Reversible Processes and the Mechanical Energy Balance

Identify a process as reversible or irreversible given a description of the process. 

Define efficiency and apply the concept to calculate the work for an irreversible process. 

Write down the steady-state mechanical energy balance for an open system and apply it to a problem. 

In this section we examine some additional features of various types of energy changes with which you should become familiar. 

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). 

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About the same value can be calculated using Eq. (4.24) if Q - = 0, because the enthalpy change for a reversible process for 1 lb of water going from 100 psia and 100 F to 1000 psia is 2.70 Btu. Make the computation yourself. However, usually the enthalpy data for liquids other than water are missing, or not of sufficient accuracy to be valid, which forces an engineer to turn to the mechanical energy balance. 

To obtain a physical interpretation for the residual Gibbs energy, we start with an ideal-gas mixture confined to a closed vessel. As the process, we consider the reversible isothermal-isobaric conversion of the ideal-gas molecules into real ones. Although this process is hypothetical, it is a mathematically well-defined operation in statistical mechanics the process amounts to a "turning on" of intermolecular forces. We first want to obtain an expression for the work, but since the process involves a change in molecular identities, we must start with the general energy balance (3.6.3). For a system with no inlets and no outlets, (3.6.3) becomes... 

Equation (3.29) is termed the differential mechanical energy balance. It is a useful form, since the work is written in terms of the measured properties P and v as well as bulk potential and kinetic energy. It is applicable to reversible, steady-state processes with one stream in and one stream out. 

The three-body recombination process (2-37) is the most important one in high-density quasi-equilibrium plasmas. Concentrations of molecular ions are very low in this case (because of thermal dissociation) for the fast mechanism of dissociative recombination described earlier, and the three-body reaction dominates. The recombination process starts with the three-body capture of an electron by a positive ion and formation of a highly excited atom with a binding energy of about. This highly excited atom then gradually loses energy in electron impacts. The three-body electron-ion recombination process (2-37) is a reverse one with respect to the stepwise ionization (see Section 2.1.7). For this reason, the rate coefficient of the recombination can be derived from the stepwise ionization rate coefficient kl (2-25) and from the Saha thermodynamic equation for ionization/recombination balance (see Chapter 3) ... 

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