All About Heat Pumps!: Efficiency & Formula's

When comparing the performance of heat pumps, it is best to avoid the word "efficiency" which has a very specific thermodynamic definition. The term coefficient of performance (COP) is used to describe the ratio of useful heat movement to work input. Most vapor-compression heat pumps utilize electrically powered motors for their work input. However, in most vehicle applications, shaft work, via their internal combustion engines, provide the needed work.

The design of the evaporator and condenser heat exchangers is also very important to the overall efficiency of the heat pump. The heat exchange surface areas and the corresponding temperature differential (between the refrigerant and the air stream) directly affect the operating pressures and hence the work the compressor has to do in order to provide the same heating or cooling effect. Generally the larger the heat exchanger the lower the temperature differential and the more efficient the system. Since heat exchangers are expensive, and the heat pump industry is very financially competetive, the drive towards more efficient heat pumps and air conditioners is often led by legislative measures on minimum efficiency standards.

Heat pumps are more effective for heating than for cooling if the temperature difference is held equal. This is because the compressor's input energy is largely converted to useful heat when in heating mode, and is discharged along with the moved heat via the condenser. But for cooling, the condenser is normally outdoors, and the compressor's dissipated work is rejected rather than put to a useful purpose.

For the same reason, opening a food refrigerator or freezer heats up the room rather than cooling it because its refrigeration cycle rejects heat to the indoor air. This heat includes the compressor's dissipated work as well as the heat removed from the inside of the appliance.

The COP for a heat pump in a heating or cooling application, with steady-state operation, is:

$COP_{\mathrm{heating}} = \frac{\Delta Q_{\mathrm{hot}}}{\Delta A} \leq \frac{T_{\mathrm{hot}}}{T_{\mathrm{hot}}-T_{\mathrm{cool}}}$

$COP_{\mathrm{cooling}} = \frac{\Delta Q_{\mathrm{cool}}}{\Delta A} \leq \frac{T_{\mathrm{cool}}}{T_{\mathrm{hot}}-T_{\mathrm{cool}}}$

where

$Δ Q c o o l$ is the amount of heat extracted from a cold reservoir at temperature $T c o o l$ ,
$Δ Q h o t$ is the amount of heat delivered to a hot reservoir at temperature $T h o t$ ,
$Δ A$ is the compressor's dissipated work.
All temperatures are absolute temperatures usually measured in kelvins (K).

For instance, when used for heating a building on a mild day of say 10°C, a typical air-source heat pump has a COP of 3 to 4, whereas a typical electric resistance heater has a COP of 1.0. That is, one joule of electrical energy will cause a resistance heater to produce one joule of useful heat, while under ideal conditions, one joule of electrical energy can cause a heat pump to move much more than one joule of heat from a cooler place to a warmer place.

Note that when there is a wide temperature differential, e.g., when an air-source heat pump is used to heat a house on a very cold winter day of say 0°C, it takes more work to move the same amount of heat indoors than on a mild day. Ultimately, due to Carnot efficiency limits, the heat pump's performance will approach 1.0 as the outdoor-to-indoor temperature difference increases. This typically occurs around −18 °C (0 °F) outdoor temperature for air source heat pumps. Also, as the heat pump takes heat out of the air, some moisture in the outdoor air may condense and possibly freeze on the outdoor heat exchanger. The system must periodically melt this ice. In other words, when it is extremely cold outside, it is simpler, and wears the machine less, to heat using an electric-resistance heater than to strain an air-source heat pump.

Geothermal heat pumps, on the other hand, are dependent upon the temperature underground, which is "mild" (typically 10°C at a depth of more than 1.5m for the UK) all year round. Their COP is therefore is normally in the range of 4.0 to 5.0.