How to find the Coefficient of Performance of a Heat Pump

A heat engine’s COP, or Coefficient of Performance, is the most important way to measure how efficient it is. You cannot compare heat pumps, fridges, and air conditioners without it.

If you have a water heater with an efficiency rating of 3.5, it’s much better than having a water heater with an efficiency rating of 2. It’s said that the best tankless water heaters are efficient.

Example: Most water heaters that do not use a lot of electricity have about 9,000W of power. Those with 15+ GPM can use up to 36 kWh an hour. High-COP heat pumps are essential for cutting electricity costs. For example, if you have a battery-powered portable air conditioner that does not use much energy, you’ll have a low COP.

Check out how the COP is calculated, the highest COP can be, and how the electricity bill changes when there are different HVAC units with other COPs.

How To Calculate COP? 

COP Formula

If you want to figure out how well a heat pump works, here’s the COP formula:

COP = Q/W

Q is how much heat the heater will make if we do a certain amount of work (W).

The heat we take away from a cold reservoir is called Q. Air conditioners serve several functions, including taking the heat out of a room (cold pool).

Take note that the COP for heating and cooling might be different. The best mini-split heat pumps, for example, can both cool and heat a space.

A sound mini-split system usually has a cooling COP ratio of 2 or more and a heating COP ratio of 3 or more, but this is not always the case.

Using the 1st law of thermodynamics and doing a little math, we can see the COP values for a hypothetical 100% ideal heat pump and 100% perfect air conditioner (we also call that a Carnot machine). Let’s start with the heat pump:

A Heat Pump’s Coefficient Of Performance (COP)

The following formula can be used to figure out a heat pump’s maximum COP:

COPheat pump = Thot/(Thot-Tcold)

This is the warm, comforting temperature we want during the frigid winter months (95 degrees Fahrenheit, or 308 degrees Kelvin).

Tcold denotes the freezing point when the heat pump begins to work (57F or 287K).

Theoretical maximal coefficient of performance (COP) is determined as follows:

COP heat pump = 308K / (287K-308K) = 14.67

Thus, a heat pump’s coefficient of performance (COP) may be more than 10. 

Nevertheless, a heat pump’s actual coefficient of performance (COP) is far lower.

The gold standard for calculating a heat pump’s coefficient of performance is to use Thot = 95F (308K) and Tcold = 32F (273K). This suggests that the maximum COP is 8.8 in a perfect world. However, it is more minor in practice.

Indeed, a heat pump’s maximum COP is around 4.5. There are a lot of heat pumps that use less energy if their coefficient of performance (COP) is more than 3.

                                       Cold Temperature(degree centigrade)

This graph illustrates how efficient the high coefficient of performance heat pumps is. We set the COP 2 to zero and estimated the percentage increase in efficiency of heat pumps with a higher COP.

For example, a 3.2 COP pump consumes 60% less energy than a 2 COP pump.

Coefficient Of Efficiency Of Air Conditioners

Now, let us determine a cooling device’s theoretical maximum efficiency. Specifically, a refrigerator or an air conditioner. We can infer the ‘Carnot coefficient of performance’ for a cooling device by using the first law of thermodynamics:

COPcooling= Tcold / (Thot-Tcold)

Tcold is the desired cooling temperature in your room during the summer. The term “Thot” refers to a prolonged period of intense heat.

Consider what an air conditioner’s COP would be in a standardised temperature range between Thot = 95F (308K) and Tcold = 32F (273K). We get 7.8 when we plug the temperature into the COP cooling calculation above.

If you recall, a heat pump’s maximum performance coefficient was 8.8. If you want to buy a new air conditioner, look for one with a coefficient of performance (COP) of more than 2. That is a very high coefficient of commission for a useful HVAC cooling device.

Typically, the issue is that COP values are nowhere to be found, not even on specification sheets. Energy efficiency is often quantified using EER and SEER ratings, calculated using the COP of an HVAC system. For instance, we analysed the EER ratings of the finest portable air conditioners.

SCOP Or COP Seasonal

SCOP, which stands for Seasonal Coefficient Of Performance, was launched in 2013. The coefficient of performance (COP) measures a heating or cooling system’s energy efficiency. Calculating SCOP aims to objectively determine energy efficiency throughout the winter (for heating) and summer seasons (for cooling).

SCOP and COP have a similar connection to SEER and EER.

SCOP would provide a considerably more accurate indication of an HVAC device’s energy efficiency in reality, i.e., during a forthcoming summer season.

The SCOP proposed a brand-new technique for determining seasonal cooling and heating efficiency. As a result, the SCOP ratio is uncommon on older devices. Indeed, even new devices seldom contain SCOP in their specification sheets because they have not yet been measured.

Conclusion

An ideal coefficient of performance can be found in any heat pump (COP). Several things make the coefficient of the version more minor than it should be, like mechanical or electrical losses in the fan or the compressor or mistakes in measuring devices, especially when getting the wet-bulb temperature. This is why the coefficient of performance is not as high as it should be (WBT).