Efficiency of Heat Pumps


The efficiency of a heat pump cannot be accurately described without reference to the definition of a heat pump itself. The purpose of a heat pump is to pull heat from a colder environment and transport it to a hotter environment. The efficiency, then, is a reflection of the quantity of heat that was transported, with respect to the amount of work that it took to do the transporting. This equation can be further simplified to be expressed only in terms of the temperatures of the hot and cold environments, as is the case when discussing the efficiency of any heat engine. A very general version of the equation for efficiency looks like this:


That is, where “e” represents efficiency, “Qh” represents heat that is transported, and “w” represents the work that is used to transfer the heat. When rephrased to be expressed in terms of temperatures, the equation is:


The new variable used above to represent the efficiency of a heat pump, η, is a specific variation of efficiency that is applied specifically to heat pumps and refrigerators, called the “coefficient of performance,” sometimes abbreviated COP.

The Coefficient of Performance

The coefficient of performance is the expression of the efficiency of a heat pump in terms of heat output over work input (usually both are measured in joules). The coefficient of performance must be greater than one, according to the simplified version of the equation: the hotter temperature in the numerator should always be greater than the temperature difference in the denominator. The coefficient of performance is inversely dependent on the difference between the temperatures of the external, cold environment and the internal, hot environment, so the smaller the difference, the higher the coefficient of performance. Since heat pumps are primarily used to heat building space or water, the internal temperatures are generally consistent around room temperature, leaving the external temperature as the main variable. Thus, heat pumps are designed to maximize the coefficient of performance depending on what cold environment the pump is drawing from. Generally speaking, the colder the environment, the less efficient the heat pump will be. This relationship is seen below:


Efficiency of Different Types of Heat Pumps

There are several different types of heat pumps, categorized by the environments from which they draw their heat. The main ones are geothermal (drawing from cold water reservoirs in the ground), air cycle (drawing from air outside), heat activated (drawing heat from an actual heat source), or absorption (a heat engine draws air, and powers the heat pump). When choosing the type of heat pump that should be used, it is best to consider the environment around the space that needs to be heated. If the air outside of a building is below freezing for a significant portion of the year, then it would be inefficient to choose a pump which draws from the air outside, since colder temperatures yield lower performances. Geothermal heat pumps draw from underground reservoirs where the temperature stays around 55°F. Therefore, in places that are often colder than 55°F throughout the year, geothermal heat pumps are commonly used.

The efficiency of different types of heat pumps can be compared by examining the relationship between the coefficient of performance of each heat pump and the temperature of the environment it draws heat from. Below are two charts, which examine this relationship between geothermal and air-cycle heat pumps, respectively.




Commercial heat pumps typically have a coefficient of performance between 3 and 6. In other words, an efficient heat pump will output 6 Joules of heat for every joule of work that is done.

Heating Season Performance Factor

One other way in which the efficiency of a heat pump is expressed is in terms of its heating season performance factor (HSPF). This ratio is a measure of the total amount of space or water heating required during a heating season (measured in Btu, where 1Btu=1.055kJ), over the total amount of electrical energy which is consumed by the heat pump (measured in Watt-hours). The relationship between HSPF for common commercial air-cycle heat pumps and external environment temperature is shown below:

chart-2Modifications to the engineering details of each type of heat pump also serve to maximize efficiency, so that in each type of environment, minimal energy is dissipated. Overall, the relatively high efficiency of heat pumps, as well as their versatility for different environments, make heat pumps an ideal source of heating for buildings and water.

 Personal Notes

The concept of heat pumps, as well as the many modifications that have been made to adapt different types of heat pumps to their environments, make them a great choice for heating. The fact that electrical energy is being used to do the work makes them quite efficient and clean, relative to other methods like wood- or gas-burning systems. I especially appreciate the geothermal heat pumps, since that method can be used with minimal modifications to efficiently heat just about any environment. I can also see that efficiency can be improved further particularly for air-cycle heat pumps in environments whose ambient outside temperature has a vast range.



  • Engel, Thomas; and Reid, Philip. Thermodynamics, Statistical Thermodynamics, and Kinetics. 3rd ed. Pearson, 2013. p.108-110.
  • Giancoli, Douglas C. Physics for Scientists and Engineers with Modern Physics, Pearson New International Edition. Pearson Education Limited, 2014. p. 622-624.
  • http://www.engineeringtoolbox.com/heat-pump-efficiency-ratings-d_1117.html
  • http://the-green-product.blogspot.com/2011/03/air-to-water-air-source-heat-pumps.html
  • http://www.homepower.com/articles/solar-water-heating/domestic-hot-water/heat-pump-water-heaters
  • http://heatpumps.co.uk/graphs.htm
  • http://energy.gov/energysaver/heat-pump-systems
  • http://what-when-how.com/energy-engineering/heat-pumps-energy-engineering/

Engineering Details of Heat Pumps

Known as a device that transfers heat energy from a source of heat to a destination called a “heat sink”. Heat pumps move thermal energy in the opposite direction of spontaneous heat flow (i.e. cold space to warmer space)
Examples: refrigerators, air conditioners, freezers
All of which exploit a volatile evaporating and condensing fluid known as refrigerant

Operating Principles
“Mechanical heat pumps exploit the physical properties of a volatile evaporating and condensing fluid known as a refrigerant. The heat pump compresses the refrigerant to make it hotter on the side to be warmed, and releases the pressure at the side where heat is absorbed.

