11–1C Why is the reversed Carnot cycle executed within the saturation dome not a realistic model for refrigeration cycles?
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11–2
A steady-flow Carnot refrigeration cycle uses refrigerant-134a as the
working fluid. The refrigerant changes from saturated vapor to saturated
liquid at 30°C in the condenser as it rejects heat. The evaporator
pressure is 160 kPa. Show the cycle on a T-s diagram relative to
saturation lines, and determine (a) the coefficient of performance, (b)
the amount of heat absorbed from the refrigerated space, and (c) the net
work input. Answers: (a) 5.64, (b) 147 kJ/kg, (c) 26.1 kJ/kg
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11–3E
Refrigerant-134a enters the condenser of a steadyflow Carnot
refrigerator as a saturated vapor at 90 psia, and it leaves with a
quality of 0.05. The heat absorption from the refrigerated space takes
place at a pressure of 30 psia. Show the cycle on a T-s diagram relative
to saturation lines, and determine (a) the coefficient of performance,
(b) the quality at the beginning of the heat-absorption process, and (c)
the net work input. Ideal and Actual Vapor-Compression Refrigeration
Cycles
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11–4C Does the ideal vapor-compression refrigeration cycle involve any internal irreversibilities?
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11–5C Why is the throttling valve not replaced by an isentropic turbine in the ideal vapor-compression refrigeration cycle?
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11–6C
It is proposed to use water instead of refrigerant134a as the working
fluid in air-conditioning applications where the minimum temperature
never falls below the freezing point. Would you support this proposal?
Explain.
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11–7C
In a refrigeration system, would you recommend condensing the
refrigerant-134a at a pressure of 0.7 or 1.0 MPa if heat is to be
rejected to a cooling medium at 15°C? Why?
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11–8C
Does the area enclosed by the cycle on a T-s diagram represent the net
work input for the reversed Carnot cycle? How about for the ideal
vapor-compression refrigeration cycle?
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11–9C
Consider two vapor-compression refrigeration cycles. The refrigerant
enters the throttling valve as a saturated liquid at 30°C in one cycle
and as subcooled liquid at 30°C in the other one. The evaporator
pressure for both cycles is the same. Which cycle do you think will have
a higher COP?
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11–10C
The COP of vapor-compression refrigeration cycles improves when the
refrigerant is subcooled before it enters the throttling valve. Can the
refrigerant be subcooled indefinitely to maximize this effect, or is
there a lower limit? Explain.
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11–11
A commercial refrigerator with refrigerant-134a as the working fluid is
used to keep the refrigerated space at -30°C by rejecting its waste
heat to cooling water that enters the condenser at 18°C at a rate of
0.25 kg/s and leaves at 26°C. The refrigerant enters the condenser at
1.2 MPa and 65°C and leaves at 42°C. The inlet state of the compressor
is 60 kPa and -34°C and the compressor is estimated to gain a net heat
of 450 W from the surroundings. Determine (a) the quality of the
refrigerant at the evaporator inlet, (b) the refrigeration load, (c) the
COP of the refrigerator, and (d) the theoretical maximum refrigeration
load for the same power input to the compressor.
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11–12
A refrigerator uses refrigerant-134a as the working fluid and operates
on an ideal vapor-compression refrigeration cycle between 0.12 and 0.7
MPa. The mass flow rate of the refrigerant is 0.05 kg/s. Show the cycle
on a T-s diagram with respect to saturation lines. Determine (a) the
rate of heat removal from the refrigerated space and the power input to
the compressor, (b) the rate of heat rejection to the environment, and
(c) the coefficient of performance. Answers: (a) 7.41 kW, 1.83 kW, (b)
9.23 kW, (c) 4.06
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11–13 Repeat Prob. 11–12 for a condenser pressure of 0.9 MPa.
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11–14
If the throttling valve in Prob. 11–12 is replaced by an isentropic
turbine, determine the percentage increase in the COP and in the rate of
heat removal from the refrigerated space. Answers: 4.2 percent, 4.2
percent
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11–15
Consider a 300 kJ/min refrigeration system that operates on an ideal
vapor-compression refrigeration cycle with refrigerant-134a as the
working fluid. The refrigerant enters the compressor as saturated vapor
at 140 kPa and is compressed to 800 kPa. Show the cycle on a T-s diagram
with respect to saturation lines, and determine (a) the quality of the
refrigerant at the end of the throttling process, (b) the coefficient of
performance, and (c) the power input to the compressor.
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11–16
Reconsider Prob. 11–15. Using EES (or other) software, investigate the
effect of evaporator pressure on the COP and the power input. Let the
evaporator pressure vary from 100 to 400 kPa. Plot the COP and the power
input as functions of evaporator pressure, and discuss the results.
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11–17
Repeat Prob. 11–15 assuming an isentropic efficiency of 85 percent for
the compressor. Also, determine the rate of exergy destruction
associated with the compression process in this case. Take T0 = 298 K.
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11–18
Refrigerant-134a enters the compressor of a refrigerator as superheated
vapor at 0.14 MPa and -10°C at a rate of 0.12 kg/s, and it leaves at
0.7 MPa and 50°C. The refrigerant is cooled in the condenser to 24°C and
0.65 MPa, and it is throttled to 0.15 MPa. Disregarding any heat
transfer and pressure drops in the connecting lines between the
components, show the cycle on a T-s diagram with respect to saturation
lines, and determine (a) the rate of heat removal from the refrigerated
space and the power input to the compressor, (b) the isentropic
efficiency of the compressor, and (c) the COP of the refrigerator.
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11–19E
An ice-making machine operates on the ideal vapor-compression cycle,
using refrigerant-134a. The refrigerant enters the compressor as
saturated vapor at 20 psia and leaves the condenser as saturated liquid
at 80 psia. Water enters the ice machine at 55°F and leaves as ice at
25°F. For an ice production rate of 15 lbm/h, determine the power input
to the ice machine (169 Btu of heat needs to be removed from each lbm of
water at 55°F to turn it into ice at 25°F).
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11–20
Refrigerant-134a enters the compressor of a refrigerator at 140 kPa and
-10°C at a rate of 0.3 m3/min and leaves at 1 MPa. The isentropic
efficiency of the compressor is 78 percent. The refrigerant enters the
throttling valve at 0.95 MPa and 30°C and leaves the evaporator as
saturated vapor at -18.5°C. Show the cycle on a T-s diagram with respect
to saturation lines, and determine (a) the power input to the
compressor, (b) the rate of heat removal from the refrigerated space,
and (c) the pressure drop and rate of heat gain in the line between the
evaporator and the compressor.
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11–21
Reconsider Prob. 11–20. Using EES (or other) software, investigate the
effects of varying the compressor isentropic efficiency over the range
60 to 100 percent and the compressor inlet volume flow rate from 0.1 to
