Thermodynamics

446 | ThermodynamicsOutersurroundingsT 0(environment)T 0ImmediatesurroundingsSYSTEMFIGURE 8–34Exergy destroyed outside systemboundaries can be accounted for bywriting an exergy balance on theextended system that includes thesystem and its immediatesurroundings.Qwhere Q k is the heat transfer through the boundary at temperature T k at locationk. Dividing the previous equation by the time interval t and taking thelimit as t → 0 gives the rate form of the exergy balance for a closed system,Rate form: a a 1 T 0b Q # k a W # P dV system(8–42)T 0 b Tk dt0 S # gen dX systemdtNote that the relations above for a closed system are developed by takingthe heat transfer to a system and work done by the system to be positivequantities. Therefore, heat transfer from the system and work done on thesystem should be taken to be negative quantities when using those relations.The exergy balance relations presented above can be used to determinethe reversible work W rev by setting the exergy destruction term equal to zero.The work W in that case becomes the reversible work. That is, W W revwhen X destroyed T 0 S gen 0.Note that X destroyed represents the exergy destroyed within the system boundaryonly, and not the exergy destruction that may occur outside the systemboundary during the process as a result of external irreversibilities. Therefore,a process for which X destroyed 0 is internally reversible but not necessarilytotally reversible. The total exergy destroyed during a process can be determinedby applying the exergy balance to an extended system that includes thesystem itself and its immediate surroundings where external irreversibilitiesmight be occurring (Fig. 8–34). Also, the exergy change in this case is equalto the sum of the exergy changes of the system and the exergy change of theimmediate surroundings. Note that under steady conditions, the state and thusthe exergy of the immediate surroundings (the “buffer zone”) at any pointdoes not change during the process, and thus the exergy change of the immediatesurroundings is zero. When evaluating the exergy transfer between anextended system and the environment, the boundary temperature of theextended system is simply taken to be the environment temperature T 0 .For a reversible process, the entropy generation and thus the exergydestruction are zero, and the exergy balance relation in this case becomesanalogous to the energy balance relation. That is, the exergy change of thesystem becomes equal to the exergy transfer.Note that the energy change of a system equals the energy transfer forany process, but the exergy change of a system equals the exergy transferonly for a reversible process. The quantity of energy is always preservedduring an actual process (the first law), but the quality is bound to decrease(the second law). This decrease in quality is always accompanied by anincrease in entropy and a decrease in exergy. When 10 kJ of heat is transferredfrom a hot medium to a cold one, for example, we still have 10 kJ ofenergy at the end of the process, but at a lower temperature, and thus at alower quality and at a lower potential to do work.EXAMPLE 8–9General Exergy Balance for Closed SystemsStarting with energy and entropy balances, derive the general exergy balancerelation for a closed system (Eq. 8–41).Solution Starting with energy and entropy balance relations, a general relationfor exergy balance for a closed system is to be obtained.