Modern Engineering Thermodynamics

10.11 Energy Efficiency Based on the Second Law 347
and, if T 0 = T H , the second law efficiency of a refrigerator or air conditioner that rejects heat to the local environment
reduces to
Second law efficiency of a refrigerator or air conditioner that rejects heat to the local environment
When T 0 = T H , ε R/AC
=
COP actual
ref or air cond
COP Carnot
ref or air cond
(10.35)
where the coefficient of performance of a Carnot refrigerator or air conditioner given in Eq. (7.20) is used. The following
example illustrates the use of this material.
EXAMPLE 10.14
A common window air conditioner has an actual COP of 8.92. If the inside temperature is T 0 = T L = 20.0°C and the outside
temperature is T H = 35.0°C, determine the second law availability efficiency of this air conditioner.
Solution
First draw a sketch of the system (Figure 10.19).
The unknown is the second law availability efficiency of this air conditioner.
Equation (7.20) gives the coefficient of performance of a Carnot refrigerator or
air conditioner as
COP = 8.92
COP Carnot =
ref: or air cond:
T L
T H − T L
=
20:0 + 273:15 K
ð35:0 + 273:15 KÞ − ð20:0 + 273:15 KÞ = 19:6
then, Eq. (10.35) can be used to determine the second law efficiency as
T inside = 20.0°C
Window
air
conditioner
T outside = 35.0°C
ε R/AC
=
COP actual
ref: or air cond:
COP Carnot
ref: or air cond:
= 8:92 = 0:455 = 45:5%
19:6
Exercises
41. Determine the second law thermal efficiency of the air conditioner
in Example 10.14 if the outside air temperature is increased from
35.0°C to40.0°C. Assume all the other variables remain unchanged.
Answer: ε R/AC
= 60.9%.
FIGURE 10.19
Example 10.14.
42. If the inside air temperature in Example 10.14 increases from 20.0°C to 22.0°C, determine the new second
law thermal efficiency of the window air conditioner. Assume all the other variables remain unchanged.
Answer: ε R/AC
= 39.3%.
43. When the outside temperature in Example 10.14 increases from 35.0°C to 40.0°C, the actual COP of the air
conditioner decreases from 8.92 to 7.5. Determine the new second law thermal efficiency of the air conditioner.
Answer: ε R/AC
= 51.2%.
When we deal with heat exchangers in which the fluids do not mix, the desirable result is the increase in
temperature of the cold stream (we could choose the desired result to be the decrease in temperature of the hot
stream if we wished). Thus, the corresponding _A desired result is the increase in the available energy rate of the cold
stream, or from Figure 10.20a,
_A desirable result = _m C ða f 4 − a f 3 Þ
and the source availability is the decrease in the available energy rate of the hot stream:
_A initial or = _m H ða f 1 − a f 2 Þ
net input
Then, the second law availability efficiency for a nonmixing heat exchanger is the ratio of these two terms:
Second law efficiency of a nonmixing heat exchanger
ε nonmixing HX = _m Cða f 4 − a f 3 Þ
_m H ða f 1 − a f 2 Þ
(10.36)