1.0 m3/min on the power input and the rate of refrigeration. Plot the
rate of refrigeration and the power input to the compressor as functions
of compressor efficiency for compressor inlet volume flow rates of 0.1,
0.5, and 1.0 m3/min, and discuss the results.
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11–22
A refrigerator uses refrigerant-134a as the working fluid and operates
on the ideal vapor-compression refrigeration cycle. The refrigerant
enters the evaporator at 120 kPa with a quality of 30 percent and leaves
the compressor at 60°C. If the compressor consumes 450 W of power,
determine (a) the mass flow rate of the refrigerant, (b) the condenser
pressure, and (c) the COP of the refrigerator. Answers: (a) 0.00727
kg/s, (b) 672 kPa, (c) 2.43
Selecting the Right Refrigerant
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11–23C When selecting a refrigerant for a certain application, what qualities would you look for in the refrigerant?
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11–24C
Consider a refrigeration system using refrigerant134a as the working
fluid. If this refrigerator is to operate in an environment at 30°C,
what is the minimum pressure to which the refrigerant should be
compressed? Why?
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11–25C
A refrigerant-134a refrigerator is to maintain the refrigerated space
at -10°C. Would you recommend an evaporator pressure of 0.12 or 0.14 MPa
for this system? Why?
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11–26
A refrigerator that operates on the ideal vaporcompression cycle with
refrigerant-134a is to maintain the refrigerated space at -10°C while
rejecting heat to the environment at 25°C. Select reasonable pressures
for the evaporator and the condenser, and explain why you chose those
values.
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11–27
A heat pump that operates on the ideal vaporcompression cycle with
refrigerant-134a is used to heat a house and maintain it at 22°C by
using underground water at 10°C as the heat source. Select reasonable
pressures for the evaporator and the condenser, and explain why you
chose those values.
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11–28C Do you think a heat pump system will be more cost-effective in New York or in Miami? Why?
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11–29C
What is a water-source heat pump? How does the COP of a water-source
heat pump system compare to that of an air-source system?
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11–30E
A heat pump that operates on the ideal vaporcompression cycle with
refrigerant-134a is used to heat a house and maintain it at 75°F by
using underground water at 50°F as the heat source. The house is losing
heat at a rate of 60,000 Btu/h. The evaporator and condenser pressures
are 50 and 120 psia, respectively. Determine the power input to the heat
pump and the electric power saved by using a heat pump instead of a
resistance heater. Answers: 2.46 hp, 21.1 hp
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11–31
A heat pump that operates on the ideal vaporcompression cycle with
refrigerant-134a is used to heat water from 15 to 45°C at a rate of 0.12
kg/s. The condenser and evaporator pressures are 1.4 and 0.32 MPa,
respectively. Determine the power input to the heat pump.
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11–32
A heat pump using refrigerant-134a heats a house by using underground
water at 8°C as the heat source. The house is losing heat at a rate of
60,000 kJ/h. The refrigerant enters the compressor at 280 kPa and 0°C,
and it leaves at 1 MPa and 60°C. The refrigerant exits the condenser at
30°C. Determine (a) the power input to the heat pump, (b) the rate of
heat absorption from the water, and (c) the increase in electric power
input if an electric resistance heater is used instead of a heat pump.
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11–33
Reconsider Prob. 11–32. Using EES (or other) software, investigate the
effect of varying the compressor isentropic efficiency over the range 60
to 100 percent. Plot the power input to the compressor and the electric
power saved by using a heat pump rather than electric resistance
heating as functions of compressor efficiency, and discuss the results.
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11–34
Refrigerant-134a enters the condenser of a residential heat pump at 800
kPa and 55°C at a rate of 0.018 kg/s and leaves at 750 kPa subcooled by
3°C. The refrigerant enters the compressor at 200 kPa superheated by
4°C. Determine (a) the isentropic efficiency of the compressor, (b) the
rate of heat supplied to the heated room, and (c) the COP of the heat
pump. Also, determine (d) the COP and the rate of heat supplied to the
heated room if this heat pump operated on the ideal vapor-compression
cycle between the pressure limits of 200 and 800 kPa.
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11–35
A heat pump with refrigerant-134a as the working fluid is used to keep a
space at 25°C by absorbing heat from geothermal water that enters the
evaporator at 50°C at a rate of 0.065 kg/s and leaves at 40°C. The
refrigerant enters the evaporator at 20°C with a quality of 23 percent
and leaves at the inlet pressure as saturated vapor. The refrigerant
loses 300 W of heat to the surroundings as it flows through the
compressor and the refrigerant leaves the compressor at 1.4 MPa at the
same entropy as the inlet. Determine (a) the degrees of subcooling of
the refrigerant in the condenser, (b) the mass flow rate of the
refrigerant, (c) the heating load and the COP of the heat pump, and (d)
the theoretical minimum power input to the compressor for the same
heating load. Answers: (a) 3.8°C, (b) 0.0194 kg/s, (c) 3.07 kW, 4.68,
(d) 0.238 kW Innovative Refrigeration Systems
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11–36C What is cascade refrigeration? What are the advantages and disadvantages of cascade refrigeration?
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11–37C
How does the COP of a cascade refrigeration system compare to the COP
of a simple vapor-compression cycle operating between the same pressure
limits?
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11–38C
A certain application requires maintaining the refrigerated space at
-32°C. Would you recommend a simple refrigeration cycle with
refrigerant-134a or a two-stage cascade refrigeration cycle with a
different refrigerant at the bottoming cycle? Why?
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11–39C
Consider a two-stage cascade refrigeration cycle and a two-stage
compression refrigeration cycle with a flash chamber. Both cycles
operate between the same pressure limits and use the same refrigerant.
Which system would you favor? Why?
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11–40C
Can a vapor-compression refrigeration system with a single compressor
handle several evaporators operating at different pressures? How?
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11–41C In the liquefaction process, why are gases compressed to very high pressures?
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11–42
Consider a two-stage cascade refrigeration system operating between the
pressure limits of 0.8 and 0.14 MPa.
Each stage operates on the ideal vapor-compression refrigeration cycle
with refrigerant-134a as the working fluid. Heat rejection from the
lower cycle to the upper cycle takes place in an adiabatic counterflow
heat exchanger where both streams enter at about 0.4 MPa. If the mass
flow rate of the refrigerant through the upper cycle is 0.24 kg/s,
determine (a) the mass flow rate of the refrigerant through the lower
cycle, (b) the rate of heat removal from the refrigerated space and the
power input to the compressor, and (c) the coefficient of performance of
this cascade refrigerator.
