Moran M.J., Shapiro H.N. Fundamentals of Engineering Thermodynamics
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476 Chapter 10 Refrigeration and Heat Pump Systems
3. There are no pressure drops through the heat exchangers.
4. Kinetic and potential energy effects are negligible.
5. The working fluid is air modeled as an ideal gas.
Analysis: The analysis begins by determining the specific enthalpy at each numbered state of the cycle. At state 1, the tem-
perature is 270 K. From Table A-22, h
1
270.11 kJ/kg, p
r1
0.9590. Since the compressor process is isentropic, h
2s
can be
determined by first evaluating p
r
at state 2s. That is
Then, interpolating in Table A-22, we get h
2s
370.1 kJ/kg.
The temperature at state 3 is given as T
3
300 K. From Table A-22, h
3
300.19 kJ/kg, p
r3
1.3860. The specific en-
thalpy at state 4s is found by using the isentropic relation
Interpolating in Table A-22, we obtain h
4s
219.0 kJ/kg.
(a) The net power input is
This requires the mass flow rate which can be determined from the volumetric flow rate and the specific volume at the
compressor inlet:
Since v
1
()
Finally
(b) The refrigeration capacity is
(c) The coefficient of performance is
b
Q
#
in
W
#
cycle
92.36
33.97
2.72
92.36 kW
11.807 kg/s21270.11 2192 kJ/kg a
1 kW
1 kJ/s
b
Q
#
in
m
#
1h
1
h
4s
2
33.97 kW
W
#
cycle
11.807 kg/s231370.1 270.112 1300.19 219.024 kJ/kg a
1 kW
1 kJ/s
b
1.807 kg/s
11.4 m
3
/s2 11 bar2
a
8.314 kJ
28.97
b 1270 K2
a
10
5
N/m
2
1 bar
b a
1 kJ
10
3
N
#
m
b
m
#
1AV 2
1
p
1
1R
M2T
1
T
1
p
1
R
M
m
#
1AV2
1
v
1
m
#
,
W
#
cycle
m
#
31h
2s
h
1
2 1h
3
h
4s
24
p
r4
p
r3
p
4
p
3
11.38602 11
32 0.462
p
r2
p
2
p
1
p
r1
13210.95902 2.877
Irreversibilities within the compressor and turbine serve to decrease the coefficient of per-
formance significantly from that of the corresponding ideal cycle because the compressor
work requirement is increased and the turbine work output is decreased. This is illustrated
in the example to follow.
10.7 Gas Refrigeration Systems 477
EXAMPLE 10.5 Brayton Refrigeration Cycle with Irreversibilities
Reconsider Example 10.4, but include in the analysis that the compressor and turbine each have an isentropic efficiency of
80%. Determine for the modified cycle (a) the net power input, in kW, (b) the refrigeration capacity, in kW, (c) the coefficient
of performance, and interpret its value.
SOLUTION
Known: A Brayton refrigeration cycle operates with air. Compressor inlet conditions, the turbine inlet temperature, and the
compressor pressure ration are given. The compressor and turbine each have an efficiency of 80%.
Find: Determine the net power input and the refrigeration capacity, each in kW. Also, determine the coefficient of per-
formance and interpret its value.
Schematic and Given Data:
T
s
4s
4
1
T
1
= 270 K
T
3
= 300 K
3
2s
2
p = 3 bars
p = 1 bar
Figure E10.5
Assumptions:
1. Each component of the cycle is analyzed as a control volume at
steady state.
