Exergy: A Detailed Explanation PDF

Energy is conserved in every device or process. It cannot be destroyed. Energy entering a system with fuel, electricity, flowing streams of matter, and so on can be accounted for in the products and by-products. However, the energy conservation idea alone is inadequate for depicting some importan...

Energy is conserved in every device or process. It cannot be destroyed. Energy entering a system with fuel, electricity, flowing streams of matter, and so on can be accounted for in the products and by-products. However, the energy conservation idea alone is inadequate for depicting some important aspects of resource utilization. Figure 7.1*a* shows an *isolated system* consisting initially of a small container of fuel surrounded by air in abundance. Suppose the fuel burns (Fig. 7.1*b*) so that finally there is a slightly warm mixture of combustion products and air as shown in Fig. 7.1*c.* The total *quantity* of energy associated with the system is constant because no energy transfers take place across the boundary of an isolated system. Still, the initial fuel--air combination is intrinsically more useful than the final warm mixture. For instance, the fuel might be used in some device to generate electricity or produce superheated steam, whereas the uses of the final slightly warm mixture are far more limited in scope. We can say that the system has a greater *potential for* *use* initially than it has finally. Since nothing but a final warm mixture is achieved in the process, this potential is largely wasted. More precisely, the initial potential is largely *destroyed* because of the irreversible nature of the process. b b b b b Anticipating the main results of this chapter, *exergy* is the property that quantifies *potential for use.* The foregoing example illustrates that, unlike energy, exergy is not conserved but is destroyed by irreversibilities. Subsequent discussion shows that exergy not only can be destroyed by irreversibilities but also can be transferred *to* and *from* systems. Exergy transferred from a system to its surroundings without use typically represents a *loss.* Improved energy resource utilization can be realized by reducing exergy destruction within a system and/or reducing losses. An objective in exergy analysis is to identify sites where exergy destructions and losses occur and rank order them for significance. This allows attention to be centered on aspects of system operation that offer the greatest opportunities for cost-effective improvements. Returning to Fig. 7.1, note that the fuel present initially has economic value while the final slightly warm mixture has little value. Accordingly, economic value decreases in this process. From such considerations we might infer there is a link between exergy and economic value, and this is the case as we will see in subsequent discussions. The introduction to the second law in Chap. 5 provides a basis for the exergy concept, as considered next. Principal conclusions of the discussion of Fig. 5.1 given on p. 242 are that - a potential for developing work exists whenever two systems at different states arebrought into communication, and - work can be developed as the two systems are allowed to come into equilibrium. In Fig. 5.1*a*, for example, a body initially at an elevated temperature *T*i placed in contact with the atmosphere at temperature *T*0 cools spontaneously. To conceptualize how work might be developed in this case, see Fig. 7.2. The figure shows an *overall* system with three elements: the body, a power cycle, and the atmosphere at *T*0 and *p*0. The atmosphere is presumed to be large enough that its temperature and pressure remain constant. *W*c denotes the work of the overall system. Instead of the body cooling spontaneously as considered in Fig. 5.1*a*, Fig. 7.2 shows that if the heat transfer *Q* during cooling is passed to the power cycle, work *W*c can be developed, while *Q*0 is discharged to the atmosphere. These are the only energy transfers. The work *W*c is *fully available* for lifting a weight or, equivalently, as shaft work or electrical work. Ultimately the body cools to *T*0, and no more work would be developed. At equilibrium, the body and atmosphere each possess energy, but there no longer is any potential for developing work from the two because no further interaction can occur between them. Note that work *W*c also could be developed by the system of Fig. 7.2 if the initial temperature of the body were *less* than that of the atmosphere: *T*i , *T*0. In such a case, the directions of the heat transfers *Q* and *Q*0 shown on Fig. 7.2 would each reverse. Work could be developed as the body *warms* to equilibrium with the atmosphere. Since there is no net change of state for the power cycle of Fig. 7.2, we conclude that the work *W*c is realized solely because the initial state of the body differs from that of the atmosphere. *Exergy is the maximum theoretical value of such work.* **7.2.1 Environment and Dead State** For thermodynamic analysis involving the exergy concept, it is necessary to model the atmosphere used in the foregoing discussion. The resulting model is called the **exergy reference environment**, or simply the **environment**. In this book the environment is regarded to be a simple compressible system that is *large* in extent and *uniform* in temperature, *T*0, and pressure, *p*0. In keeping with the idea that the environment represents a portion of the physical world, the values for both *p*0 and *T*0 used throughout a particular analysis are normally taken as typical ambient conditions, such as 1 atm and 258C (778F). Additionally, the intensive properties of the environment do not change significantly as a result of any process under consideration, and the environment is free of irreversibilities. When a system of interest is at *T*0 and *p*0 and *at rest* relative to the environment, we say the system is at the **dead state**. At the dead state there can be no interaction between system and environment and, thus, no potential for developing work. **7.2.2 Defining Exergy** The discussion to this point of the current section can be summarized by the following **definition of exergy**: Exergy is the maximum theoretical work obtainable from an overall system consisting of a system and the environment as the system comes into equilibrium with the environment (passes to the dead state). Interactions between the system and the environment may involve auxiliary devices, such as the power cycle of Fig. 7.2, that at least in principle allow the realization of the work. The work developed is fully available for lifting a weight or, equivalently, as shaft work or electrical work. We might expect that the maximum theoretical work would be obtained when there are no irreversibilities. As considered in the next section, this *is* the case. **7.3.1 Exergy Aspects** In this section, we list five important aspects of the exergy concept: 1\. Exergy is a measure of the departure of the state of a system from that of the environment. It is therefore an attribute of the system and environment together. However, once the environment is specified, a value can be assigned to exergy in terms of property values for the system only, so exergy can be regarded as a property of the system. Exergy is an extensive property. 