Thermodynamics

462 | Thermodynamics(c) The second-law efficiency of a turbine is the ratio of the actual workdelivered to the reversible work,That is, 7.7 percent of the work potential is wasted during this process.(d) The difference between the reversible work and the actual useful work isthe exergy destroyed, which is determined to beX # destroyed W # rev,out W # out 4665 4306 359 kWThat is, the potential to produce useful work is wasted at a rate of 359 kWduring this process. The exergy destroyed could also be determined by firstcalculating the rate of entropy generation S . gen during the process.(e) The exergy (maximum work potential) of the steam at the inlet conditionsis simply the stream exergy, and is determined fromc 1 1h 1 h 0 2 T 0 1s 1 s 0 2 V 2 1 →0 gz 1→02 1h 1 h 0 2 T 0 1s 1 s 0 2 13344.9 104.832kJ>kg 1298 K217.0856 0.36722 kJ>kg # K 1238 kJ/kgW# outh II W # 4306 kW 0.923 or 92.3%rev,out4665 kWThat is, not counting the kinetic and potential energies, every kilogram ofthe steam entering the turbine has a work potential of 1238 kJ. This correspondsto a power potential of (8 kg/s)(1238 kJ/kg) 9904 kW. Obviously,the turbine is converting 4306/9904 43.5 percent of the available workpotential of the steam to work.EXAMPLE 8–16Exergy Destroyedduring Mixing of Fluid Streams150°F Mixingchamber240°F 20 psia2180 Btu/min3130°FT 0 = 70°FFIGURE 8–46Schematic for Example 8–16.Water at 20 psia and 50°F enters a mixing chamber at a rate of300 lbm/min, where it is mixed steadily with steam entering at 20 psiaand 240°F. The mixture leaves the chamber at 20 psia and 130°F, andheat is being lost to the surrounding air at T 0 70°F at a rate of180 Btu/min (Fig. 8–46). Neglecting the changes in kinetic and potentialenergies, determine the reversible power and the rate of exergy destructionfor this process.Solution Liquid water and steam are mixed in a chamber that is losingheat at a specified rate. The reversible power and the rate of exergy destructionare to be determined.Analysis This is a steady-flow process, which was discussed in Example7–20 with regard to entropy generation. The mass flow rate of the steam wasdetermined in Example 7–20 to be ṁ 2 22.7 lbm/min.