2. The compressor and turbine are adiabatic.
3. There are no pressure drops through the heat exchangers.
4. Kinetic and potential energy effects are negligible.
5. The working fluid is air modeled as an ideal gas.
Analysis:
(a) The power input to the compressor is evaluated using the isentropic compressor efficiency,
c
. That is
The value of the work per unit mass for the isentropic compression, ( )
s
, is determined with data from the solution in
Example 10.4 as 99.99 kJ/kg. The actual power required is then
The turbine power output is determined in a similar manner, using the turbine isentropic efficiency
t
. Thus,
()
s
. Using data form the solution to Example 10.4 gives ( )
s
The actual turbine work is
then
The net power input to the cycle is
W
#
cycle
225.9 117.4 108.5 kW
117.4 kW
W
#
t
m
#
h
t
1W
#
t
m
#
2
s
11.807 kg/s210.82181.19 kJ/kg2
81.19 kJ /kg.W
#
t
m
#
W
#
t
m
#
W
#
t
m
#
h
t
225.9 kW
W
#
c
m
#
1W
#
c
m
#
2
s
h
c
11.807 kg/s2199.99 kJ/kg2
10.82
W
#
c
m
#
W
#
c
m
#
1W
#
c
m
#
2
s
h
c
478 Chapter 10 Refrigeration and Heat Pump Systems
(b) The specific enthalpy at the turbine exit, h
4
, is required to evaluate the refrigeration capacity. This enthalpy can be deter-
mined by solving ( ) to obtain Inserting known values
The refrigeration capacity is then
(c) The coefficient of performance is
The value of the coefficient of performance in this case is less than unity. This means that the refrigeration effect is smaller
than the net work required to achieve it. Additionally, note that irreversibilities in the compressor and turbine have a significant
effect on the performance of gas refrigeration systems. This is brought out by comparing the results of the present example
with those of Example 10.4. Irreversibilities result in an increase in the work of compression and a reduction in the work
output of the turbine. The refrigeration capacity is also reduced. The overall effect is that the coefficient of performance is
decreased significantly.
b
Q
#
in
W
#
cycle
63.08
108.5
0.581
Q
#
in
m
#
1h
1
h
4
2 11.80721270.11 235.22 63.08 kW
h
4
300.19 a
117.4
1.807
b 235.2 kJ/kg
h
4
h
3
W
#
t
m
#
.h
3
h
4
W
#
t
m
#
ADDITIONAL GAS REFRIGERATION APPLICATIONS
To obtain even moderate refrigeration capacities with the Brayton refrigeration cycle, equip-
ment capable of achieving relatively high pressures and volumetric flow rates is needed. For
most applications involving air conditioning and for ordinary refrigeration processes, vapor-
compression systems can be built more cheaply and can operate with higher coefficients of
performance than gas refrigeration systems. With suitable modifications, however, gas re-
frigeration systems can be used to achieve temperatures of about 150C, which are well
below the temperatures normally obtained with vapor systems.
Figure 10.14 shows the schematic and T–s diagram of an ideal Brayton cycle modified
by the introduction of a regenerative heat exchanger. The heat exchanger allows the air en-
tering the turbine at state 3 to be cooled below the warm region temperature T
H
. In the sub-
sequent expansion through the turbine, the air achieves a much lower temperature at state 4
than would have been possible without the regenerative heat exchanger. Accordingly, the
refrigeration effect, achieved from state 4 to state b, occurs at a correspondingly lower average
temperature.
a
b
1
3
4
2
Q
in
·
Q
out
·
W
cycle
·
Heat
exchanger
Turbine Compressor
T
s
T
H
3
a
2
1
b
4
Figure 10.14 Brayton refrigeration cycle with a regenerative heat exchanger.
Chapter Summary and Study Guide 479
Auxiliary
power
Auxiliary
turbine
Air extracted for
cabin cooling
Heat transfer
to ambient
Main jet
engine
compressor
Ambient
air in
To
combustor
Cool air
to cabin
Figure 10.15 An application of gas
refrigeration to aircraft cabin cooling.
An example of the application of gas refrigeration to cabin cooling in an aircraft is
illustrated in Fig. 10.15. As shown in the figure, a small amount of high-pressure air is
extracted from the main jet engine compressor and cooled by heat transfer to the ambi-
ent. The high-pressure air is then expanded through an auxiliary turbine to the pressure
maintained in the cabin. The air temperature is reduced in the expansion and thus is able
to fulfill its cabin cooling function. As an additional benefit, the turbine expansion can
provide some of the auxiliary power needs of the aircraft. Size and weight are important
considerations in the selection of equipment for use in aircraft. Open-cycle systems, like
the example given here, utilize compact high-speed rotary turbines and compressors. Fur-
thermore, since the air for cooling comes directly from the surroundings, there are fewer
heat exchangers than would be needed if a separate refrigerant were circulated in a closed
vapor-compression cycle.
Chapter Summary and Study Guide
In this chapter we have considered refrigeration and heat
pump systems, including vapor systems where the refrigerant
is alternately vaporized and condensed, and gas systems where
the refrigerant remains a gas. The three principal types of re-
frigeration and heat pump systems discussed are the vapor-
compression, absorption, and reversed Brayton cycles.
The performance of simple vapor refrigeration systems is
described in terms of the vapor-compression cycle. For this
cycle, we have evaluated the principal work and heat trans-
fers along with two important performance parameters: the
coefficient of performance and the refrigeration capacity. We
have considered the effect on performance of irreversibilities
during the compression process and in the expansion across
the valve, as well as the effect of irreversible heat transfer be-
tween the refrigerant and the warm and cold regions. Varia-
tions of the basic vapor-compression refrigeration cycle also
have been considered, including cascade cycles and multistage
compression with intercooling.
