Thermodynamics

First law of thermodynamicsThe first law of thermodynamics deals with the quantity of energy and asserts that energy cannot be created or destroyed.

Second law of thermodynamicsThe second law deals with the quality of energy.

Exergy EFrom book Fundamentals

Energy is conserved in every device or process. It cannot be destroyed. Energy enteringa system with fuel, electricity, flowing streams of matter, and so on can be accountedfor in the products and by-products. However, the energy conservation idea alone isinadequate for depicting some important aspects of resource utilization.

EXAMPLE

Figure 7.1a shows an isolated system consisting initially of a smallcontainer of fuel surrounded by air in abundance. Suppose the fuel burns (Fig. 7.1b)so that finally there is a slightly warm mixture of combustion products and air asshown in Fig. 7.1c. The total quantity of energy associated with the system is constantbecause 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 warmmixture. For instance, the fuel might be used in some device to generate electricityor produce superheated steam, whereas the uses of the final slightly warm mixtureare far more limited in scope. We can say that the system has a greater potential foruse initially than it has finally. Since nothing but a final warm mixture is achieved inthe process, this potential is largely wasted. More precisely, the initial potential islargely destroyed because of the irreversible nature of the process.

Anticipating the main results of this chapter, exergy is the property that quantifiespotential for use. The foregoing example illustrates that, unlike energy, exergy is notconserved but is destroyed by irreversibilities.

Subsequent discussion shows that exergy not only can be destroyed by irreversibilitiesbut also can be transferred to and from systems. Exergy transferred from asystem to its surroundings without use typically represents a loss. Improved energyresource utilization can be realized by reducing exergy destruction within a systemand/or reducing losses. An objective in exergy analysis is to identify sites where exergydestructions and losses occur and rank order them for significance. This allows attentionto be centered on aspects of system operation that offer the greatest opportunitiesfor cost-effective improvements.

Environment and Dead StateFor thermodynamic analysis involving the exergy concept, it is necessary to modelthe atmosphere used in the foregoing discussion. The resulting model is called theexergy reference environment, or simply the environment.In this book the environment is regarded to be a simple compressible system thatis large in extent and uniform in temperature, T0, and pressure, p0. In keeping with theidea that the environment represents a portion of the physical world, the values forboth p0 and T0 used throughout a particular analysis are normally taken as typicalambient conditions, such as 1 atm and 258C (778F). Additionally, the intensive propertiesof the environment do not change significantly as a result of any process underconsideration, and the environment is free of irreversibilities.When a system of interest is at T0 and p0 and at rest relative to the environment,we say the system is at the dead state. At the dead state there can be no interactionbetween system and environment, and thus no potential for developing work.

Defining ExergyThe discussion to this point of the current section can be summarized by the followingdefinition of exergy:Exergy is the maximum theoretical work obtainable from an overall system consistingof 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 theoreticalwork would be obtained when there are no irreversibilities. As considered in thenext section, this is the case.

TAKE NOTE...In this book, E and e areused for exergy and specificexergy, respectively, while Eand e denote energy andspecific energy, respectively.Such notation is in keepingwith standard practice. Theappropriate concept, exergyor energy, will be clear incontext. Still, care is requiredto avoid mistaking thesymbols for these concepts.

Exergy of a SystemThe exergy of a system, E, at a specified state is given by the expression

where U, KE, PE, V, and S denote, respectively, internal energy, kinetic energy,potential energy, volume, and entropy of the system at the specified state. U0, V0,and S0 denote internal energy, volume, and entropy, respectively, of the systemwhen at the dead state. In this chapter kinetic and potential energy are evaluatedrelative to the environment. Thus, when the system is at the dead state, it is at restrelative the environment and the values of its kinetic and potential energies arezero: KE0 5 PE0 5 0. By inspection of Eq. 7.1, the units of exergy are seen to bethe same as those of energy.Equation 7.1 can be derived by applying energy and entropy balances to the overallsystem shown in Fig. 7.3 consisting of a closed system and an environment. Seethe box for the derivation of Eq. 7.1.