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11–43 Repeat Prob. 11–42 for a heat exchanger pressure of 0.55 MPa.
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11–44
A two-stage compression refrigeration system operates with
refrigerant-134a between the pressure limits of 1 and 0.14 MPa. The
refrigerant leaves the condenser as a saturated liquid and is throttled
to a flash chamber operating at 0.5 MPa. The refrigerant leaving the
low-pressure compressor at 0.5 MPa is also routed to the flash chamber.
The vapor in the flash chamber is then compressed to the condenser
pressure by the high-pressure compressor, and the liquid is throttled to
the evaporator pressure. Assuming the refrigerant leaves the evaporator
as saturated vapor and both compressors are isentropic, determine (a)
the fraction of the refrigerant that evaporates as it is throttled to
the flash chamber, (b) the rate of heat removed from the refrigerated
space for a mass flow rate of 0.25 kg/s through the condenser, and (c)
the coefficient of performance.
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11–45
Reconsider Prob. 11–44. Using EES (or other) software, investigate the
effect of the various refrigerants for compressor efficiencies of 80,
90, and 100 percent. Compare the performance of the refrigeration system
with different refrigerants.
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11–46 Repeat Prob. 11–44 for a flash chamber pressure of 0.32 MPa.
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11–47
Consider a two-stage cascade refrigeration system operating between the
pressure limits of 1.2 MPa and 200 kPa with refrigerant-134a as the
working fluid. Heat rejection from the lower cycle to the upper cycle
takes place in an adiabatic counterflow heat exchanger where the
pressure in the upper and lower cycles are 0.4 and 0.5 MPa,
respectively. In both cycles, the refrigerant is a saturated liquid at
the condenser exit and a saturated vapor at the compressor inlet, and
the isentropic efficiency of the compressor is 80 percent. If the mass
flow rate of the refrigerant through the lower cycle is 0.15 kg/s,
determine (a) the mass flow rate of the refrigerant through the upper
cycle, (b) the rate of heat removal from the refrigerated space, and (c)
the COP of this refrigerator.
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11–48
Consider a two-stage cascade refrigeration system operating between the
pressure limits of 1.2 MPa and 200 kPa with refrigerant-134a as the
working fluid. The refrigerant leaves the condenser as a saturated
liquid and is throttled to a flash chamber operating at 0.45 MPa. Part
of the refrigerant evaporates during this flashing process, and this
vapor is mixed with the refrigerant leaving the low-pressure compressor.
The mixture is then compressed to the condenser pressure by the
high-pressure compressor. The liquid in the flash chamber is throttled
to the evaporator pressure and cools the refrigerated space as it
vaporizes in the evaporator. The mass flow rate of the refrigerant
through the low-pressure compressor is 0.15 kg/s. Assuming the
refrigerant leaves the evaporator as a saturated vapor and the
isentropic efficiency is 80 percent for both compressors, determine (a)
the mass flow rate of the refrigerant through the high-pressure
compressor, (b) the rate of heat removal from the refrigerated space,
and (c) the COP of this refrigerator. Also, determine (d) the rate of
heat removal and the COP if this refrigerator operated on a single-stage
cycle between the same pressure limits with the same compressor
efficiency and the same flow rate as in part (a).
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11–49C How does the ideal-gas refrigeration cycle differ from the Brayton cycle?
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11–50C Devise a refrigeration cycle that works on the reversed Stirling cycle. Also, determine the COP for this cycle.
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11–51C How does the ideal-gas refrigeration cycle differ from the Carnot refrigeration cycle?
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11–52C How is the ideal-gas refrigeration cycle modified for aircraft cooling?
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11–53C
In gas refrigeration cycles, can we replace the turbine by an expansion
valve as we did in vapor-compression refrigeration cycles? Why?
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11–54C How do we achieve very low temperatures with gas refrigeration cycles?
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11–55
An ideal gas refrigeration cycle using air as the working fluid is to
maintain a refrigerated space at -23°C while rejecting heat to the
surrounding medium at 27°C. If the pressure ratio of the compressor is
3, determine (a) the maximum and minimum temperatures in the cycle, (b)
the coefficient of performance, and (c) the rate of refrigeration for a
mass flow rate of 0.08 kg/s.
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11–56
Air enters the compressor of an ideal gas refrigeration cycle at 12°C
and 50 kPa and the turbine at 47°C and 250 kPa. The mass flow rate of
air through the cycle is 0.08 kg/s. Assuming variable specific heats for
air, determine (a) the rate of refrigeration, (b) the net power input,
and (c) the coefficient of performance.
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11–57
Reconsider Prob. 11–56. Using EES (or other) software, study the
effects of compressor and turbine isentropic efficiencies as they are
varied from 70 to 100 percent on the rate of refrigeration, the net
power input, and the COP. Plot the T-s diagram of the cycle for the
isentropic case.
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11–58E
Air enters the compressor of an ideal gas refrigeration cycle at 40°F
and 10 psia and the turbine at 120°F and 30 psia. The mass flow rate of
air through the cycle is 0.5 lbm/s. Determine (a) the rate of
refrigeration, (b) the net power input, and (c) the coefficient of
performance.
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11–59
Repeat Prob. 11–56 for a compressor isentropic efficiency of 80 percent
and a turbine isentropic efficiency of 85 percent.
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11–60
A gas refrigeration cycle with a pressure ratio of 3 uses helium as the
working fluid. The temperature of the helium is -10°C at the compressor
inlet and 50°C at the turbine inlet. Assuming adiabatic efficiencies of
80 percent for both the turbine and the compressor, determine (a) the
minimum temperature in the cycle, (b) the coefficient of performance,
and (c) the mass flow rate of the helium for a refrigeration rate of 18
kW.
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11–61
A gas refrigeration system using air as the working fluid has a
pressure ratio of 4. Air enters the compressor at -7°C. The
high-pressure air is cooled to 27°C by rejecting heat to the
surroundings. It is further cooled to -15°C by regenerative cooling
before it enters the turbine. Assuming both the turbine and the
compressor to be isentropic and using constant specific heats at room
temperature, determine (a) the lowest temperature that can be obtained
by this cycle, (b) the coefficient of performance of the cycle, and (c)
the mass flow rate of air for a refrigeration rate of 12 kW. Answers:
(a) -99.4°C, (b) 1.12, (c) 0.237 kg/s
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11–62 Repeat Prob. 11–61 assuming isentropic efficiencies of 75 percent for the compressor and 80 percent for the turbine.
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11–63
A gas refrigeration system using air as the working fluid has a
pressure ratio of 5. Air enters the compressor at 0°C. The high-pressure
air is cooled to 35°C by rejecting heat to the surroundings. The
refrigerant leaves the turbine at -80°C and then it absorbs heat from
