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

448 | Thermodynamics

this process since the state and thus the exergy of the wall do not change

anywhere in the wall. 3 Heat transfer through the wall is one-dimensional.

Analysis We first take the wallas the system (Fig. 8–36). This is a closed

systemsince no mass crosses the system boundary during the process. We

note that heat and exergy are entering from one side of the wall and leaving

from the other side.

Applying the rate form of the exergy balance to the wall gives

Rate of net exergy transfer Rate of exergy Rate of change

by heat, work, and mass destruction in exergy

Solving, the rate of exergy destruction in the wall is determined to be

Note that exergy transfer with heat at any location is (1 T 0 /T)Qat that

location, and the direction of exergy transfer is the same as the direction of

heat transfer.

To determine the rate of total exergy destruction during this heat trans-

fer process, we extend the system to include the regions on both sides of

the wall that experience a temperature change. Then one side of the sys-

tem boundary becomes room temperature while the other side, the tem-

perature of the outdoors. The exergy balance for this extended system

(system + immediate surroundings) is the same as that given above,

except the two boundary temperatures are 300 and 273 K instead of 293

and 278 K, respectively. Then the rate of total exergy destruction becomes

The difference between the two exergy destructions is 41.2 W and repre-

sents the exergy destroyed in the air layers on both sides of the wall. The

exergy destruction in this case is entirely due to irreversible heat transfer

through a finite temperature difference.

Discussion This problem was solved in Chap. 7 for entropy generation. We

could have determined the exergy destroyed by simply multiplying the

entropy generations by the environment temperature of T 0 
273 K.

X

#

destroyed,total
^1 1035 W2a^1 

273 K

300 K

b 1 1035 W2a 1 

273 K

273 K

b
93.2 W

X

#

destroyed
52.0 W

1 1035 W2a 1 

273 K

293 K

b 1 1035 W2a 1 

273 K

278 K

bX

#

destroyed
^0

Q

#

a 1 

T 0

T

b

in

Q

#

a 1 

T 0

T

b

out

X

#

destroyed
^0

X

#

inX

#

out¬ ^ X

#

destroyed^ 
dXsystem>dt^ 
^0

EXAMPLE 8–11 Exergy Destruction during Expansion of Steam

A piston–cylinder device contains 0.05 kg of steam at 1 MPa and 300°C.

Steam now expands to a final state of 200 kPa and 150°C, doing work. Heat

losses from the system to the surroundings are estimated to be 2 kJ during this

process. Assuming the surroundings to be at T 0 
25°C and P 0 
100 kPa,

·

Brick
wall
27 °C0°C

Q

30 cm

20 °C 5 °C

FIGURE 8–36

Schematic for Example 8–10.

⎭⎪⎬⎪⎫ ⎭⎪⎬⎪⎫ ⎭⎪⎪⎪⎪⎬⎪⎪⎪⎪⎫

0 (steady)

¡