7-21
7-86 An experimentalist claims to have developed a refrigerator. The experimentalist reports temperature, heat transfer, and
work input measurements. The claim is to be evaluated.
Analysis The highest coefficient of performance a refrigerator can have when removing heat from a cool medium at –30°C
to a warmer medium at 25°C is
1
1
7-87 The refrigerated space and the environment temperatures of a Carnot refrigerator and the power consumption are
given. The rate of heat removal from the refrigerated space is to be determined.
Assumptions The Carnot refrigerator operates steadily.
Analysis The coefficient of performance of a Carnot refrigerator depends on the
7-88 The cooled space and the outdoors temperatures for a Carnot air-conditioner and the rate of heat removal from the air–
conditioned room are given. The power input required is to be determined.
Assumptions The air-conditioner operates steadily.
Analysis The COP of a Carnot air conditioner (or Carnot refrigerator) depends on the temperature limits in the cycle only,
kW 0.463 kJ/min .827
27.0
kJ/min 750
COP maxR,
innet, L
Q
W
22C
House
24C
7-22
7-89 The validity of a claim by an inventor related to the operation of a heat pump is to be evaluated.
Assumptions The heat pump operates steadily.
2.67
kW 75
kW 200
COP
innet,
HP W
QH
7-90 The power input and the COP of a Carnot heat pump are given. The temperature of the low-temperature reservoir and
the heating load are to be determined.
293 K
H
Q
7-23
7-92 An inventor claims to have developed a refrigerator. The inventor reports temperature and COP measurements. The
claim is to be evaluated.
7-93 A heat pump maintains a house at a specified temperature. The rate of heat loss of the house and the power
consumption of the heat pump are given. It is to be determined if this heat pump can do the job.
Assumptions The heat pump operates steadily.
Analysis The power input to a heat pump will be a minimum when the heat pump operates in a reversible manner. The
–12C
maximum rate of heat removal from the air-conditioned space is to be determined.
Assumptions The air-conditioner operates steadily.
Analysis The rate of heat removal from a house will be a maximum when the air-conditioning system operates in a
7-25
7-97 A commercial refrigerator with R-134a as the working fluid is considered. The condenser inlet and exit states are
specified. The mass flow rate of the refrigerant, the refrigeration load, the COP, and the minimum power input to the
kJ/kg 19.110
C3.41
MPa 2.1
C3.4153.46
kJ/kg 28.278
C50
MPa 2.1
2
2
2
subcoolMPa sat@1.22
1
1
1
h
T
P
TTT
h
T
P
kJ/kg 54.75
0
C18
1,
1,
1,
w
w
w
h
x
T
The energy decrease of the refrigerant is equal to the energy increase of the water in the condenser. That is,
kg/s 0.0498
kJ/kg )19.11028.278(
kW 367.8
)(
21
21 hh
Q
mhhmQ H
RRH
in
W
(d) The COP of a reversible refrigerator operating between the same temperature limits is
1
1
COPmax
QH
1.2 MPa
5C subcool
Condenser
Compressor
Expansion
valve
1.2 MPa
50C
Win
Water
18C
26C
7-26
7-98 A heat pump maintains a house at a specified temperature in winter. The maximum COPs of the heat pump for
different outdoor temperatures are to be determined.
Analysis The coefficient of performance of a heat pump will be a maximum when the heat pump operates in a reversible
manner. The coefficient of performance of a reversible heat pump depends on the temperature limits in the cycle only, and
/1
HL TT
7-99E A heat pump maintains a house at a specified temperature. The rate of heat loss of the house is given. The minimum
power inputs required for different source temperatures are to be determined.
Assumptions The heat pump operates steadily.
