Modern Engineering Thermodynamics

216 CHAPTER 7: Second Law of Thermodynamics and Entropy Transport and Production Mechanisms
EXAMPLE 7.2 (Continued )
and thus the actual thermal efficiency is
b. From Eq. (7.16), we have
η T =
5:00 MW − j− 0:100 MWj
12:9MW
=
12:9MW− 8:00 MW
12:9MW
= 0:380 = 38:0%
ðη T Þ max
= ðη T Þ Carnot
= 1 − T L
T H
= 0:380
so that
T H =
T L ð10:0 + 273:15Þ K
=
1 − 0:380 0:620
= 457 K = 184°C
The calculations of part a are perfectly valid for this power plant since they deal with actual input and output energy values.
The answer to part b, however, is unrealistically lower than the actual coal flame temperature in the boiler due to the many
irreversibilities that exist within a real power plant.
Exercises
3. If the combustion temperature of the power plant discussed in Example 7.2 were 2000.°C, determine the maximum
(reversible or Carnot) thermal efficiency of the facility. Answer: (η T ) max = 87.5%.
4. If the heat transfer to the boiler in Example 7.2 were 3.50 × 10 7 Btu/h, the heat transfer from the condenser were 2.10 ×
10 7 Btu/h, and the power into the boiler feed pump were 1.50 hp, determine (a) the power output from the turbine/
generator in MW and (b) the actual thermal efficiency of the power plant. Answers: (a) W act = 4:10 MW, (b) η T = 40.%.
7.6 HEAT ENGINES RUNNING BACKWARD
When a heat engine is run thermodynamically backward, it becomes a heat pump, a refrigerator, or an air conditioner,
depending on your point of view. Figure 7.9 shows that, when a heat engine is thermodynamically reversed,
the directions of all the energy flows are reversed. Thus, a work input W in causes a thermal energy transfer Q L from a
low-temperature reservoir and a thermal energy transfer Q H to a high-temperature reservoir. Consequently, the backward
running heat engine appears to “pump” heat from a low-temperature reservoir to a high-temperature reservoir.
However, since heat is really a thermal energy transport phenomenon and not a fluid, it is somewhat misleading to
refer to it as being “pumped.” Yet it is common practice in the heating, ventilating, and air conditioning (HVAC)
industry to refer to these devices as heat pumps when they are used to provide a thermal energy transfer to a warm
environment (e.g., a house) from a cold environment (e.g., the outside air).
High-temperature
thermal source
at temperature T H
Q H
Heat
engine
High-temperature
thermal source
at temperature T H
Q H
Heat
pump
Thermo
cycle
W out
Thermo
cycle
W in
Q L
Low-temperature
thermal sink
at temperature T L
Q L
Low-temperature
thermal sink
at temperature T L
Refrigeration
or
air conditioning
(a)
(b)
FIGURE 7.9
(a) Heat engine; (b) thermodynamically reversed heat engine (heat pump, refrigerator, or air conditioner).