Qualitative discussions are presented of refrigerant prop-
erties and of considerations in selecting refrigerants. Absorp-
tion refrigeration and heat pump systems are also discussed
qualitatively. A discussion of vapor-compression heat pump
systems is provided, and the chapter concludes with a study
of gas refrigeration systems.
480 Chapter 10 Refrigeration and Heat Pump Systems
The following list provides a study guide for this chapter.
When your study of the text and end-of-chapter exercises has
been completed, you should be able to
write out the meanings of the terms listed in the margin
throughout the chapter and understand each of the re-
lated concepts. The subset of key concepts listed below
is particularly important.
sketch the T–s diagrams of vapor-compression refrigera-
tion and heat pump cycles and of Brayton refrigeration
cycles, correctly showing the relationship of the refriger-
ant temperature to the temperatures of the warm and
cold regions.
apply the first and second laws along with property data
to determine the performance of vapor-compression
refrigeration and heat pump cycles and of Brayton refrig-
eration cycles, including evaluation of the power re-
quired, the coefficient of performance, and the capacity.
sketch schematic diagrams of vapor-compression cycle
modifications, including cascade cycles and multistage
compression with intercooling between the stages. In
each case be able to apply mass and energy balances,
the second law, and property data to determine
performance.
explain the operation of absorption refrigeration systems.
Key Engineering Concepts
vapor-compression
refrigeration p. 457
refrigeration
capacity p. 458
ton of
refrigeration p. 458
absorption
refrigeration p. 469
vapor-compression
heat pump p. 472
Brayton refrigeration
cycle p. 474
Exercises: Things Engineers Think About
1. What are the temperatures inside the fresh food and freezer
compartments of your refrigerator? Do you know what values are
recommended for these temperatures?
2. How might the variation in the local ambient temperature
affect the thermal performance of an outdoor pop machine?
3. Explain how a household refrigerator can be viewed as a heat
pump that heats the kitchen. If you knew the refrigerator’s coef-
ficient of performance, could you calculate its coefficient of per-
formance when viewed as a heat pump?
4. If it takes about 335 kJ to freeze 1 kg of water, how much ice
could an ice maker having a 1-ton refrigeration capacity produce
in 24 hours?
5. Using the T–s diagram of Fig. 10.1, an area interpretation of
the Carnot vapor refrigeration cycle coefficient of performance
is provided in Sec. 10.1. Can a similar area interpretation be
developed for the coefficient of performance of a vapor-
compression refrigeration cycle?
6. Would you recommend replacing the expansion valve of
Example 10.3 by a turbine?
7. You recharge your automobile air conditioner with refrigerant
from time to time, yet seldom, if ever, your refrigerator. Why?
8. Would water be a suitable working fluid for use in a refrigerator?
9. Sketch the T–s diagram of an ideal vapor-compression refrig-
eration cycle in which the heat transfer to the warm region occurs
with the working fluid at a supercritical pressure.
10. Would you recommend a domestic heat pump for use in
Duluth, Minnesota? In San Diego, California?
11. What components are contained in the outside unit of a res-
idential heat pump?
12. You see an advertisement for a natural gas–fired absorption
refrigeration system. How can burning natural gas play a role in
achieving cooling?
13. Referring to Fig. 10.13, why is the temperature T
H
the lim-
iting value for the temperature at state 3? What practical consid-
erations might preclude this limit from being achieved?
14. When a regenerator is added to the ideal Brayton refrigera-
tion cycle, as in Fig. 10.14, does the coefficient of performance
increase or decrease?
Problems: Developing Engineering Skills
Vapor Refrigeration Systems
10.1 A Carnot vapor refrigeration cycle uses Refrigerant 134a
as the working fluid. The refrigerant enters the condenser as
saturated vapor at 28C and leaves as saturated liquid. The
evaporator operates at a temperature of 10C. Determine, in
kJ per kg of refrigerant flow,
(a) the work input to the compressor.
(b) the work developed by the turbine.
(c) the heat transfer to the refrigerant passing through the
evaporator.
What is the coefficient of performance of the cycle?
Problems: Developing Engineering Skills 481
10.2 Refrigerant 22 is the working fluid in a Carnot vapor re-
frigeration cycle for which the evaporator temperature is 0C.
