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

proportional to the amount of mass (Fig. 8–42). Again taking the positive

direction of heat transfer to be to the system and the positive direction of work

transfer to be from the system, the general exergy balance relations (Eqs. 8–36

and 8–37) can be expressed for a control volume more explicitly as

(8–44)

or

(8–45)

It can also be expressed in the rate formas

(8–46)

The exergy balance relation above can be stated as the rate of exergy change

within the control volume during a process is equal to the rate of net exergy

transfer through the control volume boundary by heat, work, and mass flow

minus the rate of exergy destruction within the boundaries of the control

volume.

When the initial and final states of the control volume are specified, the

exergy change of the control volume is X 2 
X 1 m 2 f 2 
m 1 f 1.

Exergy Balance for Steady-Flow Systems

Most control volumes encountered in practice such as turbines, compres-

sors, nozzles, diffusers, heat exchangers, pipes, and ducts operate steadily,

and thus they experience no changes in their mass, energy, entropy, and

exergy contents as well as their volumes. Therefore,dVCV/dt 0 and

dXCV/dt0 for such systems, and the amount of exergy entering a steady-

flow system in all forms (heat, work, mass transfer) must be equal to the

amount of exergy leaving plus the exergy destroyed. Then the rate form of

the general exergy balance (Eq. 8–46) reduces for a steady-flow processto

(Fig. 8–43)

Steady-flow: (8–47)

For a single-stream(one-inlet, one-exit) steady-flow device, the relation

above further reduces to

Single-stream: (8–48)

where the subscripts 1 and 2 represent inlet and exit states,m

.

is the mass

flow rate, and the change in the flow exergy is given by Eq. 8–23 as

c 1 
c 2  1 h 1 
h 22 
T 01 s 1 
s 22 

V 12 
V 22

2

g 1 z 1 
z 22

aa^1 

T 0

Tk

bQ

#

k
W

#

m

#

1 c 1 
c 22 
X

#

destroyed^0

aa^1 

T 0

Tk

bQ

#

k
W

#

a

in

m#c
a

out

m#c
X

#

destroyed^0

aa^1 

T 0

Tk

bQ

#

k
aW

#


P 0

dVCV

dt

ba

in

m#c
a

out

m#c
X

#

destroyed

dXCV

dt

aa^1 

T 0

Tk

bQk
 3 W
P 01 V 2 
V 124 a

in

mc
a

out

mc
Xdestroyed 1 X 2 
X 12 CV

Xheat
XworkXmass,in
Xmass,out
Xdestroyed 1 X 2 
X 12 CV

458 | Thermodynamics

Steady flow

system

Xdestroyed

Xin Xout

Heat

Work

Mass

Heat

Work

Mass

· ·

·

FIGURE 8–43

The exergy transfer to a steady-flow

system is equal to the exergy transfer

from it plus the exergy destruction

within the system.

SurroundingsSurroundings

Q

ControlControl

volumevolume

XCVCV

T

mi

ci

me

ce

W

Xworkwork

Xheatheat

FIGURE 8–42

Exergy is transferred into or out of a

control volume by mass as well as

heat and work transfer.

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