Work, ‘lost

Work tliat is wasted as the result of irreversibilities in a process is called lost work, and is defined as the difference between the actual work of a process and die ideal work for the process. Thus by definition, 

The right sides of diis equation and Eq. (5.32) are identical dierefore, 

Since die second law of themiodynaniics requires that So 0, it follows tliat Wlost 0-When a process is completely reversible, the equality holds, and die lost work is zero. For irreversible processes the inequality holds, and the lost work, i.e., die energy drat becomes unavailable for work, is positive. 

The engineering significance of this result is clear The greater the irreversibility of a process, the greater the rate of entropy production and the greater the amount of energy that becomes unavailable for work. Thus every irreversibility carries with it a price. 

For tlie special case of a single stream flowing through the control volume, 

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Lost work, EW, is the irreversible loss in exergy that occurs because a process operates with driving forces or mixes material at different temperatures or compositions. 

Second-law analysis looks at the individual components of an overall process to define the causes of lost work. Sometimes it focuses on the efficiency of a step and ratios the theoretical work needed to accomplish a change, eg, a separation, to that actually used. 

Table 2. Lost-Work Analysis for a Fired Heater...

Fired Heater as a Heat-Exchangee System. Improved efficiency in fired heaters has tended to focus on heat lost with the stack gases. When stack temperatures exceed 150°C, such attention is proper, but other losses can be much bigger when viewed from a lost-work perspective. For example, a reformer lost-work analysis by Monsanto gave the breakdown shown in Table 2. 

Although the electrolytic process industries are confronted with a wide range of ha2ards, their safety record has been excellent. The U.S. Bureau of Labor has reported lost work days (injuries and illnesses) per 100 hill-time workers for the year 1990 (140). 

The second law can also suggest appropriate corrective action. Eor example, in combustion, preheating the air or firing at high pressure in a gas turbine, as is done for an ethylene (qv) cracking furnace, improves energy efficiency by reducing the lost work of combustion (Eig. 4). 

Many processes consist of a number of steps, and lost-work calculations are then made for each step separately. Writing Eq. (4-372) for each step of the process and summing gives... 

Thus, an analysis of the lost work, made by calculation of the fraction that each individual lost-work term represents of the total lost work, is the same as an analysis of the rate of entropy generation, made by expressing each individual entropy-generation term as a fraclion of the sum of all entropy-generation terms. 

An alternative to the lost-work or entropy-generation analysis is a work analysis. This is based on Eq. (4-366), written... 

The lost work due to irreversibility within the control volume CV is = [(Wcv)rev]x [(W )cvJx... 

If the heat transferred from the control volume is not used externally to create work, but is simply lost to the atmosphere in which further entropy is created, then Equj can be said to be equal to /quj, a lost work term, due to external irreversibility. Another form of Eq. (2.23) is thus... 

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. 

Young and Wilcock [7] have recently provided an alternative to this simple approach. They also follow step (a), but rather than obtaining as in (b) they determine the constituent entropy increa.ses (due to the various irreversible thermal and mixing effects). Essentially, they determine the downstream state from the properties To and the entropy. v, rather than T), and po- This approach is particularly convenient if the rational efficiency of the plant is sought. The lost work or the irreversibility ( f = "lay be subtracted... 

The calculation of indirect COI can be based on different methodologies, and there is no generally accepted standard for all circumstances. The most common approach to calculate the indirect costs of illness is the human capital method. The loss of welfare of a society in the form of nongenerated commodities and services mainly depends on the lost working hours. The method assumes that if a person had... 

AR is the most common atopic disease in the United States. It affects between 9% and 24% of adults and up to 42% of children.2,3 More than 80 million Americans experience 7 or more days of nasal-ocular symptoms annually as a result of AR.3 Additionally, AR is responsible for 3.5 million lost work days and 2 million missed school days annually in the United States.4 In addition to decreased quality of life from AR symptoms, patients also suffer from disrupted sleep, resulting in fatigue, irritability, memory deficits, excessive daytime somnolence, and depression that further reduce quality of life.5... 

Lost Work Associated with Two-Stage CTL Processes... 

Table 17.4 shows the actual work carried by the two stages when they operate at temperatures other than the Carnot temperature, as well as the work lost due to these operating temperatures. Usually the synthesis section is operated at high pressure (30 bar), which will also contribute to the lost work. In total, the lost work amounts to 112 kJ/mol. 

It is apparent from the above discussion that to reduce the lost work in a CTL process, one would require that AGstagel for the first stage is not too much larger than AGprocess, and one would also want to operate near the Carnot temperature of the processes. 

The thermodynamic variables as well as the lost work associated with this process are given in Table 17.5. 

It is clear from Table 17.5 that in terms of the gasification stage, both enthalpy and Gibbs energy values are significantly smaller than those of the conventional CTL route. The lost work associated with this first stage is also comparatively smaller. In terms of the synthesis section, we note that it operates close to its Carnot temperature (TCarnot = 480 K), and thus the lost work from this process is reduced significantly. Overall, the lost work amounts to 19 kJ/mol, as compared to the 112 kJ/mol for the conventional route. 

Lost Work Associated with the C02 Route CTL Process... 

FIGURE 17.6 Comparison of two CTL routes in terms of (a) carbon efficiency and (b) lost work. 

Figure 17.6 shows a comparison of the two CTL processes in terms of carbon efficiency and lost work. It is clear the newly developed process has the advantage of being more efficient, producing less carbon dioxide, and also less lost work. 

De Nevers, N., and Seader, J. D. 1980. Lost work A measure of thermodynamic efficiency. Energy 5 757-69. 

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