The efficiency of refrigeration systems and heat pumps is denoted by its Coefficient Of Performance (COP). The COP is determined by the ratio between energy usage of the compressor and the amount of useful cooling at the evaporator (for a refrigeration instalation) or useful heat extracted from the condensor (for a heat pump). A high COP value represents a high efficiency.
CoP=qC /qH − qC
The COP is therefore a measurement of efficiency; the higher the number, the more efficient the system is. The COP is dimensionless because the input power and output power are measured in Watt. The COP is also an instantaneous measurement in that the units are power which can be measured at one point in time.
Consider a simple electric heater. All of the electricity that is input to the unit is converted to heat. There is no waste and the power output (in heat) equals the power input (in electricity), so the COP is one. The COP can be used to describe any system, not just heating and cooling.
An air conditioning system uses power to move heat from one place to another place. When cooling, the air conditioning system is moving heat from the space being cooled (usually a room), to somewhere it is unwanted (usually outside). A heat pump uses the same principles, but it is moving heat from outside (the cold side) to the space being heated inside (the living space).
For engines: desired output = w; necessary input = QH, hence
CoPE =w/QH=QH − QC/QH
• For refrigerators: desired output = qC; necessary input = W, hence
CoPR =qC /W=qC /qH − qC
For heat pump: desired output = qH; necessary input = W, hence:
CoPP =qH/W=qH/qH − qC
note: CoPE < 1 always; CoPR may be > 1 or < 0 (usually > 1 in practice); CoPP > 1
always. Real engines are optimised to work in one direction, and are not reversible.
However, for idealized reversible engines, only the signs of work and heat will change
CoPPrev =1/CoPErev