First and Second Law Efficiencies

Consider a flow process that involves several input and output streams. Each stream has an amount of energy and exergy associated with it. We define the first (//) and second law efficiencies as follows  

E stands for all forms of energy (thermal, mechanical, enthalpy, etc.), and the summation over i covers the usefiil output streams otdy, while the summation over m covers all the input streams. 

Typical first and second law efficiencies are presented in Table 5.2 (Kenney, p. 19). The drastically lower nf values, as compared to those for ti, demonstrate that energy degradation, i.e. the creation of anergy, occurs even in processes that are rather efficient from the first law point 

We demonstrate the calculation of first and second law efficiencies in the following two Examples, and close the Section with some comments on their evaluation. 

Calculate the first and second law efficiencies of a boiler that generates saturated steam at 15 bar, used for process heating. Assume that  

---

The first and second law efficiencies are actual heat stored... 

The work performed by the system lowers the temperature of the exhaust gases to -2200 K, where the gases can be effectively utilized by conventional steam-driven power generating plants. Thus, by use of an MHD topping cycle, both the first and second law efficiencies of conventional power plants can be improved. 

The error in energy analyses is that they attribute all the inefficiencies to losses, and then mis-calculate those. As was demonstrated for the coal-fired boiler, the first law efficiency (85%) was a poor approximation to the true efficience (33.8%). (Furthermore, perturbation studies show that the trends in first and second law efficiencies can move in opposite directions. For the coal-fired boiler problem, if the steam conditions were changed to 811°K/6.87 MPa (1000°F/1000 psia) and if the first law efficiency were decreased to 83%, the result would be an increase to 34.3% in second law efficiency.) The major inefficiencies were due to heat transfer (njj = 47.3%) and combustion (Hjj = 73.8%), with the stack losses accounting for only 5.5% of the available energy input with the coal. In contrast, an energy analysis shows the combustion process to be 100% efficient and... 

TABLE I. FIRST AND SECOND LAW EFFICIENCIES UTILIZING SYSTEMS. (Largely from... 

We proceed with a presentation of the quantitative criteria used to determine the degree of efficient energy utilization in a given process first and second law efficiencies, followed by a brief description of one of the methods used to obtain increased such efficiencies in the use of thermal energy. Cogeneration. We demonstrate the energy savings achieved and discuss the limitations involved and the ways around them. 

Calculate the first and second law efficiencies for the power plant of Example 3.12. Assume, as in Example 5.7, that the temperature of the flue gases in the boiler is 1800°C, with a first law efficiency of 90% in fuel heating value utilization. 

Notice that our definitions of first and second law efficiencies, Eqs 5.7.1 and 5.7.2 respectively, are pragmatic for they consider the useful output streams only. If we consider all exit streams, then ... 

We discuss next how improved first and second law efficiencies in the use of thermal energy can be realized through a very interesting approach, Cogeneration. 

How can the low second law efficiency of the boiler in Example 5.7 and the low first and second law efficiencies of the power plant of Example 5.8 be improved How, in other words, can we improve the utilization of the fuel heating value, thus effecting energy conservation ... 

---