the refrigerated space before entering the regenerator. The mass flow
rate of air is 0.4 kg/s. Assuming isentropic efficiencies of 80 percent
for the compressor and 85 percent for the turbine and using constant
specific heats at room temperature, determine (a) the effectiveness of
the regenerator, (b) the rate of heat removal from the refrigerated
space, and (c) the COP of the cycle. Also, determine (d) the
refrigeration load and the COP if this system operated on the simple gas
refrigeration cycle. Use the same compressor inlet temperature as
given, the same turbine inlet temperature as calculated, and the same
compressor and turbine efficiencies. Answers: (a) 0.434, (b) 21.4 kW,
(c) 0.478, (d) 24.7 kW, 0.599 Absorption Refrigeration Systems
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11–64C
What is absorption refrigeration? How does an absorption refrigeration
system differ from a vapor-compression refrigeration system?
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11–65C What are the advantages and disadvantages of absorption refrigeration?
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11–66C Can water be used as a refrigerant in air-conditioning applications? Explain.
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11–67C In absorption refrigeration cycles, why is the fluid in the absorber cooled and the fluid in the generator heated?
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11–68C How is the coefficient of performance of an absorption refrigeration system defined?
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11–69C What are the functions of the rectifier and the regenerator in an absorption refrigeration system?
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11–70
An absorption refrigeration system that receives heat from a source at
130°C and maintains the refrigerated space at -5°C is claimed to have a
COP of 2. If the environment temperature is 27°C, can this claim be
valid? Justify your answer.
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11–71
An absorption refrigeration system receives heat from a source at 120°C
and maintains the refrigerated space at 0°C. If the temperature of the
environment is 25°C, what is the maximum COP this absorption
refrigeration system can have?
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11–72
Heat is supplied to an absorption refrigeration system from a
geothermal well at 130°C at a rate of 5 x 105 kJ/h. The environment is
at 25°C, and the refrigerated space is maintained at -30°C. Determine
the maximum rate at which this system can remove heat from the
refrigerated space.
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11–73E
Heat is supplied to an absorption refrigeration system from a
geothermal well at 250°F at a rate of 105 Btu/h. The environment is at
80°F, and the refrigerated space is maintained at 0°F. If the COP of the
system is 0.55, determine the rate at which this system can remove heat
from the refrigerated space.
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11–74
A reversible absorption refrigerator consists of a reversible heat
engine and a reversible refrigerator. The system removes heat from a
cooled space at -10°C at a rate of 22 kW. The refrigerator operates in
an environment at 25°C. If the heat is supplied to the cycle by
condensing saturated steam at 200°C, determine (a) the rate at which the
steam condenses and (b) the power input to the reversible refrigerator.
(c) If the COP of an actual absorption chiller at the same temperature
limits has a COP of 0.7, determine the second law efficiency of this
chiller.
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11–75C What is a thermoelectric circuit?
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11–76C Describe the Seebeck and the Peltier effects.
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11–77C
Consider a circular copper wire formed by connecting the two ends of a
copper wire. The connection point is now heated by a burning candle. Do
you expect any current to flow through the wire?
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11–78C
An iron and a constantan wire are formed into a closed circuit by
connecting the ends. Now both junctions are heated and are maintained at
the same temperature. Do you expect any electric current to flow
through this circuit?
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11–79C
A copper and a constantan wire are formed into a closed circuit by
connecting the ends. Now one junction is heated by a burning candle
while the other is maintained at room temperature. Do you expect any
electric current to flow through this circuit?
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11–80C How does a thermocouple work as a temperature measurement device?
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11–81C Why are semiconductor materials preferable to metals in thermoelectric refrigerators?
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11–82C Is the efficiency of a thermoelectric generator limited by the Carnot efficiency? Why?
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11–83E
A thermoelectric generator receives heat from a source at 340°F and
rejects the waste heat to the environment at 90°F. What is the maximum
thermal efficiency this thermoelectric generator can have?
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11–84
A thermoelectric refrigerator removes heat from a refrigerated space at
-5°C at a rate of 130 W and rejects it to an environment at 20°C.
Determine the maximum coefficient of performance this thermoelectric
refrigerator can have and the minimum required power input.
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11–85
A thermoelectric cooler has a COP of 0.15 and removes heat from a
refrigerated space at a rate of 180 W. Determine the required power
input to the thermoelectric cooler, in W.
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11–86E
A thermoelectric cooler has a COP of 0.15 and removes heat from a
refrigerated space at a rate of 20 Btu/min. Determine the required power
input to the thermoelectric cooler, in hp.
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11–87
A thermoelectric refrigerator is powered by a 12-V car battery that
draws 3 A of current when running. The refrigerator resembles a small
ice chest and is claimed to cool nine canned drinks, 0.350-L each, from
25 to 3°C in 12 h. Determine the average COP of this refrigerator.
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11–88E
Thermoelectric coolers that plug into the cigarette lighter of a car
are commonly available. One such cooler is claimed to cool a 12-oz
(0.771-lbm) drink from 78 to 38°F or to heat a cup of coffee from 75 to
130°F in about 15 min in a well-insulated cup holder. Assuming an
average COP of 0.2 in the cooling mode, determine (a) the average rate
of heat removal from the drink, (b) the average rate of heat supply to
the coffee, and (c) the electric power drawn from the battery of the
car, all in W.
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11–89
It is proposed to run a thermoelectric generator in conjunction with a
solar pond that can supply heat at a rate of 106 kJ/h at 80°C. The waste
heat is to be rejected to the environment at 30°C. What is the maximum
power this thermoelectric generator can produce?
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11–90
Consider a steady-flow Carnot refrigeration cycle that uses
refrigerant-134a as the working fluid. The maximum and minimum
temperatures in the cycle are 30 and -20°C, respectively. The quality of
the refrigerant is 0.15 at the beginning of the heat absorption process
and 0.80 at the end. Show the cycle on a T-s diagram relative to
saturation lines, and determine (a) the coefficient of performance, (b)
the condenser and evaporator pressures, and (c) the net work input.
Get 11.90 exercise solution

