Irreversible processes/systems

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... 

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. 

Machlup S and Onsager L 1953 Fluctuations and irreversible processes. II. Systems with kinetic energy Rhys. Rev. 91 1512... 

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. 

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 entropy of the system plus surroundings is unchanged by reversible processes the entropy of the system plus surroundings increases for irreversible processes. 

On the other hand, in any irreversible process although the system may gain (or lose) entropy and the surroundings lose (or gain) entropy, the system plus surrounding will always gain in entropy (equation 20.141). Thus for a real process proceeding spontaneously at a finite rate... 

In this case there is an increase of entropy in an irreversible process, whilst the energy remains constant. This result brings out clearly the independence of the two fundamental principles of thermodynamics, the first law dealing with the energy of a system of bodies, and the second law with the entropy. 

In this discussion, we will limit our writing of the Pfaffian differential expression bq, for the differential element of heat flow in thermodynamic systems, to reversible processes. It is not possible, generally, to write an expression for bq for an irreversible process in terms of state variables. The irreversible process may involve passage through conditions that are not true states" of the system. For example, in an irreversible expansion of a gas, the values of p. V, and T may not correspond to those dictated by the equation of state of the gas. 

Equation (2.66) indicates that the entropy for a multipart system is the sum of the entropies of its constituent parts, a result that is almost intuitively obvious. While it has been derived from a calculation involving only reversible processes, entropy is a state function, so that the property of additivity must be completely general, and it must apply to irreversible processes as well. 

Irreversible and Quasi-Reversible Systems For irreversible processes (those with sluggish electron exchange), the individual peaks are reduced in size and widely separated (Figure 2-5, curve A). Totally irreversible systems are characterized by a shift of the peak potential with the scan rate ... 

The increase in the entropy of an irreversible process may be illustrated in the following manner. Considering the spontaneous transfer of a quantity of heat 8q from one part of a system at a temperature T, to another part at a temperature 7, then the net change in the entropy of the system as a whole is then ... 

Besides the reversible and irreversible processes, there are other processes. Changes implemented at constant pressure are called isobaric process, while those occurring at constant temperature are known as isothermal processes. When a process is carried out under such conditions that heat can neither leave the system nor enter it, one has what is called an adiabatic process. A vacuum flask provides an excellent example a practical adiabatic wall. When a system, after going through a number of changes, reverts to its initial state, it is said to have passed through a cyclic process. 

The processes that occur at a finite rate, with finite differences of temperature and pressure between parts of a system or between a system and its surroundings, are irreversible processes. It has been shown that the entropy of an isolated system increases in every natural (i.e., irreversible) process. It may be noted that this statement is restricted to isolated systems and that entropy in this case refers to the total entropy of the system. When natural processes occur in an isolated system, the entropy of some portions of the system may decrease and that of other portions may increase. The total increment, however, is always greater than the total decrement. The entropy of a nonisolated system may either increase or decrease, depending on whether heat is added to it or removed from it and whether irreversible processes occur within it. Considered all in all, it is necessary to define clearly the system under consideration when increases and decreases in entropy are discussed. 

Chemical reactions in the system are irreversible processes, affecting transport processes, as they result in the formation and disappearance of components of the system and in the release or consumption of thermal energy. 

Some of the elements of thermodynamics of irreversible processes were described in Sections 2.1 and 2.3. Consider the system represented by n fluxes of thermodynamic quantities and n driving forces it follows from Eqs (2.1.3) and (2.1.4) that n(n +1) independent experiments are needed for determination of all phenomenological coefficients (e.g. by gradual elimination of all the driving forces except one, by gradual elimination of all the fluxes except one, etc.). Suitable selection of the driving forces restricted by relationship (2.3.4) leads to considerable simplification in the determination of the phenomenological coefficients and thus to a complete description of the transport process. 

Eigen s theory describes the self-organisation of biological macromolecules on the basis of kinetic considerations and mathematical formulations, which are in turn based on the thermodynamics of irreversible systems. Evolutionary processes are irreversibly linked to the flow of time. Classical thermodynamics alone cannot describe them but must be extended to include irreversible processes, which take account of the arrow of time (see Sect. 9.2). Eigen s theory is based on two vital concepts ... 

Equilibrium thermodynamics was developed about 150 years ago. It is concerned only with the achievement of an equilibrium state, without taking into account the time which a system requires for the transition from an initial to a final state. Thus, only the thermodynamics of irreversible processes can be used to describe processes which lead to the formation of self-organising systems. Here, the time factor, and thus also the rate at which material reactions occur, is taken into account. Evolutionary processes are irreversibly coupled with temporal sequences, so that classical thermodynamics no longer suffices to describe them (Schuster and Sigmund, 1982). 

The relationships between the components of the Hantzsch triangle were considered in-depth in the monograph 2 and references therein. Although the problem of reactivity of ambident substrates has been studied over many years and from different points of view, the complexity of the starting system and its numerous reaction pathways do not allow one to reliably predict the results of O-alkylation in each particular case, because it is necessary to take into account the rates of numerous reversible and irreversible processes as well as the thermodynamic factors responsible for the position of the equilibrium it is necessary to take solvent effects into consideration when estimating the thermodynamic factors. All accumulated observations are approximated by several empirical mles included in monographs 2 and 3. 

The usual emphasis on equilibrium thermodynamics is somewhat inappropriate in view of the fact that all chemical and biological processes are rate-dependent and far from equilibrium. The theory of non-equilibrium or irreversible processes is based on Onsager s reciprocity theorem. Formulation of the theory requires the introduction of concepts and parameters related to dynamically variable systems. In particular, parameters that describe a mechanism that drives the process and another parameter that follows the response of the systems. The driving parameter will be referred to as an affinity and the response as a flux. Such quantities may be defined on the premise that all action ceases once equilibrium is established. 

Hence, when Tk is zero the system is in equilibrium, but for non-zero Tk an irreversible process that takes the system towards equilibrium, occurs. The quantity Tkl which is the difference between intensive parameters in entropy representation, acts as the driving force, or affinity of the non-equilibrium process. 

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