Saturated vapor enters the condenser at 40C, and saturated
liquid exits at the same temperature. The mass flow rate of re-
frigerant is 3 kg/min. Determine
(a) the rate of heat transfer to the refrigerant passing through
the evaporator, in kW.
(b) the net power input to the cycle, in kW.
(c) the coefficient of performance.
10.3 An ideal vapor-compression refrigeration cycle operates at
steady state with Refrigerant 134a as the working fluid. Satu-
rated vapor enters the compressor at 10C, and saturated liq-
uid leaves the condenser at 28C. The mass flow rate of
refrigerant is 5 kg/min. Determine
(a) the compressor power, in kW.
(b) the refrigerating capacity, in tons.
(c) the coefficient of performance.
10.4 Modify the cycle in Problem 10.3 to have saturated vapor
entering the compressor at 1.6 bar and saturated liquid leav-
ing the condenser at 9 bar. Answer the same questions for the
modified cycle as in Problem 10.3.
10.5 Plot each of the quantities calculated in Problem 10.4 ver-
sus evaporator pressure ranging from 0.6 to 4 bar, while the
condensor pressure remains fixed at 6, 9, and 12 bar.
10.6 Refrigerant 22 enters the compressor of an ideal vapor-
compression refrigeration system as saturated vapor at 40C
with a volumetric flow rate of 15 m
3
/min. The refrigerant leaves
the condenser at 32C, 9 bar. Determine
(a) the compressor power, in kW.
(b) the refrigerating capacity, in tons.
(c) the coefficient of performance.
10.7 An ideal vapor-compression refrigeration cycle, with am-
monia as the working fluid, has an evaporator temperature of
20C and a condenser pressure of 12 bar. Saturated vapor
enters the compressor, and saturated liquid exits the condenser.
The mass flow rate of the refrigerant is 3 kg/min. Determine
(a) the coefficient of performance.
(b) the refrigerating capacity, in tons.
10.8 To determine the effect of changing the evaporator tem-
perature on the performance of an ideal vapor-compression re-
frigeration cycle, plot the coefficient of performance and the
refrigerating capacity, in tons, for the cycle in Problem 10.7
for saturated vapor entering the compressor at temperatures
ranging from 40 to 10C. All other conditions are the same
as in Problem 10.7.
10.9 To determine the effect of changing condenser pressure
on the performance of an ideal vapor-compression refrigera-
tion cycle, plot the coefficient of performance and the refrig-
erating capacity, in tons, for the cycle in Problem 10.7 for
condenser pressures ranging from 8 to 16 bar. All other con-
ditions are the same as in Problem 10.7.
10.10 Modify the cycle in Problem 10.4 to have an isentropic
compressor efficiency of 80% and let the temperature of the
liquid leaving the condenser be 32C. Determine, for the
modified cycle,
(a) the compressor power, in kW.
(b) the refrigerating capacity, in tons.
(c) the coefficient of performance.
(d) the rates of exergy destruction in the compressor and
expansion valve, each in kW, for T
0
28C.
10.11 A vapor-compression refrigeration system circulates Re-
frigerant 134a at a rate of 6 kg/min. The refrigerant enters the
compressor at 10C, 1.4 bar, and exits at 7 bar. The isen-
tropic compressor efficiency is 67%. There are no appreciable
pressure drops as the refrigerant flows through the condenser
and evaporator. The refrigerant leaves the condenser at 7 bar,
24C. Ignoring heat transfer between the compressor and its
surroundings, determine
(a) the coefficient of performance.
(b) the refrigerating capacity, in tons.
(c) the rates of exergy destruction in the compressor and ex-
pansion valve, each in kW.
(d) the changes in specific flow exergy of the refrigerant pass-
ing through the evaporator and condenser, respectively,
each in kJ/kg.
Let T
0
21C, p
0
1 bar.
10.12 If the minimum and maximum allowed refrigerant pres-
sures are 1 and 10 bar, respectively, which of the following
can be used as the working fluid in a vapor-compression
refrigeration system that maintains a cold region at 0C,
while discharging energy by heat transfer to the surrounding
air at 30C: Refrigerant 22, Refrigerant 134a, ammonia,
propane?
10.13 In a vapor-compression refrigeration cycle, ammonia exits
the evaporator as saturated vapor at 22C. The refrigerant
enters the condenser at 16 bar and 160C, and saturated liquid
exits at 16 bar. There is no significant heat transfer between the
compressor and its surroundings, and the refrigerant passes
through the evaporator with a negligible change in pressure. If
the refrigerating capacity is 150 kW, determine
(a) the mass flow rate of refrigerant, in kg/s.
