Lost work Carnot efficiency

In this chapter, we show that it is not so much energy that is consumed but its quality, that is, the extent to which it is available for work. The quality of heat is the well-known thermal efficiency, the Carnot factor. If quality is lost, work has been consumed and lost. Lost work can be expressed in the products of flow rates and driving forces of a process. Its relation to entropy generation is established, which will allow us later to arrive at a universal relation between lost work and the driving forces in a process. 

This chapter establishes a direct relation between lost work and the fluxes and driving forces of a process. The Carnot cycle is revisited to investigate how the Carnot efficiency is affected by the irreversibilities in the process. We show to what extent the constraints of finite size and finite time reduce the efficiency of the process, but we also show that these constraints still allow a most favorable operation mode, the thermodynamic optimum, where the entropy generation and thus the lost work are at a minimum. Attention is given to the equipartitioning principle, which seems to be a universal characteristic of optimal operation in both animate and inanimate dynamic systems. 

Finally, we want to point out that the concept of the endoreversible engine is a simplification that leads to a quick and clear insight into the role and thermodynamic cost of transfer processes in reducing the Carnot efficiency into smaller and more realistic values. But for finding the real optimum conditions, the concept of endoreversibility has to be sacrificed. This will complicate the matter to some extent but will allow for including all contributions to the lost work ... 

Consider lkg/s of coal that is combusted with an adequate amount of air (approximately zero exergy contribution). The rate at which exergy flows into the system is therefore 23,583 kW. The combustion releases heat, namely, at a rate of 21,860 kW at a temperature T. Since we have created a heat source at temperature T, it is straightforward to compute the work potential (exergy) of this heat source. All we need to do is multiply the heat release rate (21,860 kW) by the Carnot factor 1 - (T0/T). This means that if the combustion takes place at temperature T = 1200 K for a fluidized bed reactor (Table 9.1), the efficiency of the combustion alone is combustion = (21,860/23,583) [1 - (T0/T)] = 0.93 [1 - (T0/T)] = 0.93 [1 - (298.15/1200)] = 0.7 This means that already 30% of the maximum work has been lost We summarize this simplified analysis in Figure 9.15. 

The heat is available at 1200 K, but there will be temperature differences in the heat exchanger, so more available work will be lost in the heat exchange process. What can we learn from this example If we examine the Carnot factor, the answer seems to be clear. If we increase the operating temperature of the combustor, we can increase the efficiency and lose less work in the process. For example, if we had chosen an operating temperature of 2000 K, as could be possible in the suspended bed, we would have obtained an efficiency of 0.79, which is quite considerable. However, any gain in efficiency could be offset by the increase in work necessary to pulverize the coal For the sake of simplicity, we have not included these in this analysis. From the point of view of efficiency of combustion,... 

We caution the reader that applying Carnot s analysis is based on the assumptions that the heat is available at temperature T and that the heat reservoir is infinite. This means that if we use the adiabatic flame temperature for T, we will end up with a maximum attainable efficiency, since the exchange of heat will inevitably lead to a reduction in the temperature of the reservoir. From our analysis, it is not clear whether we used an adiabatic flame temperature [11]. Note that the adiabatic temperature is the highest temperature that can be reached by the system if all the heat generated is used to elevate the flame temperature. However, we can safely state that at least 30% of the maximum work potential has been lost. We will return to this subtle point at a later stage, when we examine the combustion of natural gas. 

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