Modern Engineering Thermodynamics

538 CHAPTER 14: Vapor and Gas Refrigeration Cycles
EXAMPLE 14.1
A new die-casting operation has a large amount of waste heat available at 200.°C in a location where the local environmental
temperature is 20.0°C. As chief engineer in charge of thermal energy management, investigate the possibility of recovering
some of this waste heat by determining
a. The thermal efficiency of a Carnot engine operating between these temperatures.
b. The coefficient of performance of a Carnot heat pump operating between these temperatures.
c. The coefficient of performance of a Carnot refrigerator or air conditioner operating between these temperatures.
Solution
First, draw a sketch of the system (Figure 14.2).
Die-casting
machine
at 200.°C
Die-casting
machine
at 200.°C
Die-casting
machine
at 200.°C
Waste heat Heat out Waste heat
Carnot
heat
engine
Carnot
Carnot
refrigerator
Work heat Work Work
or air
pump
conditioner
Heat out Heat in Heat out
Environment
at 20.0°C
Environment
at 20.0°C
Environment
at 20.0°C
(a) (b) (c)
FIGURE 14.2
Example 14.1.
a. Equation (13.2) gives the thermal efficiency of a Carnot engine operating between the temperature limits of 200. +
273.15 = 473.15 K and 20.0 + 273.15 = 293.15 K as
ðη T Þ Carnot = 1 − T L
= 1 − 293:15 K = 0:380 = 38:0%
T H 473:15 K
b. Equation (14.4) gives the coefficient of performance of the same Carnot engine running backward as a heat pump as
COP Carnot HP =
T H 473:15 K
=
T H − T L 473:15 − 293:15 K = 2:63
c. Equation (14.5) gives the coefficient of performance of the same Carnot engine running backward as a refrigerator or air
conditioner as
COP Carnot R/AC =
T L
=
293:15 K
T H − T L 473:15 − 293:15 K = 1:63
Note that the COP Carnot HP = COP Carnot R/AC + 1 as Eq. (14.1) requires, and that Eqs. (14.2) and (14.3) are also
satisfied here.
Thermal energy management is a serious problem in the industrial environment. Lost thermal energy often reflects poor process
design and lost money. It can be remedied by considering the waste heat as an energy source and applying a technology that can
utilize it in some fashion.
Exercises
1. Suppose the waste heat in Example 14.1 is available at 35.0°C instead of 200.°C while the environmental temperature
remains at 20.0°C. Determine the thermal efficiency of a Carnot engine operating between these temperatures and the
coefficient of performance of a Carnot air conditioning unit. Answer: (η T ) Carnot = 4.90%, and COP Carnot AC = 20.5.
2. During winter, the environmental temperature in the die-casting facility in Example 14.1 drops to 0.00°C. Recompute
the thermal efficiency and coefficient of performance, assuming the waste heat temperature remains at 200.°C. Answer:
(η T ) Carnot = 42.3%, COP Carnot HP = 2.37, and COP Carnot R/AC = 1.37.