Thermodynamics

Dividing Eq. 8–48 by ṁ gives the exergy balance on a unit-mass basis asChapter 8 | 459Per-unitmass:a a 1 T 0T kb q k w 1c 1 c 2 2 x destroyed 01kJ>kg2(8–49)where q Q . /ṁ and w Ẇ/ṁ are the heat transfer and work done per unitmass of the working fluid, respectively.For the case of an adiabatic single-stream device with no work interactions,the exergy balance relation further simplifies to Ẋ destroyed ṁ(c 1 c 2 ), whichindicates that the specific exergy of the fluid must decrease as it flows througha work-free adiabatic device or remain the same (c 2 c 1 ) in the limiting caseof a reversible process regardless of the changes in other properties of the fluid.Reversible Work, W revThe exergy balance relations presented above can be used to determine thereversible work W rev by setting the exergy destroyed equal to zero. The workW in that case becomes the reversible work. That is,General: W W rev when X destroyed 0(8–50)For example, the reversible power for a single-stream steady-flow device is,from Eq. 8–48,Single stream: W # rev m # 1c 1 c 2 2 a a 1 T 0b Q # (8–51)Tk1kW2kwhich reduces for an adiabatic device toAdiabatic, single stream: W # rev m # 1c 1 c 2 2(8–52)Note that the exergy destroyed is zero only for a reversible process, andreversible work represents the maximum work output for work-producingdevices such as turbines and the minimum work input for work-consumingdevices such as compressors.Second-Law Efficiency of Steady-Flow Devices, h IIThe second-law efficiency of various steady-flow devices can be determinedfrom its general definition, h II (Exergy recovered)/(Exergy supplied). Whenthe changes in kinetic and potential energies are negligible, the second-lawefficiency of an adiabatic turbine can be determined fromh II,turb ww rev h 1 h 2c 1 c 2orh II,turb 1 (8–53)where s gen s 2 s 1 . For an adiabatic compressor with negligible kineticand potential energies, the second-law efficiency becomesh II,comp w rev,inw in c 2 c 1h 2 h 1orh II,comp 1 T 0 s genc 1 c 2T 0 s genh 2 h 1(8–54)where again s gen s 2 s 1 .For an adiabatic heat exchanger with two unmixed fluid streams(Fig. 8–44), the exergy supplied is the decrease in the exergy of the hotstream, and the exergy recovered is the increase in the exergy of theHotstreamT 01 243ColdstreamFIGURE 8–44A heat exchanger with two unmixedfluid streams.