(b) the power input to the compressor, in kW.
(c) the coefficient of performance.
(d) the isentropic compressor efficiency.
10.14 A vapor-compression refrigeration system with a capac-
ity of 10 tons has superheated Refrigerant 134a vapor enter-
ing the compressor at 15C, 4 bar, and exiting at 12 bar. The
compression process can be modeled by pv
1.01
constant. At
the condenser exit, the pressure is 11.6 bar, and the tempera-
ture is 44C. The condenser is water-cooled, with water enter-
ing at 20C and leaving at 30C with a negligible change in
pressure. Heat transfer from the outside of the condenser can
be neglected. Determine
(a) the mass flow rate of the refrigerant, in kg/s.
(b) the power input and the heat transfer rate for the com-
pressor, each in kW.
(c) the coefficient of performance.
482 Chapter 10 Refrigeration and Heat Pump Systems
(d) the mass flow rate of the cooling water, in kg/s.
(e) the rates of exergy destruction in the condenser and ex-
pansion valve, each expressed as a percentage of the power
input. Let T
0
20C.
10.15 Figure P10.15 shows a steam jet refrigeration system that
produces chilled water in a flash chamber. The chamber is
maintained at a vacuum pressure by the steam ejector, which
removes the vapor generated by entraining it in the low-
pressure jet and discharging into the condenser. The vacuum
pump removes air and other noncondensable gases from the
condenser shell. For the conditions shown on the figure, de-
termine the make-up water and cooling water flow rates, each
in kg/h.
10.17 Figure P10.17 shows a Refrigerant 22 vapor-compression
refrigeration system with mechanical subcooling. A counter-
flow heat exchanger subcools a portion of the refrigerant leav-
ing the condenser below the ambient temperature as follows:
Saturated liquid exits the condenser at 12 bars. A portion of
the flow exiting the condenser is diverted through an expan-
sion valve and passes through the counterflow heat exchanger
with no pressure drop, leaving as saturated vapor at 6C. The
diverted flow is then compressed isentropically to 12 bars and
reenters the condenser. The remainder of the flow exiting the
condenser passes through the other side of the heat exchanger
and exits at 40C, 12 bars. The evaporator has a capacity of
50 tons and produces 28C saturated vapor at its exit. In the
main compressor, the refrigerant is compressed isentropically
to 12 bars. Determine at steady state
(a) the mass flow rate at the inlet to each compressor, in
kg/s.
(b) the power input to each compressor, in kW.
(c) the coefficient of performance.
5°C
Ejector nozzle
Steam jet
Vacuum
pump
Saturated vapor
at 200 kPa
Air
Sat
vapor
p = 4 kPa
Condenser
Cooling
water in
at 15°C
25°C
Condensate
return
to drain
Pump
25,000
kg/h
Cooling
load
142 tons
Make-up
water
at 15°C
Figure P10.15
Cascade and Multistage Systems
10.16 A vapor-compression refrigeration system uses the
arrangement shown in Fig. 10.8 for two-stage compression with
intercooling between the stages. Refrigerant 134a is the work-
ing fluid. Saturated vapor at 30C enters the first compressor
stage. The flash chamber and direct contact heat exchanger op-
erate at 4 bar, and the condenser pressure is 12 bar. Saturated
liquid streams at 12 and 4 bar enter the high- and low-pressure
expansion valves, respectively. If each compressor operates
isentropically and the refrigerating capacity of the system is 10
tons, determine
(a) the power input to each compressor, in kW.
(b) the coefficient of performance.
Counterflow
heat exchanger
p
4
=
T
4
=
12 bars
4°C
4
3
Saturated liquid
p
3
= 12 bars
Q
out
·
Q
in
·
W
c2
·
W
c1
·
Condenser
87
p
8
= 12 bars
2
p
2
= 12 bars
Main
compressor
1
Saturated vapor
T
1
= 28°C
Evaporator
5
Expansion
valve
Expansion
valve
Saturated vapor
T
7
= 6°C
Compressor
Figure P10.17
10.18 Figure P10.18 shows the schematic diagram of a vapor-
compression refrigeration system with two evaporators using
Refrigerant 134a as the working fluid. This arrangement is used
to achieve refrigeration at two different temperatures with a
single compressor and a single condenser. The low-temperature
evaporator operates at 18C with saturated vapor at its exit
and has a refrigerating capacity of 3 tons. The higher-
temperature evaporator produces saturated vapor at 3.2 bar at
its exit and has a refrigerating capacity of 2 tons. Compression
Problems: Developing Engineering Skills 483
is isentropic to the condenser pressure of 10 bar. There are no
significant pressure drops in the flows through the condenser
and the two evaporators, and the refrigerant leaves the con-
denser as saturated liquid at 10 bar. Calculate
(a) the mass flow rate of refrigerant through each evaporator,
in kg/min.
