Thermodynamics

Chapter 8 | 433That is, engine A is converting 60 percent of the available work potential touseful work. This ratio is only 43 percent for engine B.The second-law efficiency can also be expressed as the ratio of the usefulwork output and the maximum possible (reversible) work output:h II W uW rev1work-producing devices2(8–7)This definition is more general since it can be applied to processes (in turbines,piston–cylinder devices, etc.) as well as to cycles. Note that the secondlawefficiency cannot exceed 100 percent (Fig. 8–17).We can also define a second-law efficiency for work-consuming noncyclic(such as compressors) and cyclic (such as refrigerators) devices as the ratioof the minimum (reversible) work input to the useful work input:Source1000 Kη η th = 70%ΙΙ η rev = 70%Sink300 K100%(8–8)For cyclic devices such as refrigerators and heat pumps, it can also beexpressed in terms of the coefficients of performance ash II h II W revW u1work-consuming devices2COPCOP rev1refrigerators and heat pumps2(8–9)Again, because of the way we defined the second-law efficiency, its valuecannot exceed 100 percent. In the above relations, the reversible work W revshould be determined by using the same initial and final states as in theactual process.The definitions above for the second-law efficiency do not apply to devicesthat are not intended to produce or consume work. Therefore, we need a moregeneral definition. However, there is some disagreement on a general definitionof the second-law efficiency, and thus a person may encounter differentdefinitions for the same device. The second-law efficiency is intended to serveas a measure of approximation to reversible operation, and thus its valueshould range from zero in the worst case (complete destruction of exergy) toone in the best case (no destruction of exergy). With this in mind, we definethe second-law efficiency of a system during a process as (Fig. 8–18)Exergy recoveredh II Exergy supplied 1 Exergy destroyedExergy supplied(8–10)Therefore, when determining the second-law efficiency, the first thing weneed to do is determine how much exergy or work potential is consumedduring a process. In a reversible operation, we should be able to recoverentirely the exergy supplied during the process, and the irreversibility in thiscase should be zero. The second-law efficiency is zero when we recovernone of the exergy supplied to the system. Note that the exergy can be suppliedor recovered at various amounts in various forms such as heat, work,kinetic energy, potential energy, internal energy, and enthalpy. Sometimesthere are differing (though valid) opinions on what constitutes suppliedexergy, and this causes differing definitions for second-law efficiency. At alltimes, however, the exergy recovered and the exergy destroyed (the irreversibility)must add up to the exergy supplied. Also, we need to define thesystem precisely in order to identify correctly any interactions between thesystem and its surroundings.FIGURE 8–17Second-law efficiency of all reversibledevices is 100 percent.Hotwater80°CHeatAtmosphere25°CFIGURE 8–18The second-law efficiency of naturallyoccurring processes is zero if none ofthe work potential is recovered.