11–91
A large refrigeration plant is to be maintained at -15°C, and it
requires refrigeration at a rate of 100 kW. The condenser of the plant
is to be cooled by liquid water, which experiences a temperature rise of
8°C as it flows over the coils of the condenser. Assuming the plant
operates on the ideal vapor-compression cycle using refrigerant-134a
between the pressure limits of 120 and 700 kPa, determine (a) the mass
flow rate of the refrigerant, (b) the power input to the compressor, and
(c) the mass flow rate of the cooling water.
Get 11.91 exercise solution

11–92
Reconsider Prob. 11–91. Using EES (or other) software, investigate the
effect of evaporator pressure on the COP and the power input. Let the
evaporator pressure vary from 120 to 380 kPa. Plot the COP and the power
input as functions of evaporator pressure, and discuss the results.
Get 11.92 exercise solution

11–93
Repeat Prob. 11–91 assuming the compressor has an isentropic efficiency
of 75 percent. Also, determine the rate of exergy destruction
associated with the compression process in this case. Take T0 = 25°C.
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11–94
A heat pump that operates on the ideal vaporcompression cycle with
refrigerant-134a is used to heat a house. The mass flow rate of the
refrigerant is 0.32 kg/s. The condenser and evaporator pressures are 900
and 200 kPa, respectively. Show the cycle on a T-s diagram with respect
to saturation lines, and determine (a) the rate of heat supply to the
house, (b) the volume flow rate of the refrigerant at the compressor
inlet, and (c) the COP of this heat pump.
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11–95
Derive a relation for the COP of the two-stage refrigeration system
with a flash chamber as shown in Fig. 11–12 in terms of the enthalpies
and the quality at state 6. Consider a unit mass in the condenser.
Get 11.95 exercise solution