(b) the compressor power input, in kW.
(c) the rate of heat transfer from the refrigerant passing
through the condenser, in kW.
10.19 An ideal vapor-compression refrigeration cycle is modi-
fied to include a counterflow heat exchanger, as shown in
Fig. P10.19. Ammonia leaves the evaporator as saturated vapor
at 1.0 bar and is heated at constant pressure to 5C before en-
tering the compressor. Following isentropic compression to 18
bar, the refrigerant passes through the condenser, exiting at
40C, 18 bar. The liquid then passes through the heat ex-
changer, entering the expansion valve at 18 bar. If the mass
flow rate of refrigerant is 12 kg/min, determine
(a) the refrigeration capacity, in tons of refrigeration.
(b) the compressor power input, in kW.
(c) the coefficient of performance.
Discuss possible advantages and disadvantages of this
arrangement.
Vapor-Compression Heat Pump Systems
10.20 An ideal vapor-compression heat pump cycle with Re-
frigerant 134a as the working fluid provides heating at a rate
of 15 kW to maintain a building at 20C when the outside
temperature is 5C. Saturated vapor at 2.4 bar leaves the
evaporator, and saturated liquid at 8 bar leaves the condenser.
Calculate
(a) the power input to the compressor, in kW.
(b) the coefficient of performance.
(c) the coefficient of performance of a Carnot heat pump cycle
operating between thermal reservoirs at 20 and 5C.
10.21 A vapor-compression heat pump system uses ammonia
as the working fluid. The refrigerant enters the compressor at
2.5 bar, 5C, with a volumetric flow rate of 0.6 m
3
/min.
Compression is adiabatic to 14 bar, 140C, and saturated liquid
exits the condenser at 14 bar. Determine
(a) the power input to the compressor, in kW.
(b) the heating capacity of the system, in kW and tons.
(c) the coefficient of performance.
(d) the isentropic compressor efficiency.
10.22 On a particular day when the outside temperature is 5C,
a house requires a heat transfer rate of 12 kW to maintain the
inside temperature at 20C. A vapor-compression heat pump
with Refrigerant 22 as the working fluid is to be used to pro-
vide the necessary heating. Specify appropriate evaporator and
condenser pressures of a cycle for this purpose. Let the re-
frigerant be saturated vapor at the evaporator exit and saturated
liquid at the condenser exit. Calculate
(a) the mass flow rate of refrigerant, in kg/min.
(b) the compressor power, in kW.
(c) the coefficient of performance.
Condenser
Evaporator
2
Evaporator
1
Q
out
·
2
78
56
3
Expansion
valve
Expansion
valve
Expansion
valve
14
Q
in,2
= 2 tons
·
Q
in,1
= 3 tons
·
Compressor
W
c
·
Figure P10.18
W
c
·
Condenser
Evaporator
Compressor
Heat exchanger
Q
out
·
Q
in
·
2
1
4
3
56
Expansion
valve
Figure P10.19
484 Chapter 10 Refrigeration and Heat Pump Systems
10.23 Repeat the calculations of Problem 10.22 for Refrigerant
134a as the working fluid. Compare the results with those of
Problem 10.22 and discuss.
10.24 A vapor-compression heat pump with a heating capacity
of 500 kJ/min is driven by a power cycle with a thermal effi-
ciency of 25%. For the heat pump, Refrigerant 134a is com-
pressed from saturated vapor at 10C to the condenser
pressure of 10 bar. The isentropic compressor efficiency is
80%. Liquid enters the expansion valve at 9.6 bar, 34C. For
the power cycle, 80% of the heat rejected is transferred to the
heated space.
(a) Determine the power input to the heat pump compressor,
in kW.
(b) Evaluate the ratio of the total rate that heat is delivered to
the heated space to the rate of heat input to the power cycle.
Discuss.
10.25 A residential heat pump system operating at steady state
is shown schematically in Fig. P10.25. Refrigerant 22 circu-
lates through the components of the system, and property data
at the numbered states are given on the figure. The compres-
sor operates adiabatically. Kinetic and potential energy changes
are negligible as are changes in pressure of the streams pass-
ing through the condenser and evaporator. Let T
0
273 K.
Determine
(a) the power required by the compressor, in kW, and the isen-
tropic compressor efficiency.
