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The heat-pump coefficient of performance relates useful heat delivered to work supplied.
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Formula
COP dimensionless; QH and Win in J or W over the same time basis
| Symbol | Meaning | Unit |
|---|---|---|
| COPHP | Heating coefficient of performance | dimensionless |
| Heat delivered to the warm reservoir | J | |
| Work supplied | J |
\mathrm{COP}_{HP}=\frac{Q_H}{W_{in}}For power ratios use heat-transfer rate and input power; for energy ratios use the same cycle or interval. COP is not a fraction bounded by one: it can exceed one because the device also transfers environmental heat. The reversible limit between reservoirs is TH/(TH−TC).
For power ratios use heat-transfer rate and input power; for energy ratios use the same cycle or interval. COP is not a fraction bounded by one: it can exceed one because the device also transfers environmental heat. The reversible limit between reservoirs is TH/(TH−TC).
The heat-pump coefficient of performance relates useful heat delivered to work supplied.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Heat-pump coefficient of performance” and check its unit and magnitude.
A unit delivering 6 kWh of heat for 2 kWh of electrical work has COPHP=3; the remaining 4 kWh comes from its heat source.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: COP dimensionless; QH and Win in J or W over the same time basis.
Formula cluster
The heat-pump coefficient of performance relates useful heat delivered to work supplied.
A unit delivering 6 kWh of heat for 2 kWh of electrical work has COPHP=3; the remaining 4 kWh comes from its heat source.
Compare heat-pump heating output with electrical input for the same operating condition.
Here is how to work through a typical Heat-pump coefficient of performance (COPHP = QH/Win) task step by step:
Task
Work through the numerical example for “Heat-pump coefficient of performance” and check its unit and magnitude.
Solution path
A unit delivering 6 kWh of heat for 2 kWh of electrical work has COPHP=3; the remaining 4 kWh comes from its heat source.
A heat pump does not produce all delivered heat from electrical work. It also transfers heat from air, ground or water into the heating circuit. Thus QH/Win can exceed one without violating energy conservation: QH includes source heat plus input work. Compare heat and work over the same interval or use their rates; COP can exceed one because source heat is also moved. Application: Compare heat-pump heating output with electrical input for the same operating condition. The numerical example A unit delivering 6 kWh of heat for 2 kWh of electrical work has COPHP=3; the remaining 4 kWh comes from its heat source anchors the idea in a concrete measurement case.
Either is valid, but numerator and denominator need the same time basis. For steady operation use heating rate divided by electrical power. For a full cycle use delivered heat energy divided by work input. Do not mix instantaneous heating power with annual energy in kilowatt-hours. Compare heat and work over the same interval or use their rates; COP can exceed one because source heat is also moved. The corresponding units are COP dimensionless; QH and Win in J or W over the same time basis. A unit delivering 6 kWh of heat for 2 kWh of electrical work has COPHP=3; the remaining 4 kWh comes from its heat source. This checks that the reference quantities are compatible.
The simple ratio describes a specified operating condition or interval. A seasonal value must account for outdoor temperatures, defrost, part load, pumps and controls. For real units, a standardized seasonal metric is often more informative than one COP point. Compare heat and work over the same interval or use their rates; COP can exceed one because source heat is also moved. Scope: For power ratios use heat-transfer rate and input power; for energy ratios use the same cycle or interval. COP is not a fraction bounded by one: it can exceed one because the device also transfers environmental heat. The reversible limit between reservoirs is TH/(TH−TC). A practical application is Compare heat-pump heating output with electrical input for the same operating condition.
Write the quantity and unit from the variable list next to every value: COP dimensionless; QH and Win in J or W over the same time basis. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example A unit delivering 6 kWh of heat for 2 kWh of electrical work has COPHP=3; the remaining 4 kWh comes from its heat source. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Compare heat and work over the same interval or use their rates; COP can exceed one because source heat is also moved.
The background states this starting condition: For power ratios use heat-transfer rate and input power; for energy ratios use the same cycle or interval.. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Compare heat and work over the same interval or use their rates; COP can exceed one because source heat is also moved.
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Which formula describes Heat-pump coefficient of performance?
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How do you rearrange Heat-pump coefficient of performance for Base equation for the target quantity?
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Which common mistake happens with Heat-pump coefficient of performance?
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