Thermodynamics

orChapter 8 | 445X inXSystemoutX in X out X destroyed ¢X system (8–35) Mass ∆X MasssystemHeatHeatThis relation is referred to as the exergy balance and can be stated as theexergy change of a system during a process is equal to the differencebetween the net exergy transfer through the system boundary and the exergydestroyed within the system boundaries as a result of irreversibilities.We mentioned earlier that exergy can be transferred to or from a systemby heat, work, and mass transfer. Then the exergy balance for any systemundergoing any process can be expressed more explicitly asGeneral: X in X out X destroyed ¢X system 1kJ2(8–36)WorkX destroyedFIGURE 8–32Mechanisms of exergy transfer.Workor, in the rate form, as⎫ ⎪⎬⎪⎭⎫⎪⎬⎪⎭⎫⎪⎬⎪⎭⎫ ⎪⎬⎪⎭⎫⎪⎬⎪⎭⎫⎪⎬⎪⎭Net exergy transfer Exergy Changeby heat, work, and mass destruction in exergyGeneral, rate form: X # in X # out X # destroyed dX system >dt 1kW2 (8–37)Rate of net exergy transfer Rate of exergy Rate of changeby heat, work, and mass destruction in exergywhere the rates of exergy transfer by heat, work, and mass are expressedas X . heat (1 T 0 /T )Q. , X . work Ẇ useful , and X. mass ṁc, respectively. Theexergy balance can also be expressed per unit mass asGeneral, unit-mass basis: 1x in x out 2 x destroyed ¢x system 1kJ>kg2 (8–38)where all the quantities are expressed per unit mass of the system. Note thatfor a reversible process, the exergy destruction term X destroyed drops out fromall of the relations above. Also, it is usually more convenient to find theentropy generation S gen first, and then to evaluate the exergy destroyeddirectly from Eq. 8–33. That is,(8–39)When the environment conditions P 0 and T 0 and the end states of the systemare specified, the exergy change of the system X system X 2 X 1 can bedetermined directly from Eq. 8–17 regardless of how the process is executed.However, the determination of the exergy transfers by heat, work, andmass requires a knowledge of these interactions.A closed system does not involve any mass flow and thus any exergytransfer associated with mass flow. Taking the positive direction of heattransfer to be to the system and the positive direction of work transfer to befrom the system, the exergy balance for a closed system can be expressedmore explicitly as (Fig. 8–33)Closed system: X heat X work X destroyed ¢X system(8–40)orX destroyed T 0 S gen orX # destroyed T 0 S # genClosed system: a a1 T 0b Q (8–41)T k 3W P 0 1V 2 V 1 24 T 0 S gen X 2 X 1kWX work∆X systemX destroyedX heatQX heat – X work – X destroyed = ∆X systemFIGURE 8–33Exergy balance for a closed systemwhen the direction of heat transfer istaken to be to the system and thedirection of work from the system.