Closed system reversible processes

Although derived for a reversible process, equation 46 relates properties only, irrespective of the process, and therefore apphes to any change in the equiUbtium state of a homogeneous, closed, nonreacting system. 

All applications are for closed systems with constant mass. If a process is reversible and only p-V work is done, the first law and differentials can be expressed as follows. 

For closed systems of this land, the work of a reversible process may always be calculated from... 

Consider a single-phase closed system in which there are no chemical reactions. Under these restric tious the composition is fixed. If such a system undergoes a differential, reversible process, then by Eq. (4-1)... 

Although derived for a reversible process, this equation relates properties only and is valid for any change between equilibrium states in a closed system. It may equally well be written... 

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. 

A liquid solution may be separated into its constituents by crystallising out either pure solvent or pure solute, the latter process occurring only with saturated solutions. (At one special temperature, called the cryohydric temperature, both solvent and solute crystallise out side by side in unchanging proportions.) We now consider what happens when a small quantity of solute is separated from or taken up by the saturated solution by reversible processes. Let the saturated solution, with excess of solute, be placed in a cylinder closed below by a semipermeable septum, and the w7hole immersed in pure solvent. The system is in equilibrium if a pressure P, equal to the osmotic pressure of the saturated solution when the free surface of the pure solvent is under atmospheric pressure, is applied to the solution. Dissolution or precipitation of solute can now be brought about by an infinitesimal decrease or increase of the external pressure, and the processes are therefore reversible. If the infinitesimal pressure difference is maintained, and the process conducted so slowly that all changes are isothermal, the heat absorbed when a mol of solute passes into a solution kept always infinitely... 

Entropy can be described by considering a closed system undergoing a reversible process. The entropy change, dS, of the system is defined by the relationship... 

TdS = dU+PdV This holds good for any process reversible or irreversible, undergone by a closed system, since it is a relationship among properties which are not dependent on path. 

If the system is neither closed nor thermally insulated, then the change in the entropy with time consists of two quantities of the time change in the entropy as a result of processes occurring within the system S and of entropy changes in the surroundings, caused by transfer of the entropy from the system in the reversible process Sc... 

As far as the velocity and the extent of the conversion are concerned, the two processes are, however, altogether different. Whereas an acid is practically instantaneously and completely converted into a salt by an equivalent amount of a sufficiently strong base (neutralisation), a process on which, indeed, alkalimetry and acidimetry depend, it is not possible to obtain from equimolecular amounts of acid and alcohol the theoretical (calculated) amount of ester. A certain maximal quantity of ester is formed, but always falls short of the theoretical, and it is impossible, even by indefinitely extending the duration of the reaction, to make the unchanged acid and alcohol produce ester in excess of that maximum. If, for example, equimolecular amounts of acetic acid and alcohol are allowed to interact in a closed system, only two-thirds of each enter into reaction, and it is impossible to induce the remaining third of acetic acid to react with that of alcohol. The maximum yield of ester therefore amounts to only two-thirds, or 66-7 per cent, of the theoretical quantity. The quantitative difference in the course of the two reactions mentioned above depends on the fact that esterification is a so-called reversible reaction , i.e. one in which the reaction products represented on the right-hand side of the equation (ester and water) also interact in the opposite direction ... 

Temperature and enthalpy are not the only conditions that determine whether a change is favourable. Consider the process shown in Figure 7.5. A closed valve links two flasks together. The left flask contains an ideal gas. The right flask is evacuated. When the valve is opened, you expect the gas to diffuse into the evacuated flask until the pressure in both flasks is equal. You do not expect to see the reverse process—with all the gas molecules ending up in one of the flasks—unless work is done on the system. 

Stacks in series approach reversibility. MCFC stack networks produce more power than conventional configurations because they more closely approximate a reversible process. To illustrate this fact, consider Figure 9-20, which compares the maximum power that could be generated by three different MCFC systems having identical feed stream compositions. ... 

The differential equations above are valid for reversible processes taking place in closed systems in which there is no flow of matter among the various phases. 

