| 6B-1 : |
Home Heat Pump COP |
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4 pts |
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| A heat pump provides 75 MJ / h to a house. If the compressor requires an electrical energy input of 4 kW, calculate the COP. |
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| If electricity costs $0.08 per kW-h and the heat pump operates 100 hours per month, how much money does the homeowner save by using the heat pump instead of an electrical resistance heater ? |
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| Read : |
| This is a straightforward application of the definition of the COP of a heat pump . |
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| Given: |
QH |
75 |
MJ/h |
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Find: |
COPHP |
??? |
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WHP = |
4 |
kW |
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Price |
0.08 |
$/kW-h |
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OpTime |
100 |
h/month |
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| Diagram: |
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| Assumptions: |
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1 - |
The heat pump operates at steady-state. |
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2 - |
There is no loss of efficiency when the heat pump is started up or shut down by the thermostatic control system. |
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| Equations / Data / Solve : |
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Begin by writing the definition for the COP of a heat pump : |
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Eqn 1 |
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We can use Eqn 1 to evaluate the COPHP. Watch the units ! |
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QH |
20.83 |
kW |
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COPHP |
5.21 |
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First let's see how much it would cost to deliver QH to the home using an electrical resistance heater. |
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An electrical resistance heater, at best, converts all of the electrical work supplied, W, into heat released into the home, QH. Therefore, in order to get 20.83 kW into your home, you must buy 20.83 kW of electrical power. |
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Wresist |
20.83 |
kW |
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Now, we can determine how much it would cost to operate the resistance heater for 200 hr/month. |
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Eqn 2 |
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Costresist |
166.67 |
$/month |
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Now, we can apply Eqn 2 to determine the cost of operating the heat pump for a month. |
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CostHP |
32.00 |
$/month |
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The difference between these two costs is the monthly savings: |
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Savings |
134.67 |
$/month |
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| Verify : |
We cannot verify the steady-state assumption based on the information given in the problem statement. |
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| Answers : |
COPHP |
5.2 |
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Savings |
134.67 |
$/month |
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Electrical resistance heaters are not very popular, especially in cold climates. |
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The thermal efficiency of a heat pump drops significantly as the outside temperature falls. |
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When the outside temperature drops far enough that the COPHP ~ 1, it becomes more practical to use the resistance heater ! |
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