NationMaster - Encyclopedia: Coefficient of performance

The coefficient of performance, or COP (sometimes CP), of a heat pump is the ratio of the output heat to the supplied work or A diagram of a phase change heat pump: 1) condenser coil, 2) expansion valve, 3) evaporator coil, 4) compressor. ... In physics, heat is defined as energy in transit. ...

$COP = frac{|Q|}{W}$
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) Work (abbreviated W) is the energy transferred by a force to a moving object. ...

According to the first law of thermodynamics, $Q h o t = Q c o l d + W$ and $W = Q h o t - Q c o l d$ , where $Q h o t$ is the heat given off by the warm heat reservoir and $Q c o l d$ is the heat taken in by the cold heat reservoir.
Therefore, by substituting for W,
$COP_{heating}=frac{Q_{hot}}{Q_{hot}-Q_{cold}}$
It can be shown that $frac{Q_{hot}}{T_{hot}}=frac{Q_{cold}}{T_{cold}}$ and $Q_{cold}=frac{Q_{hot}T_{cold}}{T_{hot}}$ , where $T h o t$ and $T c o l d$ are the temperatures of the hot and cold heat reservoirs respectively. The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: the increase in the internal energy of a system is equal to the amount of energy added to the system by heating, plus the amount added in the form of work done on...

Hence,
$COP_{heating}=frac{T_{hot}}{T_{hot}-T_{cold}}$
Similarly,
$COP_{cooling}=frac{Q_{cold}}{Q_{hot}-Q_{cold}} =frac{T_{cold}}{T_{hot}-T_{cold}}$

It can also be shown that $C O P c o o l i n g = C O P h e a t i n g - 1$

$C O P h e a t i n g$ applies to heat pumps and $C O P c o o l i n g$ applies to air conditioners or refrigerators. For heat engines, see Efficiency. Thermodynamic efficiency (e) is defined as: where W is the absolute value of the work done in one thermodynamic cycle. ...

Categories: Heat pumps | Physics stubs

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