The thermodynamic analysis of an actual Otto cycle is complicated. To simplify the analysis, we consider an ideal Otto cycle composed entirely of internally reversible processes. In the Otto cycle analysis, a closed piston-cylinder assembly is used as a control mass system. 

Second Law of Thermodynamics. There have been numerous statements of the second law. To paraphrase Clausius It is impossible to devise an engine or process which, working in a cycle, will produce no effect other than the transfer of heat from a colder to a warmer body. According to Caratheodory, the Second Law can be stated as follows Arbitrarily close to any given state of any closed system, there exists an unlimited number of other states which it is impossible to reach from a given state as a result of any adiabatic process, whether reversible or not . 

One particular pattern of behaviour which can be shown by systems far from equilibrium and with which we will be much concerned is that of oscillations. Some preliminary comments about the thermodynamics of oscillatory processes can be made and are particularly important. In closed systems, the only concentrations which vary in an oscillatory way are those of the intermediates there is generally a monotonic decrease in reactant concentrations and a monotonic, but not necessarily smooth, increase in those of the products. The free energy even of oscillatory systems decreases continuously during the course of the reaction AG does not oscillate. Nor are there specific individual reactions which proceed forwards at some stages and backwards at others in fact our simplest models will comprise reactions in which the reverse reactions are neglected completely. 

The stopcock is opened, allowing spontaneous transfer of n moles of gas from the Ph to the P reservoir. The stopcock is then closed and the reservoirs are allowed to re-equilibrate to final state B. What is ASa b = SreseTyoirsl (b) Reversible Volume Transfer. To answer the question, we must transfer the same quantity of gas by a reversible process. Consider therefore the enlarged system shown in the following diagram ... 

Any dynamic system becomes stable eventually and comes to the rest point, i.e. attains its equilibrium or steady state. For closed systems, a detailed equilibrium is achieved at this point. This is not so simple as it would seem, as substantiated by a principle of the thermodynamics of irreversible processes. At a point of detailed equilibrium not only does the substance concentration remain unchanged (dcjdt = 0), but also the rate of each direct reaction is balanced by that of its associated reverse counterpart... 

Reversible processes are those processes that take place under conditions of equilibrium that is, the forces operating within the system are balanced. Therefore, the thermodynamics associated with reversible processes are closely related to equilibrium conditions. In this chapter we investigate those conditions that must be satisfied when a system is in equilibrium. In particular, we are interested in the relations that must exist between the various thermodynamic functions for both phase and chemical equilibrium. We are also interested in the conditions that must be satisfied when a system is stable. 

A state of equilibrium exists in a process when the rate of the forward process equals the rate of the reverse process. The equilibrium condition exists in relation to thermal, mechanical, and chemical changes. For example, within a closed flask, liquid water evaporates to form vapor, and at the same time the vapor condenses to form liquid. When the rate of evaporation equals the rate of condensation, the system is said to be in a state of equilibrium ... 

In a closed system a reversible process creates no entropy so that any change dS in entropy is caused only by an amount dQm of heat reversibly transferred from the surroundings as shown in Eqs. 3.8 and 3.9 ... 

An irreversible process, by contrast, creates an amount of entropy so that the total change dS in entropy in a closed system consists not only of an entropy change dSrey due to reversible heat transfer dQrm from the surroundings but also of an amount of entropy dSlrr created by the irreversible process as shown in Eq. 3.10 ... 

For a closed system with reversible transfer of heat dQrev where an irreversible process occurs creating uncompensated heat Q, these transferred and created parts of entropy are thus given, respectively, in Eq. 3.13 ... 

Fig. 3.2. Entropy deSr reversibly transferred from the outside and entropy dtSlrr created by irreversible processes in a closed system.

As an irreversible process advances in a closed system, the creation of entropy inevitably occurs dissipating a part of the energy of the system in the form of uncompensated heat. The irreversible energy dissipation can be observed, for instance, with the generation of frictional heat in mechanical processes and with the rate-dependent heat generation in chemical reactions different from the reversible heat of reaction. In general, the creation of entropy is always caused by the presence of resistance against the advancement in irreversible processes... 

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