(b) the coefficient of performance.
(c) Perform a full exergy accounting of the compressor power
input, in kW. Discuss.
(d) Devise and evaluate an exergetic efficiency for the heat
pump system.
Gas Refrigeration Systems
10.26 Air enters the compressor of an ideal Brayton refrigera-
tion cycle at 100 kPa, 270 K. The compressor pressure ratio is
3, and the temperature at the turbine inlet is 310 K. Determine
(a) the net work input, per unit mass of air flow, in kJ/kg.
(b) the refrigeration capacity, per unit mass of air flow, in kJ/kg.
(c) the coefficient of performance.
(d) the coefficient of performance of a Carnot refrigeration cy-
cle operating between thermal reservoirs at T
C
270 K
and T
H
310 K, respectively.
10.27 Reconsider Problem 10.26, but include in the analysis
that the compressor and turbine have isentropic efficiencies of
80 and 88%, respectively. For the modified cycle
(a) determine the coefficient of performance.
(b) develop an exergy accounting of the compressor power in-
put, in kJ per kg of air flowing. Discuss
Let T
0
310 K.
10.28 Plot the quantities calculated in parts (a) through (c) of
Problem 10.26 versus the compressor pressure ratio ranging
from 2 to 6. Repeat for compressor and turbine isentropic
efficiencies of 95%, 90%, and 80%.
10.29 Air enters the compressor of an ideal Brayton refrigera-
tion cycle at 140 kPa, 270 K, and is compressed to 420 kPa.
At the turbine inlet, the temperature is 320 K and the volu-
metric flow rate is 0.4 m
3
/s. Determine
(a) the mass flow rate, in kg/s.
(b) the net power input, in kW.
(c) the refrigerating capacity, in kW.
(d) the coefficient of performance.
10.30 Air enters the compressor of a Brayton refrigeration cy-
cle at 100 kPa, 260 K, and is compressed adiabatically to 300
kPa. Air enters the turbine at 300 kPa, 300 K, and expands adi-
abatically to 100 kPa. For the cycle
(a) determine the net work per unit mass of air flow, in kJ/kg,
and the coefficient of performance if the compressor and
turbine isentropic efficiencies are both 100%.
(b) plot the net work per unit mass of air flow, in kJ/kg, and
the coefficient of performance for equal compressor and
turbine isentropic efficiencies ranging from 80 to 100%.
10.31 The Brayton refrigeration cycle of Problem 10.26 is mod-
ified by the introduction of a regenerative heat exchanger. In
the modified cycle, compressed air enters the regenerative heat
exchanger at 310 K and is cooled to 280 K before entering the
turbine. Determine, for the modified cycle,
(a) the lowest temperature, in K.
(b) the net work input per unit mass of air flow, in kJ/kg.
(c) the refrigeration capacity, per unit mass of air flow, in kJ/kg.
(d) the coefficient of performance.
10.32 Reconsider Problem 10.31, but include in the analysis
that the compressor and turbine have isentropic efficiencies of
85 and 88% respectively. Answer the same questions as in
Problem 10.31.
W
c
·
Expansion
valve
Return air
from house
Heated air
to house
p
2
=
T
2
=
56
T
6
= 50°C
14 bar
75°C
2
1
78
4
3
T
1
=
p
1
=
–5°C
3.5 bar
Air exits
at –12°C
Outside air
enters at 0°C
p
4
= 3.5 bar
p
3
=
T
3
=
14 bar
28°C
p
5
=
T
5
=
(AV)
5
=
1 bar
20°C
0.42 m
3
/s
Condenser
Evaporator
Compressor
Figure P10.25
Design & Open Ended Problems: Exploring Engineering Practice 485
10.33 Plot the quantities calculated in parts (a) through (d) of
Problem 10.31 versus the compressor pressure ratio ranging
from 3 to 7. Repeat for equal compressor and turbine isen-
tropic efficiencies of 95%, 90%, and 80%.
10.34 Air at 2 bar, 380 K is extracted from a main jet engine
compressor for cabin cooling. The extracted air enters a heat
exchanger where it is cooled at constant pressure to 320 K
through heat transfer with the ambient. It then expands adia-
batically to 0.95 bar through a turbine and is discharged into
the cabin. The turbine has an isentropic efficiency of 75%. If
the mass flow rate of the air is 1.0 kg/s, determine
(a) the power developed by the turbine, in kW.
