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An engine (or motor) may receive all it's input power from, say,
the electric mains. In such a case efficiency and COP are identical.
However, if the environment supplies part of the input power,
the COP can exceed the efficiency and may exceed unity. For
example an electric heater receives all it's input power from the
electric mains; so the COP is equal to the efficiency. On the other
hand a heat pump receives part of it's input power from the electric
mains and part of it's input power from the environment (in the
form of heat). The efficiency of a heat pump may be only 50% while
the COP may be 4 or more.
For a final example, consider a
windmill. All the input power comes from environment
(in the form of wind); so the COP is infinite.
Let me conclude with the equations for efficiency and COP.
Efficiency = (Output Power) / (Total Input Power)
Total Input Power = (Power Supplied by the Operator) +
(Power Supplied by the Environment)
COP = (Output Power) / (Power Supplied by the Operator)
Note: We must pay for the Power Supplied by the Operator.
Power Supplied by the Environment is free.
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