Thermodynamics

Chapter 8 | 451(d) Noting that the decrease in the exergy of the steam is the exergy suppliedand the useful work output is the exergy recovered, the second-law efficiencyfor this process can be determined fromh II Exergy recoveredExergy supplied W uX 1 X 25.3 0.552 or 55.2%35.0 25.4That is, 44.8 percent of the work potential of the steam is wasted duringthis process.EXAMPLE 8–12Exergy Destroyed during Stirring of a GasAn insulated rigid tank contains 2 lbm of air at 20 psia and 70°F. A paddlewheel inside the tank is now rotated by an external power source until thetemperature in the tank rises to 130°F (Fig. 8–38). If the surrounding air isat T 0 70°F, determine (a) the exergy destroyed and (b) the reversible workfor this process.Solution The air in an adiabatic rigid tank is heated by stirring it by a paddlewheel. The exergy destroyed and the reversible work for this process are tobe determined.Assumptions 1 Air at about atmospheric conditions can be treated as anideal gas with constant specific heats at room temperature. 2 The kineticand potential energies are negligible. 3 The volume of a rigid tank is constant,and thus there is no boundary work. 4 The tank is well insulated andthus there is no heat transfer.Analysis We take the air contained within the tank as the system. This is aclosed system since no mass crosses the system boundary during theprocess. We note that shaft work is done on the system.(a) The exergy destroyed during a process can be determined from an exergybalance, or directly from X destroyed T 0 S gen . We will use the second approachsince it is usually easier. But first we determine the entropy generated froman entropy balance,T 0 = 70°FAIRm = 2 lbmP 1 = 20 psiaT 1 = 70°FW pwFIGURE 8–38Schematic for Example 8–12.S in S out S gen ¢S system⎫ ⎪⎬⎪⎭⎫⎬⎭⎫⎪⎬⎪⎭Net entropy transfer Entropy Changeby heat and mass generation in entropy0 S gen ¢S system m ° c v ln T 2 R ln V 2→0¢T 1 V 1Taking c vbecomesS gen mc v ln T 2T 1 0.172 Btu/lbm · °F and substituting, the exergy destroyedX destroyed T 0 S gen T 0 mc v ln T 2T 1 1530 R212 lbm210.172 Btu>lbm # °F2ln590 R530 R 19.6 Btu