Exergy balance equation

According to Fig. 1-7 the exergy balance equation, for a steady-state open system, under isobaric conditions, is... 

The exergy balance equation is very similar to the first law of thermodynamics with the exception that useful energy is considered instead of total energy. An important difference is that exergy is not a conserved quantity it is destroyed as entropy is generated. 

Normalizing by m to develop relationships on a per unit mass basis (e.g., = the resultant energy and exergy balance equations are... 

The exergy-balance equation developed by Oh et al. [4] and the corresponding exergy cost-balance equations developed by Kimet al. [5] were used in these analyses. 

The results from an exergy analysis constitute a unique base for exergoeconomics, an exergy-aided cost reduction method. A general exergy-balance equation, applicable to any component of a thermal system may be formulated by utilizing the first and second law of thermodynamics [1], [2], [9]. 

Note that the ExQ1 and ExQ2 terms differ for the reversible and irreversible cases. The reversible case has the minimum heat input Qmm at temperature level Tb since heat is transferred reversibly without a temperature gradient. Similarly, it is rejected at Tt. It is in these two terms that the reversible and irreversible exergy balances differ. Now, first consider the reversible exergy balance, where Exlost is, by definition, equal to zero. From Equation 10.19, for the reversible case, we obtain... 

There seems to be an agreement to name equation (5) "Exergy". The lost work (called also dissipation),. in a system or a subsystem may also be computed from an "exergy balance" according to equation (6). 

Cumulative exeigy consumption can be calculated by the balance equations the rkj for the useful products equals the sum of cumulative exergy consumption of all raw materials and semifinished products in the production network. For the link j of the network and for the natural resources k, the balance equations are... 

Calculation of mass, energy and exergy balances for the total separation plant are usually done sequentially from apparatus to apparatus. They are occasionally carried out simultaneously by an iterative method, considering the corresponding equation system for the total separation process. In this case, it is necessary to develop a calculation flowchart with coded interface and ramification. The process structure is conveniently presented graphically. After mathematical formulation of the process, the number and values of the independent system variables are determined. Finally, the balance equations are solved sequentially. 

A multiobjective optimization problem is formulated for the MTBE RD column with respect to economic performance and exergy efficiency. The formulation includes the balance equations 8.1-8.5 and 8.29, the criteria definitions 8.42 and the optimization formulation 8.62. Constraints imposed by operating conditions and product specifications are included. For the sake of controlled built-up of optimization complexity the first approximation of this approach omits the response time constant as objective function. 

Combining with the entropy balance. Equation 23.50, and defining destroyed exergy as irreversibility gives. 

Thermodynamic analysis of power plants seeks to characterize efficiency and identify sources of losses. First law analysis assesses performance based on energy balance equations, while second law analysis uses exergy balances and looks for locations of exergy destruction. In this section, analysis methods are developed to apply thermodynamic balance equations to analyze heat engines and power plant components. Results are summarized in Appendix B of this chapter and detailed examples are provided in Section 23.6. 

Typically, hii (the vent flow rate for noncondensable gases) is small, so that the energy and exergy contributions in the vent stream are small and may be neglected in the analysis. Excluding the vent stream under steady-state conditions, the exergy balance from Equation 23.58 yields. 

Complete energy and exergy balances are shown in Figure 23.15. The resultant plant thermal efficiency from Equation 23.63 is... 

Heat and exergy balances are calculated in a similar manner to the previous example, except that all quantities are normalized on a per unit boiler flow basis. For example, the work and irreversibility of the low-pressure turbine are from Equations 23.77 and 23.79, modified for the flow rates are... 

When there is more than one product from a plant, a money balance cannot be solved for unique unit costs of the several products. An additional equation is needed for each unknown unit cost, besides one. The additional equations are determined by cost accounting not thermodynamic, considerations (52). Before discussing some alternative methods for determining the necessary additional equations, it will be illustrated by the following example that when there are multiple products, the use of energy to measure power leads to radical errors exergy yields rational results. 

The above equation is analogous with the entropy balance of the second law. The first term in this expression shows the exergy transfer accompanying heat when the temperature at the heat transfer medium is not constant. 

P Equations. Each exergy unit is supplied to any stream associated with the product of a component at the same average cost cp p. This cost is calculated from the cost balance and the F equations. 

The equations [Eq. (52)] and the cost balance [Eq. (51)] may be used to calculate the Cp value in Eq. (51). Then, the P equations supply the costs associated with streams 6 and 8 each exergy unit is supplied to the main steam stream and to the reheat stream at the same average cost. 

Because heat loss to the environment is very small in comparison to the heat transferred within an open heat exchanger, the first law efficiency is close to unity. However, mixing streams is an irreversible process that generates entropy and thus destroys exergy. Assuming no heat loss to the environment, using Equation 23.42 yields the energy balance of the open feed heater. 

Resultant exergy and energy balances are shown in Figure 23.22, where the irreversibilities are calculated using Equations 23.83,23.73,23.79, and 23.108, respectively,... 

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