Thermodynamics

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.The exergy destruction associated with a cycle depends on the magnitudeof the heat transfer with the high- and low-temperature reservoirs involved,and their temperatures. It can be expressed on a unit mass basis asChapter 10 | 577q out q inx dest T 0 a a (10–20)T a b1kJ>kg2b,out T b,inFor a cycle that involves heat transfer only with a source at T H and a sink atT L , the exergy destruction becomesx dest T 0 a q outT LThe exergy of a fluid stream c at any state can be determined fromc 1h h 0 2 T 0 1s s 0 2 V 2 q inT Hb1kJ>kg22 gz1kJ>kg2where the subscript “0” denotes the state of the surroundings.(10–21)(10–22)EXAMPLE 10–7Second-Law Analysis of an Ideal Rankine CycleDetermine the exergy destruction associated with the Rankine cycle (all fourprocesses as well as the cycle) discussed in Example 10–1, assuming thatheat is transferred to the steam in a furnace at 1600 K and heat is rejectedto a cooling medium at 290 K and 100 kPa. Also, determine the exergy ofthe steam leaving the turbine.Solution The Rankine cycle analyzed in Example 10–1 is reconsidered. Forspecified source and sink temperatures, the exergy destruction associatedwith the cycle and exergy of the steam at turbine exit are to be determined.Analysis In Example 10–1, the heat input was determined to be 2728.6 kJ/kg,and the heat rejected to be 2018.6 kJ/kg.Processes 1-2 and 3-4 are isentropic (s 1 s 2 , s 3 s 4 ) and therefore donot involve any internal or external irreversibilities, that is,Processes 2-3 and 4-1 are constant-pressure heat-addition and heatrejectionprocesses, respectively, and they are internally reversible. But theheat transfer between the working fluid and the source or the sink takesplace through a finite temperature difference, rendering both processes irreversible.The irreversibility associated with each process is determined fromEq. 10–19. The entropy of the steam at each state is determined from thesteam tables:Thus,s 2 s 1 s f @ 75 kPa 1.2132 kJ>kg # Ks 4 s 3 6.7450 kJ>kg # K1at 3 MPa, 350°C2x dest,23 T 0 a s 3 s 2 q in,23T sourceb 1290 K2 c16.7450 1.21322 kJ>kg # K 2728.6 kJ>kg1600 K d 1110 kJ/kgx dest,12 0andx dest,34 0