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

Exergy flow associated with a fluid stream when the fluid properties are
variable can be determined by integration from

(8–28)

where Acis the cross-sectional area of the flow and Vnis the local velocity
normal to dAc.
Note that exergy transfer by heat Xheatis zero for adiabatic systems, and the
exergy transfer by mass Xmassis zero for systems that involve no mass flow
across their boundaries (i.e., closed systems). The total exergy transfer is
zero for isolated systems since they involve no heat, work, or mass transfer.

8–6 ■ THE DECREASE OF EXERGY PRINCIPLE

AND EXERGY DESTRUCTION

In Chap. 2 we presented the conservation of energy principleand indicated
that energy cannot be created or destroyed during a process. In Chap. 7 we
established the increase of entropy principle,which can be regarded as one
of the statements of the second law, and indicated that entropy can be cre-
ated but cannot be destroyed. That is, entropy generation Sgenmust be posi-
tive (actual processes) or zero (reversible processes), but it cannot be
negative. Now we are about to establish an alternative statement of the sec-
ond law of thermodynamics, called the decrease of exergy principle,which
is the counterpart of the increase of entropy principle.
Consider an isolated systemshown in Fig. 8–30. By definition, no heat,
work, or mass can cross the boundaries of an isolated system, and thus there
is no energy and entropy transfer. Then the energyand entropybalances for
an isolated system can be expressed as

Energy balance:

Entropy balance:

Multiplying the second relation by T 0 and subtracting it from the first one
gives

(8–29)

From Eq. 8–17 we have

(8–30)

since V 2
V 1 for an isolated system (it cannot involve any moving bound-
ary and thus any boundary work). Combining Eqs. 8–29 and 8–30 gives

(8–31)

since T 0 is the thermodynamic temperature of the environment and thus a
positive quantity,Sgen0, and thus T 0 Sgen0. Then we conclude that

¢Xisolated
 1 X 2 X 12 isolated 0 (8–32)

T 0 Sgen
X 2 X 1  0

 1 E 2 E 12 T 01 S 2 S 12

X 2 X 1 
 1 E 2 E 12 P 01 V 2 V 12

Q^0

T 01 S 2 S 12

T 0 Sgen
E 2 E 1 T 01 S 2 S 12

SinQ

0

SoutQ

0

Sgen
¢SsystemSSgen
S 2 S 1

EinQ

0

EoutQ

0


¢EsystemS 0 
E 2 E 1

X

#

mass



Ac

crVn dAc¬and¬Xmass

 c dm



¢t

X

#

mass^ dt

Chapter 8 | 443

·

·

·

·

Control volume

h

s

ψ ψ

m

mh

ms

m

FIGURE 8–29

Mass contains energy, entropy, and

exergy, and thus mass flow into or out

of a system is accompanied by energy,

entropy, and exergy transfer.

No heat, work

or mass transfer

Isolated system

∆X (^) isolated ≤ 0
(or X (^) destroyed ≥ 0)
FIGURE 8–30
The isolated system considered in the
development of the decrease of exergy
principle.
SEE TUTORIAL CH. 8, SEC. 6 ON THE DVD.
INTERACTIVE
TUTORIAL