Chapter 11 | 647Consider 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 mini-
mum 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 tem-
perature of the hot fluid stream.
(c) Show, with calculations, that this process does not vio-
late 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.
Fundamentals of Engineering (FE) Exam Problems
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 satu-
rated 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
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 envi-
ronment at 20°C. The minimum required power input is
(a) 30 W (b) 33 W (c) 56 W
(d) 124 W (e) 350 W
11–112 A refrigerator operates on the ideal vapor compres-
sion 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
11–113 A heat pump operates on the ideal vapor compres-
sion 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 sup-
ply 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
11–114 An ideal vapor compression refrigeration cycle with
R-134a as the working fluid operates between the pressure lim-
its of 120 kPa and 1000 kPa. The mass fraction of the refriger-
ant 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
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
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
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 isCold
airWarm
airCompressed
airFIGURE P11–10611–107 Repeat Prob. 11–106 for a pressure of 600 kPa at
the vortex tube intake.
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.
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.