Thermodynamics

Chapter 8 | 449determine (a) the exergy of the steam at the initial and the final states, (b) theexergy change of the steam, (c) the exergy destroyed, and (d) the second-lawefficiency for the process.Solution Steam in a piston–cylinder device expands to a specified state. Theexergies of steam at the initial and final states, the exergy change, the exergydestroyed, and the second-law efficiency for this process are to be determined.Assumptions The kinetic and potential energies are negligible.Analysis We take the steam contained within the piston–cylinder device asthe system (Fig. 8–37). This is a closed system since no mass crosses thesystem boundary during the process. We note that boundary work is done bythe system and heat is lost from the system during the process.(a) First we determine the properties of the steam at the initial and finalstates as well as the state of the surroundings:State 1:State 2:Dead state:u 1 2793.7 kJ>kgP 1 1 MPaT 1 300°C f v 1 0.25799 m 3 >kg 1Table A–62s 1 7.1246 kJ>kg # KuP 2 200 kPa 2 2577.1 kJ>kgT 2 150°Cf v 2 0.95986 m 3 >kg1Table A–62s 2 7.2810 kJ>kg # KP 0 100 kPaT 0 25°Cf u 0 u f @ 25°C 104.83 kJ>kgv 0 v f @ 25°C 0.00103 m 3 >kgs 0 s f @ 25°C 0.3672 kJ>kg # K1Table A–42P 1 = 1 MPT 1 = 300°CP 0 = 100 kPaT 0 = 25°C2 kJSteamP 2 = 200 kPaT 2 = 150°CState 1 State 2FIGURE 8–37Schematic for Example 8–11.The exergies of the system at the initial state X 1 and the final state X 2 aredetermined from Eq. 8–15 to beandX 1 m3 1u 1 u 0 2 T 0 1s 1 s 0 2 P 0 1v 1 v 0 24 10.05 kg2512793.7 104.832 kJ>kg 1298 K2317.1246 0.36722 kJ>kg # K4 1100 kPa2310.25799 0.001032 m 3 >kg461kJ>kPa # m 3 2 35.0 kJX 2 m3 1u 2 u 0 2 T 0 1s 2 s 0 2 P 0 1v 2 v 0 24 10.05 kg2512577.1 104.832 kJ>kg 1298 K2317.2810 0.36722 kJ>kg # K4 1100 kPa2310.95986 0.001032 m 3 >kg461kJ>kPa # m 3 2 25.4 kJThat is, steam initially has an exergy content of 35 kJ, which drops to 25.4kJ at the end of the process. In other words, if the steam were allowed toundergo a reversible process from the initial state to the state of the environment,it would produce 35 kJ of useful work.(b) The exergy change for a process is simply the difference between theexergy at the initial and final states of the process,¢X X 2 X 1 25.4 35.0 9.6 kJ