2\. The value of exergy cannot be negative. If a system were at any state other than the dead state, the system would be able to change its condition *spontaneously* toward the dead state; this tendency would cease when the dead state was reached. No work must be done to effect such a spontaneous change. Accordingly, any change in state of the system to the dead state can be accomplished with *at least zero* work being developed, and thus the *maximum* work (exergy) cannot be negative. 3\. Exergy is not conserved but is destroyed by irreversibilities. A limiting case is when exergy is completely destroyed, as would occur if a system were permitted to undergo a spontaneous change to the dead state with no provision to obtain work. The potential to develop work that existed originally would be completely wasted in such a spontaneous process. 4\. Exergy has been viewed thus far as the *maximum* theoretical work obtainable from an *overall* system of system plus environment as the system passes *from* a given state *to* the dead state. Alternatively, exergy can be regarded as the magnitude of the *minimum* theoretical work *input* required to bring the system *from* the dead state *to* the given state. Using energy and entropy balances as above, we can readily develop Eq. 7.1 from this viewpoint. This is left as an exercise. 5\. When a system is at the dead state, it is in *thermal* and *mechanical* equilibrium with the environment, and the value of exergy is zero. More precisely, the *thermomechanical* contribution to exergy is zero. This modifying term distinguishes the exergy concept of the present chapter from another contribution to exergy introduced in Sec. 13.6, where the contents of a system at the dead state are permitted to enter into chemical reaction with environmental components and in so doing develop additional work. This contribution to exergy is called *chemical exergy.* The chemical exergy concept is important in the second law analysis of many types of systems, in particular systems involving combustion. Still, as shown in this chapter, the thermomechanical exergy concept suffices for a wide range of thermodynamic evaluations. **7.5.1 Comparing Energy and Exergy for Control** **Volumes at Steady State** Although energy and exergy share common units and exergy transfer accompanies energy transfer, energy and exergy are *fundamentally different* concepts. Energy and exergy relate, respectively, to the first and second laws of thermodynamics: c Energy is *conserved*. Exergy is *destroyed* by irreversibilities. c Exergy expresses energy transfer by work, heat, and mass flow in terms of a *common* *measure*---namely, work that is *fully available* for lifting a weight or, equivalently, as shaft or electrical work. **7.6.3 Using Exergetic Efficiencies** Exergetic efficiencies are useful for distinguishing means for utilizing fossil fuels that are thermodynamically effective from those that are less so. Exergetic efficiencies also can be used to evaluate the effectiveness of engineering measures taken to improve the performance of systems. This is done by comparing the efficiency values determined before and after modifications have been made to show how much improvement has been achieved. Moreover, exergetic efficiencies can be used to gauge the potential for improvement in the performance of a given system by comparing the efficiency of the system to the efficiency of like systems. A significant difference between these values signals that improved performance is possible. It is important to recognize that the limit of 100% exergetic efficiency should not be regarded as a practical objective. This theoretical limit could be attained only if there were no exergy destructions or losses. To achieve such idealized processes might require extremely long times to execute processes and/or complex devices, both of which are at odds with the objective of cost-effective operation. In practice, decisions are chiefly made on the basis of *total* costs. An increase in efficiency to reduce fuel consumption, or otherwise utilize fuels better, often requires additional expenditures for facilities and operations. Accordingly, an improvement might not be implemented if an increase in total cost would result. The trade-off between fuel savings and additional investment invariably dictates a lower efficiency than might be achieved *theoretically* and even a lower efficiency than could be achieved using the *best available* technology. **7.7 Thermoeconomics** *Thermal systems* typically experience significant work and/or heat interactions with their surroundings, and they can exchange mass with their surroundings in the form of hot and cold streams, including chemically reactive mixtures. Thermal systems appear in almost every industry, and numerous examples are found in our everyday lives. Their design and operation involve the application of principles from thermodynamics, fluid mechanics, and heat transfer, as well as such fields as materials, manufacturing, and mechanical design. The design and operation of thermal systems also require explicit consideration of engineering economics, for cost is always a consideration. The term **thermoeconomics** may be applied to this general area of application, although it is often applied more narrowly to methodologies combining exergy and economics for optimization studies during design of new systems and process improvement of existing systems. **7.7.1 Costing** Is costing an art or a science? The answer is a little of both. *Cost engineering* is an important engineering subdiscipline aimed at objectively applying real-world costing experience in engineering design and project management. Costing services are provided by practitioners skilled in the use of specialized methodologies, cost models, and databases, together with costing expertise and judgment garnered from years of professional practice. Depending on need, cost engineers provide services ranging from rough and rapid estimates to in-depth analyses. Ideally, cost engineers are involved with projects from the formative stages, for the *output* of cost engineering is an essential *input* to decision making. Such input can be instrumental in identifying feasible options from a set of alternatives and even pinpointing the best option. Costing of thermal systems considers costs of owning and operating them. Some observers voice concerns that costs related to the environment often are only weakly taken into consideration in such evaluations. They say companies pay for the right to extract natural resources used in the production of goods and services but rarely pay fully for depleting nonrenewable resources and mitigating accompanying environmental degradation and loss of wildlife habitat, in many cases leaving the cost burden to future generations. Another concern is who pays for the costs of controlling air and water pollution, cleaning up hazardous wastes, and the impacts of pollution and waste on human health---industry, government, the public, or some combination of all three. Yet when agreement about environmental costs is achieved among interested business, governmental, and advocacy groups, such costs are readily integrated in costing of thermal systems, including costing on an exergy basis, which is the present focus.