Modern Engineering Thermodynamics

588 CHAPTER 14: Vapor and Gas Refrigeration Cycles
47.* A new refrigerator-freezer combination unit is being designed
with a dual-evaporator system to be used in a recreational
vehicle. The freezer compartment is to be at −14.0°C and the
refrigerator compartment is to be at 8.0°C. The outlet of the
condenser is at 20.0°C. The cooling capacities of both the
refrigerator and the freezer compartments are to be 200. kJ/h
each. The system will use refrigerant R-134a with a compressor
isentropic efficiency of 70.0%. Determine
a. The coefficient of performance for this design.
b. The mass flow rate of refrigerant required.
c. The quality at the outlet of the refrigeration evaporator.
48.* A reversed Brayton cycle with an isentropic pressure ratio of 1.75
is to be used to refrigerate a food locker. The refrigerant is air.
The compressor and expander inlet temperatures are 0.00°C and
14.0°C, respectively. Determine
a. The ASC coefficient of performance of this system.
b. The Carnot coefficient of performance for a refrigerator
operating between the same temperature limits.
c. The compressor and expander outlet temperatures.
49. In calculating the reversed Carnot ASC coefficient of
performance for comparison with that of a reversed Brayton
ASC, the temperature limits are always taken as T L = “the
compressor inlet temperature,” and T H = “the expander inlet
temperature.” (a) Why is this done? (b) What would happen if
the cycle limit temperatures were used instead (i.e., taking T L =
“the expander outlet temperature” and T H = “the compressor
outlet temperature”)?
50. A reversed Brayton ASC refrigerator operates with air
between 0.00°F (the compressor inlet temperature) and
80.0°F (the expander inlet temperature) with an isentropic
pressure ratio of 2.85. Determine the ASC coefficient of
performance of this system, assuming (a) constant specific
heats and (b) temperature-dependent specific heats
(use Table C.16 in Thermodynamic Tables to accompany Modern
Engineering Thermodynamics).
51. Consider the possibility of converting an automobile
turbocharger with radiator intercooling at 100.0°F into a
reversed Brayton ASC air conditioning system. For inlet
conditions of 14.7 psia at 70.0°F and a compressor pressure
ratio of 2.00, determine
a. The ASC coefficient of performance of this system as an air
conditioner.
b. The coldest possible air conditioning temperature attainable
with this system.
52. The states in a reversed Brayton cycle air conditioner using air
(a constant specific heat ideal gas) as the working fluid are as
follows:
Station 1 Station 2s Station 3 Station 4s
Compressor Compressor Expander Expander
inlet outlet inlet outlet
T 1 = 80:0°F T 2s = 280:°F T 3 = 120:°F T 4s = − 36:0°F
p 1 = 14:0 psia p 2s = 42:0 psia p 3 = 42:0 psia p 4s = 14:0 psia
Determine the actual coefficient of performance of this cycle
if the compressor and expander isentropic efficiencies are 0.790
and 0.880, respectively. Note: Not an ASC analysis.
53. Show that Eqs. (14.22) and (14.23) for the reversed Brayton
cycle obey Eq. (14.1).
54.* 1.75 kg/s of air at 300. K enters the compressor of a reversed
Brayton cycle heat pump. The isentropic pressure ratio of the
compressor is 3.00 to 1, and the inlet temperature of the
expander is 335 K. The isentropic efficiencies of the compressor
and expander are 91.0% and 85.0%, respectively. Determine
a. The actual power output from the expander.
b. The actual power input to the compressor.
c. The coefficient of performance of the unit.
55. Show that the coefficient of performance of a reversed Brayton
ASC heat pump can be written as
COP reversed
= ðCRÞk−1
Brayton ASC
ðCRÞ k−1 − 1
HP
where CR is the compression ratio of the system.
56. Using the notation of Figure 14.27 and beginning with the
relation
COP reversed
=
Carnot ASC
R/AC
T L
T H − T L
=
T 1
T 3 − T 1
show that the minimum possible isentropic pressure ratio of a
reversed Brayton ASC refrigerator is
PR minimum = T k
3
k−1
T 1
57.* In 1862, Carnegie Kirk attained a temperature of −40.0°C with
a reversed Stirling cycle refrigerator. Assuming the environmental
temperature was 20.0°C, determine the reversed Stirling ASC
coefficient of performance for his unit.
58.* A reversed Stirling cryogenic refrigerator is used to produce a
temperature of −200.°C in an environment at 20.0°C.
Determine the reversed Stirling ASC coefficient of performance
of this unit.
59. Reversed Stirling cycle air conditioners were used to cool deep
mines until about 1930. If the temperature in the mine was
150.°F and the temperature of the air outside the mine was
60.0°F, determine the reversed Stirling ASC coefficient of
performance for the air conditioner.
60. A reversed Stirling cycle heat pump is driven by a 14.0 hp
electric motor. It produces a heat transfer rate of 75.0 × 10 3 Btu/h
into the high temperature region at 80.0°F from an environment
at 50.0°F. Determine
a. The actual coefficient of performance of the heat pump.
b. The reversed Stirling ASC coefficient of performance for
this unit.
61.* What power is required to drive a reversed Stirling cycle heat
pump with a high-temperature heat transfer rate of 14.0 kW
over the temperature difference 30.0°C and 0.00°C, if the actual
coefficient of performance is 50.0% of the ASC coefficient of
performance for this unit?
62. Determine the cooling temperature and the coefficient of
performance of an isenthalpic expansion cooler that expands air
from 1500. psia, 70.0°F to 14.7 psia. The isentropic efficiency of
the compressor is 85.0%. The mean Joule-Thomson coefficient
for this process is 0.0200°F/psi.
63.* When compressed air expands from 20.0°C, 100. atm to 1.00
atm, the mean Joule-Thomson coefficient is 0.150°C/atm.
Determine the outlet temperature and the coefficient of
performance of an expansion air conditioning system operating