Chapter 8 | 447Analysis We consider a general closed system (a fixed mass) that is free to
exchange heat and work with its surroundings (Fig. 8–35). The system under-
goes a process from state 1 to state 2. Taking the positive direction of heat
transfer to be tothe system and the positive direction of work transfer to be
fromthe system, the energy and entropy balances for this closed system can
be expressed as
Energy balance:
Entropy
balance:
Multiplying the second relation by T 0 and subtracting it from the first one gives
However, the heat transfer for the process 1-2 can be expressed as
and the right side of the above equation is, from Eq. 8–17, (X 2 X 1 )
P 0 (V 2 V 1 ). Thus,
Letting Tbdenote the boundary temperature and rearranging give
(8–43)which is equivalent to Eq. 8–41 for the exergy balance except that the inte-
gration is replaced by summation in that equation for convenience. This
completes the proof.
Discussion Note that the exergy balance relation above is obtained by
adding the energy and entropy balance relations, and thus it is not an inde-
pendent equation. However, it can be used in place of the entropy balance
relation as an alternative second law expression in exergy analysis.
21a 1 T 0
Tbb dQ 3 WP 01 V 2 V 124 T 0 SgenX 2 X 121dQT (^0)
2
1
a
dQ
T
b
boundary
WT 0 SgenX 2 X 1 P 01 V 2 V 12
Q
2
1
dQ
QT (^0)
2
1
a
dQ
T
b
boundary
WT 0 SgenE 2 E 1 T 01 S 2 S 12
SinSoutSgen¢Ssystem S (^)
2
1
a
dQ
T
b
boundary
SgenS 2 S 1
EinEout¢Esystem S QWE 2 E 1
EXAMPLE 8–10 Exergy Destruction during Heat Conduction
Consider steady heat transfer through a 5-m 6-m brick wall of a house of
thickness 30 cm. On a day when the temperature of the outdoors is 0°C, the
house is maintained at 27°C. The temperatures of the inner and outer sur-
faces of the brick wall are measured to be 20°C and 5°C, respectively, and
the rate of heat transfer through the wall is 1035 W. Determine the rate of
exergy destruction in the wall, and the rate of total exergy destruction associ-
ated with this heat transfer process.
Solution Steady heat transfer through a wall is considered. For specified
heat transfer rate, wall surface temperatures, and environment conditions,
the rate of exergy destruction within the wall and the rate of total exergy
destruction are to be determined.
Assumptions 1 The process is steady, and thus the rate of heat transfer
through the wall is constant. 2 The exergy change of the wall is zero during
Closed
system
Q
W
Tb
FIGURE 8–35
A general closed system considered in
Example 8–9.