Energy Efficient Buildings
Air Conditioning and Heat Pump Homework
1) A window air conditioner cools 250 ft3/min of 95 F and 35% RH air to saturation
at 45 F.
A) What is the total rate of heat removed from the air by the air conditioner
(Btu/hr)?
B) What is the sensible heat ratio?
C) How much moisture must be drained from the evaporator per hour?
D) If the COP of the air conditioner is 2.2, how much electrical power (kW)
does the air conditioner draw?
2) Using the performance plots shown below for a heat pump with 3.8-tons of
cooling capacity, develop linear equations that predict:
A) The cooling capacity, Q (Btu/hr), as a function of outdoor air
temperature.
B) The electrical power, W (kW), as a function of outdoor air temperature.
C) The cooling COP as a function of outdoor air temperature.
D) SEER is determined by measuring an air conditioner’s cooling capacity
and electricity use when the outdoor air temperature is 80 F. Using the
equation you developed in part C above, calculate the SEER of the air
conditioner.
E) It occurs to you that placing the outdoor condensing unit in the shade
could improve air conditioning efficiency. Assume that the average
outdoor air temperature during air conditioning season is 85 F in the sun
and 5 F cooler in the shade. If a house requires 12,000,000 Btu/yr of
cooling and electricity costs $0.10 /kWh, what would be the savings from
locating the condenser in the shade?
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3) Using the performance plots shown above for a heat pump with 4.2-tons of
heating capacity, develop linear equations that predict:
A) The heating capacity, Q (Btu/hr), as a function of outdoor air
temperature.
B) The electrical power, W (kW), as a function of outdoor air temperature.
C) The heating COP as a function of outdoor air temperature.
D) For a house with an overall UA of 600 Btu/hr-F that is maintained at Ti =
70 F, find the heat pump balance-point temperature.
E) The frequency of hourly temperatures for the October through March
heating season in Dayton, Ohio are shown below. Using this binnedtemperature data and the house characteristics in part D, find the
heating load Qenv, the heat supplied to the house by the heat pump
Qhp, the auxillary heat supplied to the house by the electric resistance
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heating elements, Qaux, the electrical energy supplied to the heat pump
Whp, and the electrical energy supplied to the electric resistance heater
and the heatpump Welec for the heating season.
F) If electricity costs $0.10 /kWh determine the total cost of electricity for
the heating system.
Ta

Q air


W hp
Ti =70F

Q env
Q hp

Q aux ( From elec resistance heating)
4.2 ton
Ta
Hours
H
-10 <= Ta < 0
0 <= Ta < 10
10 <= Ta < 20
20 <= Ta < 30
30 <= Ta < 40
40 <= Ta < 50
50 <= Ta < 60
60 <= Ta <70
Total
-5
5
15
25
35
45
55
65
17
96
359
787
1356
783
627
249
4274
Qenv
h UA (Ti-Ta)
(Btu)
Qhp
h (a+bTa)
(Btu)
Qaux
(Qenv-Qhp)+
(Btu)
84 * 10^6
196 * 10^6
3.5*10^6
fon
(Qenv/Qhp)*
Whp
h (c+dTa)fon
(kWh)
Welec
Qaux+Whp
(kWh)
9,300
10,400
4) Consider a house with the same overall UA of 600 Btu/hr-F and maintained at
the same internal air temperature of Ti = 70 F as in the previous problem. The
house has a ground-source heat pump with performance specifications shown in
the text. If electricity costs $0.10 /kWh, find the annual heating energy costs
assuming the Entering Fluid Temp is always 50 F.
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