COP Explained: Coefficient Of Performance Of AC And Heat Pump

COP Explained

Air Conditioners and Heat Pumps make up a large part of household necessities today. Without heating and cooling systems in place, we might as well be in the Victorian Era.

Only- the Victorian Era was not subject to outstandingly high temperatures in the summer nor was the winters harsh enough to freeze someone to death. So, the bottom line is these units are absolute essentials in today’s world. 

Most consumers go on to buy Air Conditioners and Heat pumps today, taking into consideration several factors like the size and capacity, energy efficiency, unit cost, upfront costs, expected electricity costs, and so on.

While these are simple ways of concluding what makes for a fairly good AC, and what makes for a bad one- there are more accurate ways to pinpoint just how useful an AC or a heat pump might be to you.

 If you’re willing to look behind the scenes and do some additional research, you’ll come across something called a ‘COP’.

The COP or the Coefficient of Performance is one of the most helpful ways to deduce the efficiency and effectiveness of an AC or a heat pump. It is also a great measure to compare and contrast between different units.

What is COP?

First, we start by defining what a COP is. Although you could condense it down to being the basis for heating or cooling unit’s efficiency- that definition is barely scratching the surface.

In its essence, the Coefficient of Performance is a ratio of how much useful heat or cold is produced by a heat pump or an AC as compared to how much energy or work is drawn or required by it. 

The COP, thus, indicates how much heat or cold can be supplied by it for every watt of energy provided to the given unit. 

Some units can generate more heat with the same amount of energy than others- and this is where COP starts to represent also the energy efficiency of a unit.

With a higher COP, thus, a unit can be expected to have higher efficiency and a lower rate of power consumption. Ultimately, this also means lower electricity costs.

The Coefficient of Performance is typically more than 1 in most heat pumps. However, Air Conditioners often have COPs ranging from 2 to 3.5.

This is because the COP formula is based on the ‘work required’, and the work or energy consumed to convert cold air to heat is usually more than the energy drawn to simply extract heat from the air and cool it, which is the process involved in Air Conditioners.

The formula for COP is as follows:


Q resembles the heat generated by a heat pump.

W stands for the work required to generate the given heat.

As mentioned, the unit ‘Q’, in terms of cooling, can mean the heat that is removed or moved from a given area (room), also known as the cold reservoir.

When it comes to COP of heating, the Q can also be interpreted as the heat removed from the cold reservoir, in addition to the input work of generating heat. In situations of heating systems, then, the work required is considerably more compared to cooling owing to their varying reservoirs and internal processes.

These formulas are in accordance with the 1st law of thermodynamics, which shows that these COP values are applicable for a 100% ideal heat pump or AC unit.

Coefficient of Performance For Heat Pump

For an assumed 100% ideal heat pump that has a theoretically all-time high COP, the formula for COP is:

COP (heat pump) = T (hot temperature generated)/ T (hot temperature generated) – T (Cold Temperature of the room)

For a heat pump, the coefficient of performance, is, thus, a result of the heat generated, or the hot temperature introduced to a cold reservoir in the winters by the heat pump, divided by the difference between given hot temperature and the initial cold/low temperature of the reservoir of the room.

The difference between the temperatures is basically figurative of the work that has been required to make the given change or put the difference into motion.

Usually, given that the hot temperature generated is greater than the heat absorbed from the cold reservoir, the COP of a heat pump is destined to be greater than 1.

If we take the theoretically maximum values over a range of heat pumps, where the resultant hot temperature is considered to be 35° C or 308° K, and the cold temperature of the reservoir is taken at an ideal 0° C or 273° K, we can attain:

COP= 308/308-273 = 8.8 COP

While this is the COP given the ideal values, you can expect the usual COPs for most heat pumps to be placed much lower.

Actually, the highest valued COP is considered to be around 4.0-4.5, and you’re incredibly lucky if your heat pump has a COP above 3 in general, as that indicates very high energy efficiency.

Coefficient of Performance For Air Conditioner

When it comes to cooling systems like air conditioners or even refrigerants, the COP is calculated as per the following formula:

COP = T (cold temperature wanted)/T(cold temperature wanted)-T(hot initial temperature of the room)

Here, the formula is an inverse of the COP for a heat pump. The COP is a result of the chilling or set low temperature that is to be achieved in a given reservoir divided by the difference between the desired or attained cold temperature and the initial hot temperature of the room. 

As you know, for a cooling system, this process is easier as it involves the removal of heat rather than the movement of it. Here, if we take into account the ideal T(cold) temperature, which is 273K, and the T (hot) temperature, which is 308 K, we get:

COP= 273/273-308 = 7.8 COP.

Again, these are the ideal values at a theoretical maximum as dictated by the thermodynamic law. In reality, however, most units are set at lower COP values.

As long as a cooling system displays a COP number above 2, it is considered to be quite energy-efficient. So, if that is a priority in your search for an air conditioner, you must keep in mind the COP.

Examples of Computing COP

Now that you know the formulas and how they work in an ideal situation, let’s try to apply them to the real world. If a heat pump generated heat worth a Q value of 4,500 W and had the work required/energy drawn to be situated around 1500 W, the COP would be as follows:

COP = Q/W = 4500/1500 = 3.

Thus, you are left with a heat pump with a COP of 3.0. Typically, this is considered to be quite high, and we’d recommend it for its good energy efficiency and electricity bill cut-down potential.

For an Air Conditioner with a given energy withdrawal W of 1200 W, and a Q (heat removed from a room) value of 3000, we can obtain the COP as follows:

COP = Q(cold)/W = 3000/1200= 2.5 COP.

As you know, for Air Conditioners, a COP above 2 is considered to be good, and this one certainly qualifies.

How can COP be improved?

There are certain factors that lead to an increase in COP of a system.

When it comes to heating systems like heat pumps or furnaces, a higher COP can generally be achieved when the difference between the temperatures is lowered, i.e, the difference between the attained hot temperature and the initial cold temperature of the room.

This generally means that the heat pump is showing a greater efficiency for the same work required.

Usually, the COP of a heating system can be improved by lowering the output temperature, which can be manipulated by making changes to the environment- like adding a piped floor, ceiling heating, and so on.

Similarly, the input temperature or the initial cold temperature could be increased as well. Growth in the size of the heat exchangers also contributes to a higher COP.

Similarly, in cooling systems like ACs and refrigerators, a visible increase in the COP can be observed with increased airflow and temperature drop, as well as absorption of groundwater rather than air as a source of cooling. Additionally, an increase in the pipe sizes would also heighten the COP of the entire system.

Indicators of COP- Seasonal Efficiency

The SCOP or the Seasonal Coefficient of Performance has come to be known as an objective measure of the energy efficiency of a heating or cooling system over the different winter and summer seasons.

This measure is considered to be more authentic than the SEER. However, units of COP and SCOP are still relatively new and haven’t been officially labeled on many manufactured heating and cooling units.

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