Temperature, dead-state

The amount of available energy which a substance has is relative and depends upon the choice of a dead state. The fundamental dead state is the state that would be attained if each constituent of the substance were reduced to complete stable equilibrium with the components (8,9,10) in the environment—a component-equilibrium dead state. (Thus, one may visualize the available energy as the maximum net work obtainable upon allowing the constituents to come to complete equilibrium with the environment.) The equilibrium is dictated by the dead state temperature T0 and, for ideal gas components, by the dead state partial pressure p-jg of each component j. (The available energy could be completely obtained, say in the form of shaft work, if equilibrium were reached via an ideal process—no dissipations or losses—involving such artifices as perfectly-selective semi-permeable membranes, reversible expanders, etc. (9,10,11).)... 

Some contend that the chemical reference datum for available energy can also be selected arbitrarily, just like a base for thermochemical tables (while admitting that the thermal reference datum—the "dead state temperature"—is not arbitrary). The contention is erroneous changing the various values of the available energy of a specific material by a constant amount (as a consequence of changing the reference datum) leads to misconceptions, to misevaluations, and to misallocations—in the determination of inefficiencies and costs. Absolute values of available energy can and should be evaluated. 

In this subsection, availability changes are computed for several simple processes to show the significant impact of the change in entropy. These are taken from the monograph by Sussman (1980), who presents many other excellent examples, including three that take into account chemical reaction, one of which deals with a complete methane reforming process. In all cases, the environmental (dead-state) temperature in the following examples is taken as 298 K = 537. ... 

In this equation, in the second term on the left-hand side, we see that the enthalpy and entropy appear together to form a combined factor that is similar to the Gibbs free energy. However, the entropy is multiplied by the dead-state temperature. To, instead of the stream temperature, T. In addition, the first term on the left side can be rewritten to give the same combination, H -, by... 

For the first example, consider the continuous two-stage compression of nitrogen gas shown in Figure 9,19. which is based on actual plant operating conditions. The system or control volume is selected to exclude the electric power generation plant and cooling-water heat sink. Assume that the temperature, T, of the cooling water is essentially equal to the dead-state temperature. To. Calculate the lost work. 

The lost work for the cycle is computed in the following maimer. First, we take the dead-state temperature. To, to be the cooling-water temperature, Tcondenser The lost work then reduces to... 

The results in Figure 921 and Table 9 5 are used to perform a second-law analysis. The dead-state temperature is taken as 100°F. The calculation of lost work for the entire process and the corresponding second-law efficiency is carried out conveniently on a spreadsheet by transferring results from ASPEN PLUS, as shown in Figure 9 28. Note that the availability function for each stream can be computed and printed by ASPEN PLUS. The overall efficiency is only 25.7%. Similar analyses are carried out readily for the separate operations in the process. The fraction of the total lost work for each operation is as follows ... 

Conceptually, the dead state can be visualized from several different angles as follows The universe contains a stable system which is composed of many stable materials existing in abundance and whose concentrations can be reasonably assumed to remain invariant (1,2,8,11,12,14,16,17). All the stable materials exist in thermodynamic equilibrium at the temperature, Tq, of 298.15 K, and under the total pressure, PQ, of 1 atm. This state is termed the "dead state" (1,2,8,16,18). The most stable materials, which are in the stable sector of the universe, i.e., the dead state, are termed "datum level materials" and have the availability (exergy) and energy (enthalpy relative to the dead state) of zero the concentration of the datum level material is the datum level concentration. 

Here, T0 is a reference temperature (dead state) and AExm a thermodynamic minimum value. The total flow J=LVXav can be written by using Eq. (5.81)... 

Often, H2O could be used. However, consider the prospect of dispersion of SOo into a desert environment it is conceivable that the dead state of the sulfur would need to be taken as the SOg, at its partial pressure in the air in the inriediate vicinity of the power plant—or even at its partial pressure in the exhaust gases—and at ambient temperature. 

That is, the change in the maximum work available from the stream is a function solely of its changes in enthalpy and entropy, and the environmental temperature. Like H and. S, is a state function, independent of path, but dependent on the temperature. To, and pressure, T o, of the dead state. If chemical reactions occur, the availability also depends on the composition of the dead state. 

Chemical reactions occurring far from equilibrium. To minimize lost work, reactions should be carried out with little or no dilution, with minimal side reactions, and at maximum yields to avoid separations and byproduct formation. This is best achieved by using selective catalysts. If the reaction is exothermic, it is best carried out at high temperature to maximize the usefulness of the energy produced. If the reaction is endothermic, it is best carried out at below ambient temperature to utilize heat from the dead state. 

The physical exergy Eph is equal to the maximum amount of work obtainable when a compound or mixture is brought from its temperature T and pressure P to environmental conditions, characterized by environmental temperature T and pressure Pq. The standard chemical exergy of a pure chemical compound Ech is equal to the maximum amount of work obtainable when a compound is brought from the environmental state, characterized by the environmental temperature To (298.15 K) and environmental pressure Po (1 atm), to the dead state, characterized by the same environmental conditions of temperature and pressure, but also by the concentration of reference substances in a standard environment. 

Table 23.3 summarizes the conditions at each state point. (Points 2s and 4s represent points the conditions for isentropic processes input properties in the table are underlined.) Point a is at atmospheric conditions (the dead state). Point 1, the compressor inlet, is reached after the atmospheric air undergoes a throttling process (constant enthalpy) and experiences a 0.2 psi pressure drop, and point 2s would be achieved in an isentropic compressor. The ratio of the reduced pressure equals the ratio of the actual pressures for an isentropic process. In point 2, the enthalpy is calculated from the compressor isentropic efficiency. In the combustion chamber, the pressure drops 2 psi and the temperature is increased to 1800°F. Point 4s and 4 are analyzed similarly to 2s and 2. Finally, the pressure drops to point 5 where the air enters the atmosphere. The accompanying h-s (or T-s) diagram shows the cycle and includes all of the pressure drops and turbine and compressor inefficiencies. 

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