Thermodynamics

442 | ThermodynamicsHeattransferEntropytransferExergytransferMEDIUM 1 MEDIUM 2WallT 1T 2QQT 1QEntropygeneratedQT 2Exergydestroyed1 – T 0 Q1 –( T 0 QT 1( T 2(FIGURE 8–27The transfer and destruction of exergyduring a heat transfer process througha finite temperature difference.P 0P 0WeightlesspistonHeatFIGURE 8–28There is no useful work transferassociated with boundary work whenthe pressure of the system ismaintained constant at atmosphericpressure.(Note that heat transfer through a finite temperature difference is irreversible,and some entropy is generated as a result. The entropy generation is alwaysaccompanied by exergy destruction, as illustrated in Fig. 8–27. Also notethat heat transfer Q at a location at temperature T is always accompanied byentropy transfer in the amount of Q/T and exergy transfer in the amount of(1 T 0 /T)Q.Exergy Transfer by Work, WExergy is the useful work potential, and the exergy transfer by work cansimply be expressed asExergy transfer by work: X work e W W surr 1for boundary work2(8–26)W 1for other forms of work2where W surr P 0 (V 2 V 1 ), P 0 is atmospheric pressure, and V 1 and V 2 are theinitial and final volumes of the system. Therefore, the exergy transfer withwork such as shaft work and electrical work is equal to the work W itself. Inthe case of a system that involves boundary work, such as a piston–cylinderdevice, the work done to push the atmospheric air out of the way duringexpansion cannot be transferred, and thus it must be subtracted. Also, duringa compression process, part of the work is done by the atmospheric air, andthus we need to supply less useful work from an external source.To clarify this point further, consider a vertical cylinder fitted with aweightless and frictionless piston (Fig. 8–28). The cylinder is filled with agas that is maintained at the atmospheric pressure P 0 at all times. Heat isnow transferred to the system and the gas in the cylinder expands. As aresult, the piston rises and boundary work is done. However, this work cannotbe used for any useful purpose since it is just enough to push the atmosphericair aside. (If we connect the piston to an external load to extractsome useful work, the pressure in the cylinder will have to rise above P 0 tobeat the resistance offered by the load.) When the gas is cooled, the pistonmoves down, compressing the gas. Again, no work is needed from an externalsource to accomplish this compression process. Thus we conclude thatthe work done by or against the atmosphere is not available for any usefulpurpose, and should be excluded from available work.Exergy Transfer by Mass, mMass contains exergy as well as energy and entropy, and the exergy, energy,and entropy contents of a system are proportional to mass. Also, the rates ofexergy, entropy, and energy transport into or out of a system are proportionalto the mass flow rate. Mass flow is a mechanism to transport exergy, entropy,and energy into or out of a system. When mass in the amount of m entersor leaves a system, exergy in the amount of mc, where c (h h 0 ) T 0 (s s 0 ) V 2 /2 gz, accompanies it. That is,Exergy transfer by mass: X mass mc(8–27)Therefore, the exergy of a system increases by mc when mass in theamount of m enters, and decreases by the same amount when the sameamount of mass at the same state leaves the system (Fig. 8–29).