Analysis (a) The power input to a heat pump will be a minimum when the heat pump operates in a reversible manner. If the
outdoor air at 25°F is used as the heat source, the COP of the heat pump and the required power input are determined to be
10.15
R 46078/R 460251
1
/1
1
COPCOP revHP,maxHP,
HL TT
and
hp 1
Btu/h 70,000
H
Q
House
78F
70,000 Btu/h
7-28
7-101 A Carnot heat engine is used to drive a Carnot refrigerator. The maximum rate of heat removal from the refrigerated
space and the total rate of heat rejection to the ambient air are to be determined.
Assumptions The heat engine and the refrigerator operate steadily.
Analysis (a) The highest thermal efficiency a heat engine operating between two specified temperature limits can have is the
Carnot efficiency, which is determined from
K 300
L
T
which is also the power input to the refrigerator,
innet,
W
.
The rate of heat removal from the refrigerated space will be a maximum if a Carnot refrigerator is used. The COP
of the Carnot refrigerator is
1
1
27C
7-30
7-104 An air-conditioner with R-134a as the working fluid is considered. The compressor inlet and exit states are specified.
The actual and maximum COPs and the minimum volume flow rate of the refrigerant at the compressor inlet are to be
determined.
Assumptions 1 The air-conditioner operates steadily. 2 The kinetic and potential energy changes are zero.
outdoor temperature are given. The COP and the power input are to be determined.
Analysis (a) The coefficient of performance of this Carnot heat pump depends on the temperature limits in the cycle only,
and is determined from
1
1
Btu/h 2545
13.4
COPHP
7-108 The work output and the source and sink temperatures of a Carnot heat engine are given. The heat supplied to and
rejected from the heat engine are to be determined.
Assumptions 1 The heat engine operates steadily. 2 Heat losses from the
working fluid at the pipes and other components are negligible.
7-109E The operating conditions of a heat pump are given. The minimum temperature of the source that satisfies the
second law of thermodynamics is to be determined.
1200°C
2500
7-34
7-112 A Carnot refrigeration cycle is executed in a closed system with a fixed mass of R-134a. The net work input and the
ratio of maximum-to-minimum temperatures are given. The minimum pressure in the cycle is to be determined.
7-35
7-113 Problem 7-112 is reconsidered. The effect of the net work input on the minimum pressure as the work input
varies from 10 kJ to 30 kJ is to be investigated. The minimum pressure in the refrigeration cycle is to be plotted as a
function of net work input.
Analysis The problem is solved using EES, and the results are tabulated and plotted below.
Analysis: The coefficient of performance of the cycle is given by”
7-36
7-114 Two Carnot heat engines operate in series between specified temperature limits. If the thermal efficiencies of both
engines are the same, the temperature of the intermediate medium between the two engines is to be determined.
Assumptions The engines are said to operate on the Carnot cycle,
which is totally reversible.
7-115 A Carnot heat engine drives a Carnot refrigerator that removes heat from a cold medium at a specified rate. The rate
of heat supply to the heat engine and the total rate of heat rejection to the environment are to be determined.
1K 258/K 300
1/
LH TT
Then power input to the refrigerator becomes
kJ/min .740
6.143
kJ/min 250
COP CR,
innet, L
Q
W
which is equal to the power output of the heat engine,
outnet,
W
.
The thermal efficiency of the Carnot heat engine is determined from
6667.0
K 900
K 300
11
Cth,
H
L
T
T
Then the rate of heat input to this heat engine is determined from the definition of thermal efficiency to be
kJ/min 40.7
outnet,
W
300 K
900 K
HE
R
–15C
250 kJ/min
QH, R
·
QH, HE
·
QL, HE
·
TH
7-38
500 600 700 800 900 1000
260
280
300
320
340
360
380
400
420
440
TH [K]
Qsurr [kJ/min]
Tsurr = 325 K
Tsurr = 300 K
Tsurr = 275 K
–20 –16 –12 -8 -4 0
0
5
10
15
20
25
30
35
TL,C [C]
QH,HE [kJ/min]
–20 -16 –12 -8 -4 0
250
255
260
265
270
275
280
285
TL,C [C]
Qsurr [kJ/min]