Lost work entropy generation

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... 

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. 

The quality of heat is defined as its maximum potential to perform work with respect to a defined environment. Usually, this is the environment within which the process takes place. The Carnot factor quantitatively expresses which fraction of heat is at most available for work. Heat in free fall from a higher to a lower temperature incurs a loss in this quality. The quality has vanished at T0, the temperature of the prevailing environment. Lost work can be identified with entropy generation in a simple relation. This relation appears to have a universal value. 

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. 

The expansion has been assumed to be adiabatic, and thus the entropy generated equals the entropy increase of the gas, AS, as the entropy change of the environment, AS0, can be set to zero because the process is adiabatic. The amount of lost work can now be calculated from the entropy values Sj and S2 of 1 mol of methane at the initial and final conditions, respectively. However, this requires knowledge not only of the final pressure P2, which is known, but also of the final temperature T2, which is unknown. Here, the first law helps us out. Applying Equation 2.39 and substituting zero for Win and Qout, we find AH = 0 or H2 = Hv From the IUPAC data series number 16, dealing with methane [1], we find that the molar enthalpy and entropy at initial conditions are, respectively,... 

A work aiialysis here expresses each of the individual work terms on the right as a fraction of tV,. A work analysis cannot be carried out in the case where a process is so inefficient that vVideal is positive, indicating ihat the process should produce work, but Ws is negative, indicating that the process in fact requires work. A lost-work or entropy-generation analysis is always possible. 

The rate of entropy generation in each of the four units of the power plant calculated by Eq. (16.1), and the lost work is then given by Eq. (16.15). 

The rate of entropy generation and the lost work for each of the individual ] of the process are calculated by Eqs. (16.1) and (16.15). Since the flow rate of methane is not given, we take 1 kg of methane entering as a basis. The rates S, W m, and Q are therefore expressed not per unit of time but per kg of entering meth The heat transfer for the compression/cooling step is calculated by an enc balance ... 

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