Modern Engineering Thermodynamics

584 CHAPTER 14: Vapor and Gas Refrigeration Cycles
and
COP reversed Stirling
ASC R=AC
T L
=
T H − T L
9. The coefficient of performance of a Joule-Thomson air standard cycle refrigerator or air conditioner is
COP J
T
R=AC
=
μ J ðp 2 − p 1 Þ
h i.
T 1 ðp 2 /p 1 Þ ðk−1Þ/k − 1 ðη s Þ c
10. The irreversibility rate produced by an adiabatic compressor is
_I adiabatic
compressor
= T 0 ð _S P Þ adiabatic
= _m ref T 0 ðs 2 − s 1 Þ
compressor
the irreversibility rate produced by a condenser is
Q
_I condenser = T 0 ð _S P Þ condenser
= T 0 _m ref ðs 3 − s 2 Þ − _
condenser
T condenser
the irreversibility rate produced by an adiabatic expansion valve is
_I adiabatic
= T 0 ð _S P Þ adiabatic
= _m ref T 0 ðs 4h − s 3 Þ
expansion valve
expansion valve
and the irreversibility rate produced inside an evaporator is
" #
_Q evaporator
_I evaporator = T 0 ð _S P Þ evaporator
= T 0 _m ref ðs 1 − s 4h Þ −
T evaporator
Problems (* indicates problems in SI units)
1. Using the definition of thermal efficiency, show that the
coefficient of performance (COP) of a heat pump is always
greater than 1.0.
2. If the coefficient of performance of a window air conditioner in
the summer is 5.70, what is the coefficient of performance of
this unit if it were used as a window heat pump in the winter?
3. The Rumford Engineering company, a supplier of yours, has just
announced that it is offering a new product line for closed
electronic cabinet cooling. It is a small refrigeration unit driven
by a 0.250 hp electric motor that removes 500. W of heat from
the cabinet. What is the coefficient of performance of this unit?
4. A heat pump with a coefficient of performance of 7.30 is used
to heat a small house at a rate of 40.0 × 10 3 Btu/h. What
horsepower electric motor is required to drive the heat pump?
5.* It is proposed to operate a reversed Carnot cycle to remove
1500. W of thermal energy from a freezer at −14.0°C and to
discharge heat to the environment at 20.0°C. Determine
a. The coefficient of performance of the system.
b. The heat transfer rate to the environment.
c. The required input power.
6.* When the outside environmental temperature is 5.00°C, to what
temperature can you heat the interior of a house with a Carnot
heat pump that has a coefficient of performance of 8.90?
7.* How much power is required to drive a Carnot refrigeration unit
used to remove 15.0 kW of heat from a commercial food
storage unit maintained at 3.00°C when the outside temperature
is 35.0°C?
8. A new plastic-molding facility has a large amount of waste heat
available at 300.°F. The local environmental temperature is
75.0°F. As an entry-level engineer, you are to investigate possible
energy savings by determining
a. The thermal efficiency of a Carnot engine operating between
these temperatures.
b. The coefficient of performance of a Carnot heat pump
operating between these temperatures.
c. The coefficient of performance of a Carnot refrigerator
operating between these temperatures.
9. A typical ice cube from your refrigerator contains about 1.50 in 3
of ice. Determine the tons of refrigeration produced if the ice
cube melts at 32.0°F in (a) 24 hours and (b) 1 hour. Assume
the density of ice at 32.0°F to be 0.0330 lbm/in 3 .
10. A large commercial refrigerator has a coefficient of performance
of 4.70 and is driven by a 7.00 hp electric motor. Determine the
refrigeration capacity of this unit in tons of refrigeration.
11. The air conditioning unit for a building uses a water chiller with a
capacity of 12.0 tons of refrigeration. Determine the coefficient of
performance of this unit if it is driven by a 14.0 hp electric motor.
12. In 1937, Dr. Willis Haviland Carrier (1876–1950) developed an
air conditioning system to cool the air in the Magma Copper
Mine in Superior, Arizona. 9 It reduced the air temperature at the
3600 ft level from 133°F to 71.0°F after 4 months of operation.
Each air conditioning unit in the system had a capacity of 140.
tons of cooling and was driven by a 200. hp electric motor.
Determine the coefficient of performance of these units.
9 In 1976, this air-conditioning system was designated the 13th National Historic Mechanical Engineering Landmark by the American Society of
Mechanical Engineers.