11–96
Consider a two-stage compression refrigeration system operating between
the pressure limits of 0.8 and 0.14 MPa. The working fluid is
refrigerant-134a. The refrigerant leaves the condenser as a saturated
liquid and is throttled to a flash chamber operating at 0.4 MPa. Part of
the refrigerant evaporates during this flashing process, and this vapor
is mixed with the refrigerant leaving the low-pressure compressor. The
mixture is then compressed to the condenser pressure by the
high-pressure compressor. The liquid in the flash chamber is throttled
to the evaporator pressure, and it cools the refrigerated space as it
vaporizes in the evaporator. Assuming the refrigerant leaves the
evaporator as saturated vapor and both compressors are isentropic,
determine (a) the fraction of the refrigerant that evaporates as it is
throttled to the flash chamber, (b) the amount of heat removed from the
refrigerated space and the compressor work per unit mass of refrigerant
flowing through the condenser, and (c) the coefficient of performance.
Answers: (a) 0.165, (b) 146.4 kJ/kg, 32.6 kJ/kg, (c) 4.49
Get 11.96 exercise solution

11–97
An aircraft on the ground is to be cooled by a gas refrigeration cycle
operating with air on an open cycle. Air enters the compressor at 30°C
and 100 kPa and is compressed to 250 kPa. Air is cooled to 70°C before
it enters the turbine. Assuming both the turbine and the compressor to
be isentropic, determine the temperature of the air leaving the turbine
and entering the cabin.
Get 11.97 exercise solution

11–98
Consider a regenerative gas refrigeration cycle using helium as the
working fluid. Helium enters the compressor at 100 kPa and -10°C and is
compressed to 300 kPa. Helium is then cooled to 20°C by water. It then
enters the regenerator where it is cooled further before it enters the
turbine. Helium leaves the refrigerated space at -25°C and enters the
regenerator. Assuming both the turbine and the compressor to be
isentropic, determine (a) the temperature of the helium at the turbine
inlet, (b) the coefficient of performance of the cycle, and (c) the net
power input required for a mass flow rate of 0.45 kg/s.
Get 11.98 exercise solution

11–99
An absorption refrigeration system is to remove heat from the
refrigerated space at -10°C at a rate of 12 kW while operating in an
environment at 25°C. Heat is to be supplied from a solar pond at 85°C.
What is the minimum rate of heat supply required?
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11–100
Reconsider Prob. 11–99. Using EES (or other) software, investigate the
effect of the source temperature on the minimum rate of heat supply. Let
the source temperature vary from 50 to 250°C. Plot the minimum rate of
heat supply as a function of source temperature, and discuss the
results.
Get 11.100 exercise solution

11–101
A typical 200-m2 house can be cooled adequately by a 3.5-ton air
conditioner whose COP is 4.0. Determine the rate of heat gain of the
house when the air conditioner is running continuously to maintain a
constant temperature in the house.
Get 11.101 exercise solution

11–102
Rooms with floor areas of up to 15-m2 are cooled adequately by window
air conditioners whose cooling capacity is 5000 Btu/h. Assuming the COP
of the air conditioner to be 3.5, determine the rate of heat gain of the
room, in Btu/h, when the air conditioner is running continuously to
maintain a constant room temperature.
Get 11.102 exercise solution

