The CRC Handbook of Mechanical Engineering. Chapter 2. Engineering Thermodynamics (776125), страница 15
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Thermoeconomics allows the real cost sources at the component level to be identified:capital investment costs, operating and maintenance costs, and the costs associated with the destructionand loss of exergy. Optimization of thermal systems can be achieved by a careful consideration of suchcost sources. From this perspective thermoeconomics is exergy-aided cost minimization.Discussions of exergy analysis and thermoeconomics are provided by Bejan et al.
(1996), Moran(1989), and Moran and Shapiro (1995). In this section salient aspects are presented.Defining ExergyAn opportunity for doing work exists whenever two systems at different states are placed in communication because, in principle, work can be developed as the two are allowed to come into equilibrium.When one of the two systems is a suitably idealized system called an environment and the other is somesystem of interest, exergy is the maximum theoretical useful work (shaft work or electrical work)obtainable as the systems interact to equilibrium, heat transfer occurring with the environment only.(Alternatively, exergy is the minimum theoretical useful work required to form a quantity of matter fromsubstances present in the environment and to bring the matter to a specified state.) Exergy is a measureof the departure of the state of the system from that of the environment, and is therefore an attribute ofthe system and environment together.
Once the environment is specified, however, a value can be assignedto exergy in terms of property values for the system only, so exergy can be regarded as an extensiveproperty of the system.Exergy can be destroyed and generally is not conserved. A limiting case is when exergy would becompletely destroyed, as would occur if a system were to come into equilibrium with the environmentspontaneously with no provision to obtain work.
The capability to develop work that existed initiallywould be completely wasted in the spontaneous process. Moreover, since no work needs to be done toeffect such a spontaneous change, the value of exergy can never be negative.EnvironmentModels with various levels of specificity are employed for describing the environment used to evaluateexergy.
Models of the environment typically refer to some portion of a system’s surroundings, theintensive properties of each phase of which are uniform and do not change significantly as a result ofany process under consideration. The environment is regarded as composed of common substancesexisting in abundance within the Earth’s atmosphere, oceans, and crust. The substances are in their stableforms as they exist naturally, and there is no possibility of developing work from interactions — physicalor chemical — between parts of the environment. Although the intensive properties of the environmentare assumed to be unchanging, the extensive properties can change as a result of interactions with othersystems.
Kinetic and potential energies are evaluated relative to coordinates in the environment, all partsof which are considered to be at rest with respect to one another.For computational ease, the temperature T0 and pressure p0 of the environment are often taken asstandard-state values, such as 1 atm and 25°C (77°F). However, these properties may be specified© 1999 by CRC Press LLC2-70Section 2differently depending on the application.
T0 and p0 might be taken as the average ambient temperatureand pressure, respectively, for the location at which the system under consideration operates. Or, if thesystem uses atmospheric air, T0 might be specified as the average air temperature. If both air and waterfrom the natural surroundings are used, T0 would be specified as the lower of the average temperaturesfor air and water.Dead StatesWhen a system is in equilibrium with the environment, the state of the system is called the dead state.At the dead state, the conditions of mechanical, thermal, and chemical equilibrium between the systemand the environment are satisfied: the pressure, temperature, and chemical potentials of the system equalthose of the environment, respectively. In addition, the system has no motion or elevation relative tocoordinates in the environment.
Under these conditions, there is no possibility of a spontaneous changewithin the system or the environment, nor can there be an interaction between them. The value of exergyis zero.Another type of equilibrium between the system and environment can be identified. This is a restrictedform of equilibrium where only the conditions of mechanical and thermal equilibrium must be satisfied.This state of the system is called the restricted dead state. At the restricted dead state, the fixed quantityof matter under consideration is imagined to be sealed in an envelope impervious to mass flow, at zerovelocity and elevation relative to coordinates in the environment, and at the temperature T0 and pressurep0.Exergy BalancesExergy can be transferred by three means: exergy transfer associated with work, exergy transfer associatedwith heat transfer, and exergy transfer associated with the matter entering and exiting a control volume.All such exergy transfers are evaluated relative to the environment used to define exergy.
Exergy is alsodestroyed by irreversibilities within the system or control volume.Exergy balances can be written in various forms, depending on whether a closed system or controlvolume is under consideration and whether steady-state or transient operation is of interest. Owing toits importance for a wide range of applications, an exergy rate balance for control volumes at steadystate is presented next.Control Volume Exergy Rate BalanceAt steady state, the control volume exergy rate balance takes the form0=∑ E˙q, j− W˙ cv +j∑ E˙ − ∑ E˙iei− E˙ De________________________rates ofexergytransfer_________(2.85a)rate ofexergydestructionor0=jj© 1999 by CRC Press LLCT0 ∑ 1 − T Q˙ − W˙ + ∑ m˙ e − ∑ m˙ ejcvi iie ee− E˙ D(2.85b)2-71Engineering ThermodynamicsẆcv has the same significance as in Equation 2.22: the work rate excluding the flow work.
Q̇ j is thetime rate of heat transfer at the location on the boundary of the control volume where the instantaneoustemperature is Tj. The associated rate of exergy transfer isT E˙ q, j = 1 − 0 Q˙ jTj (2.86)As for other control volume rate balances, the subscripts i and e denote inlets and outlets, respectively.The exergy transfer rates at control volume inlets and outlets are denoted, respectively, as E˙ i = m˙ i ei andE˙ e = m˙ e ee . Finally, Ė D accounts for the time rate of exergy destruction due to irreversibilities withinthe control volume. The exergy destruction rate is related to the entropy generation rate byE˙ D = T0 S˙gen(2.87)The specific exergy transfer terms ei and ee are expressible in terms of four components: physicalexergy ePH, kinetic exergy eKN, potential exergy ePT, and chemical exergy eCH:e = e PH + e KN + e PT + e CH(2.88)The first three components are evaluated as follows:e PH = (h − h0 ) − T0 (s − s0 )e KN =1 2v2e PT = gz(2.89a)(2.89b)(2.89c)In Equation 2.89a, h0 and s0 denote, respectively, the specific enthalpy and specific entropy at the restricteddead state.
In Equations 2.89b and 2.89c, v and z denote velocity and elevation relative to coordinatesin the environment, respectively. The chemical exergy eCH is considered next.Chemical ExergyTo evaluate the chemical exergy, the exergy component associated with the departure of the chemicalcomposition of a system from that of the environment, the substances comprising the system are referredto the properties of a suitably selected set of environmental substances.
For this purpose, alternativemodels of the environment have been developed. For discussion, see, for example, Moran (1989) andKotas (1995).Exergy analysis is facilitated, however, by employing a standard environment and a correspondingtable of standard chemical exergies. Standard chemical exergies are based on standard values of theenvironmental temperature T0 and pressure p0 — for example, 298.15 K (25°C) and 1 atm, respectively.A standard environment is also regarded as consisting of a set of reference substances with standardconcentrations reflecting as closely as possible the chemical makeup of the natural environment. Thereference substances generally fall into three groups: gaseous components of the atmosphere, solidsubstances from the lithosphere, and ionic and noninonic substances from the oceans.
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