Thermodynamics

528 | Thermodynamicsexternal to the system. A second-law analysis of these cycles reveals wherethe largest irreversibilities occur and where to start improvements.Relations for exergy and exergy destruction for both closed and steadyflowsystems are developed in Chap. 8. The exergy destruction for a closedsystem can be expressed asX dest T 0 S gen T 0 1¢S sys S in S out 2(9–30)where T b,in and T b,out are the temperatures of the system boundary whereheat is transferred into and out of the system, respectively. A similar relationfor steady-flow systems can be expressed, in rate form, asor, on a unit–mass basis for a one-inlet, one-exit steady-flow device, as(9–31)(9–32)where subscripts i and e denote the inlet and exit states, respectively.The exergy destruction of a cycle is the sum of the exergy destructions ofthe processes that compose that cycle. The exergy destruction of a cycle canalso be determined without tracing the individual processes by consideringthe entire cycle as a single process and using one of the relations above.Entropy is a property, and its value depends on the state only. For a cycle,reversible or actual, the initial and the final states are identical; thus s e s i .Therefore, the exergy destruction of a cycle depends on the magnitude ofthe heat transfer with the high- and low-temperature reservoirs involved andon their temperatures. It can be expressed on a unit–mass basis as(9–33)For a cycle that involves heat transfer only with a source at T H and a sink atT L , the exergy destruction becomes(9–34)The exergies of a closed system f and a fluid stream c at any state can bedetermined fromand T 0 c1S 2 S 1 2 sys Q inT b,in Q outT b,outd1kJ2X # dest T 0 S # gen T 0 1S # out S # in2 T 0 a aoutm # s ainm # s Q# inT b,in Q# outT b,outb1kW2X dest T 0 s gen T 0 a s e s i q inT b,in q outT b,outb1kJ>kg2x dest T 0 a aq outT b,out aq inT b,inb1kJ>kg2x dest T 0 a q outT Lf 1u u 0 2 T 0 1s s 0 2 P 0 1v v 0 2 V 2c 1h h 0 2 T 0 1s s 0 2 V 2 q inT Hb1kJ>kg22 gz1kJ>kg2where subscript “0” denotes the state of the surroundings.2 gz1kJ>kg2(9–35)(9–36)