11–103
A gas refrigeration system using air as the working fluid has a
pressure ratio of 5. Air enters the compressor at 0°C. The high-pressure
air is cooled to 35°C by rejecting heat to the surroundings. The
refrigerant leaves the turbine at -80°C and enters the refrigerated
space where it absorbs heat before entering the regenerator. The mass
flow rate of air is 0.4 kg/s. Assuming isentropic efficiencies of 80
percent for the compressor and 85 percent for the turbine and using
variable specific heats, determine (a) the effectiveness of the
regenerator, (b) the rate of heat removal from the refrigerated space,
and (c) the COP of the cycle. Also, determine (d) the refrigeration load
and the COP if this system operated on the simple gas refrigeration
cycle. Use the same compressor inlet temperature as given, the same
turbine inlet temperature as calculated, and the same compressor and
turbine efficiencies.
Get 11.103 exercise solution

11–104
An air conditioner with refrigerant-134a as the working fluid is used
to keep a room at 26°C by rejecting the waste heat to the outside air at
34°C. The room is gaining heat through the walls and the windows at a
rate of 250 kJ/min while the heat generated by the computer, TV, and
lights amounts to 900 W. An unknown amount of heat is also generated by
the people in the room. The condenser and evaporator pressures are 1200
and 500 kPa, respectively. The refrigerant is saturated liquid at the
condenser exit and saturated vapor at the compressor inlet. If the
refrigerant enters the compressor at a rate of 100 L/min and the
isentropic efficiency of the compressor is 75 percent, determine (a) the
temperature of the refrigerant at the compressor exit, (b) the rate of
heat generation by the people in the room, (c) the COP of the air
conditioner, and (d) the minimum volume flow rate of the refrigerant at
the compressor inlet for the same compressor inlet and exit conditions.
Get 11.104 exercise solution

11–105
A heat pump water heater (HPWH) heats water by absorbing heat from the
ambient air and transferring it to water. The heat pump has a COP of 2.2
and consumes 2 kW of electricity when running. Determine if this heat
pump can be used to meet the cooling needs of a room most of the time
for “free” by absorbing heat from the air in the room. The rate of heat
gain of a room is usually less than 5000 kJ/h.
Get 11.105 exercise solution

11–106
The vortex tube (also known as a Ranque or Hirsch tube) is a device
that produces a refrigeration effect by expanding pressurized gas such
as air in a tube (instead of a turbine as in the reversed Brayton
cycle). It was invented and patented by Ranque in 1931 and improved by
Hirsch in 1945, and is commercially available in various sizes. The
vortex tube is simply a straight circular tube equipped with a nozzle,
as shown in the figure. The compressed gas at temperature T1 and
pressure P1 is accelerated in the nozzle by expanding it to nearly
atmospheric pressure and is introduced into the tube tangentially at a
very high (typically supersonic) velocity to produce a swirling motion
(vortex) within the tube. The rotating gas is allowed to exit through
the full-size tube that extends to the right, and the mass flow rate is
controlled by a valve located about 30 diameters downstream. A smaller
amount of air at the core region is allowed to escape to the left
through a small aperture at the center. It is observed that the gas that
is in the core region and escapes through the central aperture is cold
while the gas that is in the peripheral region and escapes through the
full-size tube is hot. If the temperature and the mass flow rate of the
cold stream are Tc and m . c, respectively, the rate of refrigeration in
the vortex tube can be expressed as

where cp is the specific heat of the gas and T1 Tc is the temperature
drop of the gas in the vortex tube (the cooling effect). Temperature
drops as high as 60°C (or 108°F) are obtained at high pressure ratios of
about 10. The coefficient of performance of a vortex tube can be
defined as the ratio of the refrigeration rate as given above to the
power used to compress the gas. It ranges from about 0.1 to 0.15, which
is well below the COPs of ordinary vapor compression refrigerators. This
interesting phenomenon can be explained as follows: the centrifugal
force creates a radial pressure gradient in the vortex, and thus the gas
at the periphery is pressurized and heated by the gas at the core
region, which is cooled as a result. Also, energy is transferred from
the inner layers toward the outer layers as the outer layers slow down
the inner layers because of fluid viscosity that tends to produce a
solid vortex. Both of these effects cause the energy and thus the
temperature of the gas in the core region to decline. The conservation
of energy requires the energy of the fluid at the outer layers to
increase by an equivalent amount. The vortex tube has no moving parts,
and thus it is inherently reliable and durable. The ready availability
of the compressed air at pressures up to 10 atm in most industrial
facilities makes the vortex tube particularly attractive in such
settings. Despite its low efficiency, the vortex tube has found
application in small-scale industrial spot-cooling operations such as
cooling of soldered parts or critical electronic components, cooling
drinking water, and cooling the suits of workers in hot environments.
Consider a vortex tube that receives compressed air at 500 kPa and 300 K
and supplies 25 percent of it as cold air at 100 kPa and 278 K. The
ambient air is at 300 K and 100 kPa, and the compressor has an
isentropic efficiency of 80 percent. The air suffers a pressure drop of
35 kPa in the aftercooler and the compressed air lines between the
compressor and the vortex tube. (a) Without performing any calculations,
explain how the COP of the vortex tube would compare to the COP of an
actual air refrigeration system based on the reversed Brayton cycle for
the same pressure ratio. Also, compare the minimum temperatures that can
be obtained by the two systems for the same inlet temperature and
pressure. (b) Assuming the vortex tube to be adiabatic and using
specific heats at room temperature, determine the exit temperature of
the hot fluid stream. (c) Show, with calculations, that this process
does not violate the second law of thermodynamics. (d) Determine the
coefficient of performance of this refrigeration system, and compare it
to the COP of a Carnot refrigerator.
Get 11.106 exercise solution

