Exergy equation

The exergy equation (2.26) enables useful information on the irreversibilities and lost work to be obtained, in comparison with a Carnot cycle operating within the same temperature limits (T ,ax = Ey and T in = To). Note first that if the heat supplied is the same to each of the two cycles (Carnot and IJB), then the work output from the Carnot engine (Wcar) is greater than that of the IJB cycle (Wijg), and the heat rejected from the former is less than that rejected by the latter. 

Eq. (2.22) may be interpreted in terms of exergy flows, work output and work potential (Fig. 2.5). The equation may be rewritten as... 

Application of the exergy flux equation to a closed cycle... 

We next consider the application of the exergy flux equation to a closed cycle plant based on the Joule-Brayton (JB) cycle (see Fig. 1.4), but with irreversible compression and expansion processes—an irreversible Joule-Brayton (IJB) cycle. The T,.s diagram is as shown in Fig. 2.6. 

It is convenient for exergy tabulations to associate the term [ —AGq] = Grq — Gpo with the exergy of the fuel supplied (of mass My), i.e. ,0 = [—AGoJ. For a combustion process burning liquid or solid fuel (at temperature Tq) with air (subscript a, at temperature T"]), the left-hand side of the equation may be written as... 

Structural theory facilitates the evaluation of exergy cost and incorporation of thermoeconomics functional analysis (Erlach et al., 1999). It is a common formulation for the various thermoeconomic methods providing the costing equations from a set of modeling equations for the components of a system. The structural theory needs a productive structure displaying how the resource... 

Added exergy provided by the solar air heater system can be expressed in terms ofNTU and A7]m using Equation (26) as... 

A parametric study was conducted using the Engineering Equation Solver (EES) software. Figure 4 illustrates the variation of the exit temperature of the heat pump (or supply temperature of the heat distribution system) in the heating mode versus COP. Normally, in heating systems, the supply temperature of the heat distribution network plays a key role in terms of exergy loss. This temperature is determined via an optimization procedure. 

In American literature [1], the term H - T0S is often indicated as the availability function B = H - T0S, which stems from the concept "available" work. This should not suggest, as it sometimes occurs in literature, that exergy is the same as availability. It is not, because from Equation 6.12 it follows that... 

Determination of the amount of lost work does not require the introduction of the concept of exergy. With the definition of Equation 6.10, the overall AH and AS decide on the amount of minimum work required to bring about the change in conditions. More work brought into the process than is strictly necessary according to Equation 6.10 must have been the work dissipated on overcoming the process "frictions."... 

Equation 6.10 led to the definition of exergy, whereas the same expression in Equation 3.20 does not. Both equations express the minimum amount of work to transform the conditions of a defined amount of mass from those in state 1 into those of state 2. But if we choose state 1 as that of the environment, the environment suddenly acts as the datum level for a property of the amount of mass considered. The simplest example we can think of is air. 

Ignoring for the moment other constituents than nitrogen and oxygen, air at environmental conditions P0T0 is "powerless" to perform work for us. According to Equation 6.12 its exergy is indeed zero. 

The first term on the right-hand side of this equation expresses the amount of work available due to differences in pressure and temperature with the environment. The second term, the chemical exergy, expresses the amount of work available due to the differences in composition with respect to the environment. The superscript in Ex, expresses that the chemical exergy is considered at ambient conditions. 

The analysis requires the calculation of three exergy flow rates, at 0°C, 50°C, and 100°C. As no heat or work is transferred between the considered system and its environment, the first law, Equation 6.1, yields that the overall enthalpy change is zero ... 

Introducing this relation into Equation 6.22 gives us the temperature T3 of the flow leaving the mixer T3 = 323.15 K. The exergy flow rates can now be calculated from... 

Equation 6.33 provides the definition of exergy if state 1 is chosen as the state at ambient condition, namely, P, = P0 and = T0 the minimum amount of work required to transfer the system from environmental conditions to those at P2 and T2. At these conditions, this is the maximum amount of work available for the reverse process. That is the valuable idea behind the exergy concept to be able to assign to any process stream a value, its exergy, that expresses the confined work available in the stream. For the general change in state from P0r T0 to P, T, we can write the net energy input as... 

From this equation, we can show [2] that the standard chemical exergy at P0 and T0 of a pure component can be calculated from its partial pressure Pt in air with Equation 7.6 ... 

The first term on the right-hand side of this equation is the standard Gibbs energy of formation of methane, which is listed [2] as -50.460 kj/mol and thus EXch,cH4(g) can be calculated to be 831.6 kj/mol. Chapter 9 illustrates the use of this exergy value in the analysis of a natural gas-driven power station. 

In general, we can calculate the standard chemical exergy of a component from the standard chemical exergy of its elements with the equation... 

Next, we wish to calculate which fraction this lost work is of the work originally available in the gas. The chemical exergy of the gas, assumed to be methane, is significant, 831.65 kj/mol, but it should be excluded from the calculation because no chemistry is involved in the expansion step. The work available in the gas at initial and final conditions can be calculated from Equation 6.11 ... 

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