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# COP Water Heater

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 per work input. Most vapor-compression heat pumps use electrically powered motors for their work input. However, in many vehicle applications, mechanical energy from an internal combustion engine provides the needed work.

When used for heating a building on a mild day, for example 10 °C, a typical air-source heat pump (ASHP) has a COP of 3 to 4, whereas a typical electrical resistance heater has a COP of 1.0. That is, one joule of electrical energy will cause a resistance heater to produce only 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 the heat pump is more efficient on average in hotter climates than cooler ones, so when the weather is much warmer the unit will perform better than average COP. Conversely in cold weather the COP approaches 1. Thus when there is a wide temperature differential between the hot and cold reservoirs, the COP is lower (worse).

When there is a high temperature differential on a cold day, (e.g., when an air-source heat pump is used to heat a house on a very cold winter day of 0 °C), it takes more work to move the same amount of heat to 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 for colder climates (outside temperature gets colder). 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. When it is extremely cold outside, it is simpler, and wears the machine less, to heat using an electric-resistance heater rather than to overload an air-source heat pump.

On the other hand, ground-source heat pumps (GSHP) 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 year-round COP is therefore normally in the range of 4.0 to 5.0.

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 becomes.

Heat exchangers are expensive, requiring drilling for some heat-pump types or large spaces to be efficient, and the heat pump industry generally competes on price rather than efficiency. Heat pumps are already at a price disadvantage when it comes to initial investment (not long-term savings) compared to conventional heating solutions like boilers, so the drive towards more efficient heat pumps and air conditioners is often led by legislative measures on minimum efficiency standards.

In cooling mode, a heat pump's operating performance is described in the US as its energy efficiency ratio (EER) or seasonal energy efficiency ratio (SEER), and both measures have units of BTU/(h·W) (1 BTU/(h·W) = 0.293 W/W). A larger EER number indicates better performance. The manufacturer's literature should provide both a COP to describe performance in heating mode, and an EER or SEER to describe performance in cooling mode. Actual performance varies, however, and depends on many factors such as installation, temperature differences, site elevation, and maintenance.

Heat pumps are more effective for heating than for cooling an interior space if the temperature differential is held equal. This is because the compressor's input energy is also converted to useful heat when in heating mode, and is discharged along with the transported heat via the condenser to the interior space. But for cooling, the condenser is normally outdoors, and the compressor's dissipated work (waste heat) must also be transported to outdoors using more input energy, rather than being put to a useful purpose. For the same reason, opening a food refrigerator or freezer actually 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:

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

where

• $\Delta Q_{cool}$ is the amount of heat extracted from a cold reservoir at temperature $T_{cool}$,

• $\Delta Q_{hot}$ is the amount of heat delivered to a hot reservoir at temperature $T_{hot}$,

• $\Delta A$ is the compressor's dissipated work.

• All temperatures are absolute temperatures usually measured in kelvins (K).