at temperatures of 50°C-100°C, and deactivation is an irreversible process. 

For any method of heat transfer to take place, a temperature difference is necessary between two faces of a solid body, or at the boundaries of a gas or vapor. Flear transfer will take place only from a high-temperature source to a lower-temperature sink and is an irreversible process unless acted upon by another agency, as is the case with the refrigeration process. 

Adiabatic irreversible process in which entropy is generated... 

A closed system moving slowly through a series of stable states is. said to undergo a reversible process if that process can be completely reversed in all thermodynamic respects, i.e. if the original. state of the system itself can be recovered (internal reversibility) and its surroundings can be restored (external irreversibility). An irreversible process is one that cannot be reversed in this way. 

The actual work output in a real irreversible process between stable states X and Y is therefore... 

We adopt the nomenclature introduced by Hawthorne and Davis [1], in which compressor, heater, turbine and heat exchanger are denoted by C, H, T and X, respectively, and subscripts R and I indicate internally reversible and irreversible processes. For the open cycle, the heater is replaced by a burner, B. Thus, for example, [CBTX]i indicates an open irreversible regenerative cycle. Later in this book, we shall in addition, use subscripts... 

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