Exergy AspectsIn this section, we list five important aspects of the exergy concept:Exergy is a measure of the departure of the state of a system from that of theenvironment. It is therefore an attribute of the system and environment together.However, once the environment is specified, a value can be assigned to exergy interms of property values for the system only, so exergy can be regarded as a propertyof the system. Exergy is an extensive property.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 towardthe dead state; this tendency would cease when the dead state was reached. No workmust be done to effect such a spontaneous change. Accordingly, any change in stateof the system to the dead state can be accomplished with at least zero work beingdeveloped, and thus the maximum work (exergy) cannot be negative.Exergy is not conserved but is destroyed by irreversibilities. A limiting case is whenexergy is completely destroyed, as would occur if a system were permitted toundergo a spontaneous change to the dead state with no provision to obtain work.The potential to develop work that existed originally would be completely wastedin such a spontaneous process.Exergy has been viewed thus far as the maximum theoretical work obtainablefrom an overall system of system plus environment as the system passes from a givenstate to the dead state. Alternatively, exergy can be regarded as the magnitude ofthe minimum theoretical work input required to bring the system from the deadstate to the given state. Using energy and entropy balances as above, we can readilydevelop Eq. 7.1 from this viewpoint. This is left as an exercise.When a system is at the dead state, it is in thermal and mechanical equilibriumwith the environment, and the value of exergy is zero. More precisely, the thermomechanicalcontribution to exergy is zero. This modifying term distinguishes theexergy concept of the present chapter from another contribution to exergy introducedin Sec. 13.6, where the contents of a system at the dead state are permittedto enter into chemical reaction with environmental components and in so doingdevelop additional work. This contribution to exergy is called chemical exergy. Thechemical exergy concept is important in the second law analysis of many types ofsystems, in particular systems involving combustion. Still, as shown in this chapter,the thermomechanical exergy concept suffices for a wide range of thermodynamicevaluations.

7.4 Closed System Exergy Balance

Like energy, exergy can be transferred across the boundary of a closed system. Thechange in exergy of a system during a process would not necessarily equal the netexergy transferred because exergy would be destroyed if irreversibilities were presentwithin the system during the process. The concepts of exergy change, exergy transfer,and exergy destruction are related by the closed system exergy balance introducedin this section. The exergy balance concept is extended to control volumes in Sec. 7.5.Exergy balances are expressions of the second law of thermodynamics and providethe basis for exergy analysis.

7.6 Exergetic (Second Law) EfficiencyThe objective of this section is to show the use of the exergy concept in assessing theeffectiveness of energy resource utilization. As part of the presentation, the exergeticefficiency concept is introduced and illustrated. Such efficiencies are also known assecond law efficiencies

Exergy (also called availability, work potential or available energy) is the maximum useful work that can be obtained from a system at a given state in a given environment; in other words, the most work you can get out of a system.

In an exergy analysis the initial state is specified, the work output is maximized when the process between two specified states is executed in a reversible manner and the system must be in the dead state (meaning in thermodynamic equilibrium with the environment) at the end of the process to maximize the work output.

In the last several decades, exergy analysis has begun to be used for system optimization. By analyzing the exergy destroyed by each component in a process, it should be made clear where to focus our efforts to improve system efficiency. It can also be used to compare components or systems to help make informed design decisions.

Exergy associated with Kinetic and Potential EnergyKinetic and potential energy are forms of mechanical energy and can be converted to work entirely:

ek+e p=12v2+gz (kJ/kg).

Reversible work Wrev

Reversible work is the maximum useful work that can be obtained as a system undergoes a process between the specified initial and final states. This work output (or input) is obtained (or expended) when the process between the initial and final states is executed in a totally reversible manner.

If the final state is the dead state, then it will be equal to the exergy.

Irreversibility IAny difference between the reversible work W rev and the useful work W useful is due to the irreversibility present during the process, this difference is called irreversibility I.

Irreversibility is the destroyed exergy (wasted work potential). It represents energy that could have been converted into work but was instead wasted. To have high system efficiency, we want I to be as small as possible.

Xdestroyed=I=ToSgen

Second law efficiency η IIThe second law efficiency is defined as follows:

η II=exergy recoveredexergy supplied

=1−exergy destroyedexergy supplied

thermal efficiency and the reversible (maximum) thermal efficiency.

η II=ηthηth ,rev

=W useful

W rev

We can calculate the exergy, X (work potential) at a given state. The work potential is a function of the total energy of the system.

(remember that in a control mass, there will be no flow work)

XKE (exergy due to kinetic energy): V2/2 (on a per unit mass basis

XPE: gZ

Xinternal energy: u-uo+Po(v-vo)-To(s-s0)

Exergy of fixed massX = (U-U0)+P0(V – V0)–T0(S – S0) +½mVel2+mgz

Φ = (u-u0)+P0(v-v0)-T0(s-s0)+½Vel2+gz

or Φ = (e-e0)+P0(v-v0)-T0(s-s0)

Note that Φ = 0 at dead state

If the state of system or the state of the environment do not change, the exergy does not change Exergy change of steady flow devices, nozzles, compressors, turbines, pumps, heat exchangers; is zero during steady operation. Exergy of a closed system is either positive or zero.

Exergy of a flow streamFlow exergy

Ψ=(h-h0)-T0(s-s0)+½Vel2+gz

KE PE internal energy flow workX X X X X

Exergy transfer by heat work and massLike energy, exergy can be transferred in three forms:

Heato Xheat =(1-T0/T)Qo When T not constant, then Xheat =∫(1-T0/T)δQ

Worko Xwork = W – Wsurr (for boundary work)o Xwork = W (for all other forms of work)o Where Wwork = P0(V2-V1)

Masso Mass contains exergy as well as energy and entropyo X=m Ψ=m[(h-h0)-T0(s-s0)+½Vel2+gz]