11–107 Repeat Prob. 11–106 for a pressure of 600 kPa at the vortex tube intake.
Get 11.107 exercise solution

11–108
Using EES (or other) software, investigate the effect of the evaporator
pressure on the COP of an ideal vapor-compression refrigeration cycle
with R-134a as the working fluid. Assume the condenser pressure is kept
constant at 1 MPa while the evaporator pressure is varied from 100 kPa
to 500 kPa. Plot the COP of the refrigeration cycle against the
evaporator pressure, and discuss the results.
Get 11.108 exercise solution

11–109
Using EES (or other) software, investigate the effect of the condenser
pressure on the COP of an ideal vapor-compression refrigeration cycle
with R-134a as the working fluid. Assume the evaporator pressure is kept
constant at 120 kPa while the condenser pressure is varied from 400 to
1400 kPa. Plot the COP of the refrigeration cycle against the condenser
pressure, and discuss the results.
Get 11.109 exercise solution

11–110
Consider a heat pump that operates on the reversed Carnot cycle with
R-134a as the working fluid executed under the saturation dome between
the pressure limits of 140 and 800 kPa. R-134a changes from saturated
vapor to saturated liquid during the heat rejection process. The net
work input for this cycle is (a) 28 kJ/kg (b) 34 kJ/kg (c) 49 kJ/kg
(d)144 kJ/kg (e) 275 kJ/kg
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11–111
A refrigerator removes heat from a refrigerated space at -5°C at a rate
of 0.35 kJ/s and rejects it to an environment at 20°C. The minimum
required power input is (a) 30 W (b) 33 W (c) 56 W (d)124 W (e) 350 W
Get 11.111 exercise solution

11–112
A refrigerator operates on the ideal vapor compression refrigeration
cycle with R-134a as the working fluid between the pressure limits of
120 and 800 kPa. If the rate of heat removal from the refrigerated space
is 32 kJ/s, the mass flow rate of the refrigerant is (a) 0.19 kg/s (b)
0.15 kg/s (c) 0.23 kg/s (d)0.28 kg/s (e) 0.81 kg/s
Get 11.112 exercise solution

11–113
A heat pump operates on the ideal vapor compression refrigeration cycle
with R-134a as the working fluid between the pressure limits of 0.32
and 1.2 MPa. If the mass flow rate of the refrigerant is 0.193 kg/s, the
rate of heat supply by the heat pump to the heated space is (a) 3.3 kW
(b) 23 kW (c) 26 kW (d)31 kW (e) 45 kW
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11–114
An ideal vapor compression refrigeration cycle with R-134a as the
working fluid operates between the pressure limits of 120 kPa and 1000
kPa. The mass fraction of the refrigerant that is in the liquid phase at
the inlet of the evaporator is (a) 0.65 (b) 0.60 (c) 0.40 (d)0.55 (e)
0.35
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11–115
Consider a heat pump that operates on the ideal vapor compression
refrigeration cycle with R-134a as the working fluid between the
pressure limits of 0.32 and 1.2 MPa. The coefficient of performance of
this heat pump is (a) 0.17 (b) 1.2 (c) 3.1 (d)4.9 (e) 5.9
Get 11.115 exercise solution

11–116
An ideal gas refrigeration cycle using air as the working fluid
operates between the pressure limits of 80 and 280 kPa. Air is cooled to
35°C before entering the turbine. The lowest temperature of this cycle
is (a) -58°C (b) -26°C (c) 5°C (d)11°C (e) 24°C
Get 11.116 exercise solution

11–117
Consider an ideal gas refrigeration cycle using helium as the working
fluid. Helium enters the compressor at 100 kPa and -10°C and compressed
to 250 kPa. Helium is then cooled to 20°C before it enters the turbine.
For a mass flow rate of 0.2 kg/s, the net power input required is (a)
9.3 kW (b) 27.6 kW (c) 48.8 kW (d)93.5 kW (e) 119 kW
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11–118
An absorption air-conditioning system is to remove heat from the
conditioned space at 20°C at a rate of 150 kJ/s while operating in an
environment at 35°C. Heat is to be supplied from a geothermal source at
140°C. The minimum rate of heat supply is (a) 86 kJ/s (b) 21 kJ/s (c) 30
kJ/s (d)61 kJ/s (e) 150 kJ/s
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11–119
Consider a refrigerator that operates on the vapor compression
refrigeration cycle with R-134a as the working fluid. The refrigerant
enters the compressor as saturated vapor at 160 kPa, and exits at 800
kPa and 50°C, and leaves the condenser as saturated liquid at 800 kPa.
The coefficient of performance of this refrigerator is (a) 2.6 (b) 1.0
(c) 4.2 (d)3.2 (e) 4.4 Get 11.119 exercise solution

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