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

Dividing Eq. 8–48 by m

.

gives the exergy balance on a unit-mass basisas

Per-unit
mass: (8–49)

where q
Q

.

/m

.

and w
W

.

/m

.
are the heat transfer and work done per unit
mass of the working fluid, respectively.
For the case of an adiabaticsingle-stream device with no work interactions,
the exergy balance relation further simplifies to X

.

destroyed
m

.
(c 1 c 2 ), which
indicates that the specific exergy of the fluid must decrease as it flows through
a work-free adiabatic device or remain the same (c 2
c 1 ) in the limiting case
of a reversible process regardless of the changes in other properties of the fluid.

Reversible Work, Wrev

The exergy balance relations presented above can be used to determine the
reversible work Wrevby setting the exergy destroyed equal to zero. The work
Win that case becomes the reversible work. That is,

General: (8–50)

For example, the reversible power for a single-stream steady-flow device is,
from Eq. 8–48,

Single stream: (8–51)

which reduces for an adiabatic device to

Adiabatic, single stream: (8–52)

Note that the exergy destroyed is zero only for a reversible process, and
reversible work represents the maximum work output for work-producing
devices such as turbines and the minimum work input for work-consuming
devices such as compressors.

Second-Law Efficiency of Steady-Flow Devices, hII

The second-law efficiencyof various steady-flow devices can be determined
from its general definition,hII
(Exergy recovered)/(Exergy supplied). When
the changes in kinetic and potential energies are negligible, the second-law
efficiency of an adiabatic turbinecan be determined from

(8–53)

where sgen
s 2 s 1. For an adiabatic compressorwith negligible kinetic
and potential energies, the second-law efficiency becomes

(8–54)

where again sgen
s 2 s 1.
For an adiabatic heat exchanger with two unmixed fluid streams
(Fig. 8–44), the exergy supplied is the decrease in the exergy of the hot
stream, and the exergy recovered is the increase in the exergy of the

hII,comp

wrev,in

win

c 2 c 1

h 2 h 1

¬or¬hII,comp
1 

T 0 sgen

h 2 h 1

hII,turb

w

wrev

h 1 h 2

c 1 c 2

¬or¬hII,turb
1 

T 0 sgen

c 1 c 2

W

#

rev
m

#

1 c 1 c 22

W

#

rev
m

#

1 c 1 c 22 aa 1 

T 0

Tk

bQ

#

k¬¬^1 kW^2

W
Wrev¬¬when Xdestroyed
0

aa^1 

T 0

Tk

bqkw 1 c 1 c 22 xdestroyed
0 ¬¬ 1 kJ>kg 2

Chapter 8 | 459

T 0

Hot

stream

Cold

stream

12

4 3

FIGURE 8–44

A heat exchanger with two unmixed

fluid streams.