Energy irreversible adiabatic processes

If there is work along any infinitesimal path element of the irreversible adiabatic process (dw 0), we know from experience that this work would be different if the work coordinate or coordinates were changing at a different rate, because energy dissipation from internal friction would be different. In the limit of infinite slowness, with the same change of work coordinates and the process remaining adiabatic, the internal friction would vanish, the process would become reversible, and the net work and final internal energy would differ from those of the irreversible process. Because the final state of the reversible adiabatic process is different from B, there is no reversible adiabatic path between states A and B. 

Figure 15.5 shows the ideal open cycle for the gas turbine that is based on the Brayton Cycle. By assuming that the chemical energy released on combustion is equivalent to a transfer of heat at constant pressure to a working fluid of constant specific heat, this simplified approach allows the actual process to be compared with the ideal, and is represented in Figure 15.5 by a broken line. The processes for compression 1-2 and expansion 3-4 are irreversible adiabatic and differ, as shown from the ideal isentropic processes between the same pressures P and P2 -... 

For an irreversible process it may not be possible to express the relation between pressure and volume as a continuous mathematical function though, by choosing a suitable value for the constant k, an equation of the form Pv = constant may be used over a limited range of conditions. Equation 2.73 may then be used for the evaluation of / 2 v dP. It may be noted that, for an irreversible process, k will have different values for compression and expansion under otherwise similar conditions. Thus, for the irreversible adiabatic compression of a gas, k will be greater than y, and for the corresponding expansion k will be less than y. This means that more energy has to be put into an irreversible compression than will be received back when the gas expands to its original condition. 

The present volume involves several alterations in the presentation of thermodynamic topics covered in the previous editions. Obviously, it is not a trivial exercise to present in a novel fashion any material that covers a period of more than 160 years. However, as best as I can determine the treatment of irreversible phenomena in Sections 1.13, 1.14, and 1.20 appears not to be widely known. Following much indecision, and with encouragement by the editors, I have dropped the various exercises requiring numerical evaluation of formulae developed in the text. After much thought I have also relegated the Caratheodory formulation of the Second Law of Thermodynamics (and a derivation of the Debye-Hiickel equation) as a separate chapter to the end of the book. This permitted me to concentrate on a simpler exposition that directly links entropy to the reversible transfer of heat. It also provides a neat parallelism with the First Law that directly connects energy to work performance in an adiabatic process. A more careful discussion of the basic mechanism that forces electrochemical phenomena has been provided. I have also added material on the effects of curved interfaces and self assembly, and presented a more systematic formulation of the basics of irreversible processes. A discussion of critical phenomena is now included as a separate chapter. Lastly, the treatment of binary solutions has been expanded to deal with asymmetric properties of such systems. 

Equation (2.3.10) shows that in closed systems, entropy can be generated in two general ways. First, as already discussed in 2.1.2, the lost work 5Wiogt is the energy needed to overcome dissipative forces that act to oppose a mechanical process. Second, the heat-transfer term in (2.3.10) contributes when a finite temperature difference irreversibly drives heat across system boundaries. This second term is zero in two important special cases (a) for adiabatic processes, = 0, and (b) for processes in which heat is driven by a differential temperature difference, Tg t = T dT. In both of these special cases, (2.3.10) reduces to... 

During a process with irreversible work, energy dissipation can be either partial or complete. Dissipative work, such as the stirring work and electrical heating described in previous sections, is irreversible work with complete energy dissipation. The final equilibrium state of an adiabatic process with dissipative work can also be reached by a path with positive heat and no work. This is a special case of the minimal work principle. 

The process described above is irreversible. Irreversibility means that, given two states A and B of an adiabatically enclosed system of constant composition, either of the processes A - B or B —> A may be driven mechanically or electromagnetically, but not both. By such a procedure the energy difference between two states AU — Ub - Da can always be measured. 

Beyond this point one must be aware of important differences between the two laws. The performance of work is directly linked to changes in energy of a system, so that the integrating factor q relevant to the First Law is unity. Furthermore, changes in S are tracked by the reversible transfer of heat across the boundaries of the system. Other changes in S are incurred when irreversible processes occur this subject was treated in detail in Sections 1.12, 1.13, and 1.20. By contrast, alterations in E are tracked by performance of work, whether reversibly or irreversibly, under adiabatic conditions. Different changes in E are incurred when these processes take place under non-adiabatic conditions, as discussed in Section 1.7. 

Furthermore, a real machine designed for adiabatic compression does not reach the ideal point of reversible iso-entropic process, because of unavoidable irreversible transformations. The reversible work associated to the pressure increase inside a fluid can be always calculated as vdp, while the net enthalpy variation is directly related to mechanical energy consumption, which increases with irreversibilities. 

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