Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

where Qkis the heat transfer through the boundary at temperature Tkat loca-

tion k.Dividing the previous equation by the time interval 
tand taking the

limit as 
t→0 gives the rate formof the exergy balance for a closed system,

Rate form: (8–42)

Note that the relations above for a closed system are developed by taking

the heat transfer to a system and work done by the system to be positive

quantities. Therefore, heat transfer from the system and work done on the

system should be taken to be negative quantities when using those relations.

The exergy balance relations presented above can be used to determine

the reversible work Wrevby setting the exergy destruction term equal to zero.

The work Win that case becomes the reversible work. That is,WWrev

when XdestroyedT 0 Sgen0.

Note that Xdestroyedrepresents the exergy destroyed within the system bound-

aryonly, and not the exergy destruction that may occur outside the system

boundary during the process as a result of external irreversibilities. Therefore,

a process for which Xdestroyed0 is internally reversiblebut not necessarily

totallyreversible. The totalexergy destroyed during a process can be deter-

mined by applying the exergy balance to an extended systemthat includes the

system itself and its immediate surroundings where external irreversibilities

might be occurring (Fig. 8–34). Also, the exergy change in this case is equal

to the sum of the exergy changes of the system and the exergy changeof the

immediate surroundings. Note that under steady conditions, the state and thus

the exergy of the immediate surroundings (the “buffer zone”) at any point

does not change during the process, and thus the exergy change of the imme-

diate surroundings is zero. When evaluating the exergy transfer between an

extended system and the environment, the boundary temperature of the

extended system is simply taken to be the environment temperature T 0.

For a reversible process, the entropy generation and thus the exergy

destructionare zero,and the exergy balance relation in this case becomes

analogous to the energy balance relation. That is, the exergy change of the

system becomes equal to the exergy transfer.

Note that the energy changeof a system equals the energy transferfor

anyprocess, but the exergy changeof a system equals the exergy transfer

only for a reversibleprocess. The quantityof energy is always preserved

during an actual process (the first law), but the qualityis bound to decrease

(the second law). This decrease in quality is always accompanied by an

increase in entropy and a decrease in exergy. When 10 kJ of heat is trans-

ferred from a hot medium to a cold one, for example, we still have 10 kJ of

energy at the end of the process, but at a lower temperature, and thus at a

lower quality and at a lower potential to do work.

aa^1 

T 0

Tk

bQ

#

kaW

#

P 0

dVsystem

dt

bT 0 S

#

gen

dXsystem

dt

446 | Thermodynamics

ImmediateImmediate

surroundingssurroundings

SYSTEMSYSTEM

Q

T 0

OuterOuter

surroundingssurroundings

(environment)(environment)

T 0

FIGURE 8–34

Exergy destroyed outside system
boundaries can be accounted for by
writing an exergy balance on the
extended system that includes the
system and its immediate
surroundings.

EXAMPLE 8–9 General Exergy Balance for Closed Systems

Starting with energy and entropy balances, derive the general exergy balance

relation for a closed system (Eq. 8–41).

Solution Starting with energy and entropy balance relations, a general rela-

tion for exergy balance for a closed system is to be obtained.