(b) the rate of heat transfer from the air to the ambient, in kW.
10.35 Air undergoes a Stirling refrigeration cycle, which is the
reverse of the Stirling power cycle introduced in Sec. 9.11. At
the beginning of the isothermal compression, the pressure and
temperature are 100 kPa and 300 K, respectively. The com-
pression ratio is 6, and the temperature during the isothermal
expansion is 100 K. Determine
(a) the heat transfer during the isothermal expansion, in kJ per
kg of air.
(b) the net work for the cycle, in kJ per kg of air.
(c) the coefficient of performance.
10.36 Air undergoes an Ericsson refrigeration cycle, which is
the reverse of the Ericsson power cycle introduced in Sec. 9.11.
At the beginning of the isothermal compression, the pressure
and temperature are 100 kPa and 310 K, respectively. The pres-
sure ratio during the isothermal compression is 3. During the
isothermal expansion the temperature is 270 K. Determine
(a) the heat transfer for the isothermal expansion, per unit
mass of air flow, in kJ/kg.
(b) the net work, per unit mass of air flow, in kJ/kg.
(c) the coefficient of performance.
Design & Open Ended Problems: Exploring Engineering Practice
10.1D A vapor-compression refrigeration system using Refrig-
erant 134a is being designed for a household food freezer. The
refrigeration system must maintain a temperature of 18C
within the freezer compartment when the temperature of the
room is 32C. Under these conditions, the steady-state heat
transfer rate from the room into the freezer compartment is
440 W. Specify operating pressures and temperatures at key
points within the refrigeration system and estimate the refrig-
erant mass flow rate and compressor power required.
10.2D Design a bench-top-sized air-to-air vapor-compression
refrigeration system to be used in a student laboratory. Include
in your design the capability to utilize either of two expansion
devices: a capillary tube or a thermostatic expansion valve.
Provide sketches of the layout of your system, including ap-
propriate interconnecting piping. Specify the locations and
types of sensors to allow students to measure the electrical
power consumption and refrigeration capacity, as well as per-
form energy balances on the evaporator and condenser.
10.3D Refrigerant 22 is widely used as the working fluid in air
conditioners and industrial chillers. However, its use is likely
to be phased out in the future due to concerns about ozone de-
pletion. Investigate which environmentally-acceptable working
fluids are under consideration to replace Refrigerant 22 for
these uses. Determine the design issues for air conditioners and
chillers that would result from changing refrigerants. Write a
report of your findings.
10.4D An air-conditioning system is under consideration that
will use a vapor-compression ice maker during the nighttime,
when electric rates are lowest, to store ice for meeting the day-
time air-conditioning load. The maximum loads are 100 tons
during the day and 50 tons at night. Is it best to size the sys-
tem to make enough ice at night to carry the entire daytime
load or to use a smaller chiller that runs both day and night?
Base your strategy on the day–night electric rate structure of
your local electric utility company.
10.5D A heat pump is under consideration for heating and cool-
ing a 3600-ft
2
camp lodge in rural Wisconsin. The lodge is
used continuously in the summer and on weekends in the
winter. The system must provide adequate heating for winter
temperatures as low as 23C, and an associated heating load
of 30 kW. In the summer, the maximum outside temperature
is 38C, and the associated cooling load is 44 kW. The local
water table is 30 M, and the ground water temperature is 14C.
Compare the initial, operating, and maintenance costs of an
air-source heat pump to a vertical well ground-source heat
pump for this application, and make a recommendation as to
which is the best option.
10.6D Investigate the economic feasibility of using a waste
heat-recovery heat pump for domestic water heating that
employs ventilation air being discharged from a dwelling as
the source. Assume typical hot water use of a family of four
living in a single-family dwelling in your locale. Write a report
of your findings.
10.7D List the major design issues involved in using ammonia
as the refrigerant in a system to provide chilled water at 4C
for air conditioning a college campus in your locale. Develop
a layout of the equipment room and a schematic of the chilled
water distribution system. Label the diagrams with key tem-
peratures and make a list of capacities of each of the major
pieces of equipment.
10.8D Carbon dioxide (CO
2
) is an inexpensive, nontoxic, and
non-flammable candidate for use as a working fluid in vapor-
compression systems. Investigate the suitability of using CO
2
as the working fluid in a heat pump-water heater requiring a
power input ranging from 50 to 100 kW and providing hot
water ranging from 50 to 90C. Assume that ground water is