Coefficient of performance

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The coefficient of performance, or COP (sometimes CP), of a heat pump is the ratio of the output heat to the supplied work or

[COP = \frac
>]
where Q is the useful heat supplied by the condenser and W is the work consumed by the compressor. (note: COP has no units, therefore in this equation, heat and work must be expressed in the same units)

According to the first law of thermodynamics, [Q_=Q_+W ] and [W=Q_-Q_], where [Q_] is the heat given off by the warm heat reservoir and [Q_] is the heat taken in by the cold heat reservoir.
Therefore, by substituting for W,
[ COP_=\frac}-Q_}]
It can be shown that [ \frac}}=\frac}}] and [Q_=\fracT_}}], where [T_ ] and [T_] are the temperatures of the hot and cold heat reservoirs respectively.

Hence,
[ COP_=\frac}-T_} ]
Similarly,
[ COP_=\frac}-Q_} =\frac}-T_}]

It can also be shown that [ COP_=COP_-1 ]

Example

A geothermal heat pump operating at COP 3.5 is able to move 3.5 (11,946 BTUh) kwh of heat for every 1 kwh it consumes. This can also be viewed as an efficiency of 350%, which compares very favorably to high efficiency (condensing) gas burning furnaces (90-99% efficient), and electric heating (100%). (The COP of an air source heat pump may be 2.0 (200% efficiency) at low outdoor air temperatures before its backup electric resistance heating coils are turned on.)

[COP_] applies to heat pumps and [COP_] applies to air conditioners or refrigerators. For heat engines, see Efficiency.

Coefficient of performance

Example

See also