A simple stylized diagram of a heat pump’s vapor-compression refrigeration cycle: 1) condenser, 2) expansion valve, 3) evaporator, 4) compressor.

A fictitious pressure-volume diagram for a typical refrigeration cycle
The working fluid, in its gaseous state, is pressurized and circulated through the system by a compressor. On the discharge side of the compressor, the now hot and highly pressurized vapor is cooled in a heat exchanger, called a condenser, until it condenses into a high pressure, moderate temperature liquid. The condensed refrigerant then passes through a pressure-lowering device also called a metering device. This may be an expansion valve, capillary tube, or possibly a work-extracting device such as a turbine. The low-pressure liquid refrigerant then enters another heat exchanger, the evaporator, in which the fluid absorbs heat and boils. The refrigerant then returns to the compressor and the cycle is repeated.[citation needed]

It is essential that the refrigerant reach a sufficiently high temperature, when compressed, to release heat through the “hot” heat exchanger (the condenser). Similarly, the fluid must reach a sufficiently low temperature when allowed to expand, or else heat cannot flow from the ambient cold region into the fluid in the cold heat exchanger (the evaporator). In particular, the pressure difference must be great enough for the fluid to condense at the hot side and still evaporate in the lower pressure region at the cold side. The greater the temperature difference, the greater the required pressure difference, and consequently the more energy needed to compress the fluid. Thus, as with all heat pumps, the coefficient of performance (amount of thermal energy moved per unit of input work required) decreases with increasing temperature difference.

Insulation is used to reduce the work and energy required to achieve a low enough temperature in the space to be cooled.

To operate in different temperature conditions, different refrigerants are available. Refrigerators, air conditioners, and some heating systems are common applications that use this technology.”

Simple heat pump has 4 parts to it
1. Condenser
The hot and pressurized vapor is cooled
2. Expansion valve
Pressure-lowering device
3. Evaporator
The cold (low heat) is exchanged and sent along to the compressor
4. Compressor
Pressurizes the fluid (increase T) and circulates it throughout system


Until the early 90’s refrigerators used chlorofluorocarbons which depleted ozone layers. Now we use hydrofluorocarbons to power which are less efficient, however more environmentally friendly
Alternatives such as solar assisted heat pumps are the most environmentally friendly and efficient. Over time the solar cells will be worth the investment. In low temperature areas solar panels are much more efficient than any heat pumps because they lose efficiency at lower temps.




Personal Comments – Zach

Yeah, Everyone Should Look Into One of These!

The two most popular types of heat pumps extract heat energy from either the air or Earth’s stable geothermal temperature. When looking at the environmental aspects of heat pumps, the energy saving and renewable heat source outweighs any environmental downfalls. Ideally in colder regions of the world the geothermal heat pump has the advantage of a steady ground source to take heat from. In mild climate countries an air source pump will do the trick, where the temperatures don’t get to cold. To offset any short comings an auxiliary heat coil can be used. For either of these systems an energy source is needed to power the compressor. Powering with renewable energy will make any heat pump an environmentally sound choice.

Thermodynamic Principle

When the freezing temperatures of winter hit the Midwestern United States, we are given a subtle reminder that nature, while pleasant year-round otherwise, can chill us to our bones and leave us shivering for warmth. Luckily, we are able to separate ourselves from this harsh reality at the flip of a switch and the turn of a knob. The low hum of a fan kicks on, blowing hot air through our vents and into our homes, but how do these systems work?

Heat pumps are an efficient means to transfer heat from a cold reservoir (e.g. the unwelcoming land beyond our walls) to a hot reservoir (e.g. the great indoors). This process cannot just happen spontaneously, however, as that would violate the second law of thermodynamics, which according to Clausius states that heat can never pass from a colder to a warmer body without some other change occurring at the same time. An element of work is introduced in order to rectify this.


Figure 1: Clausius Statement

A heat pump is made up of four key components: an evaporator, a compressor, a condenser, and expansion valve. This system operates by passing a fluid, known as a refrigerant, through each component. Key characteristics of a refrigerant used for this purpose include a high latent heat of vaporization and relatively low boiling point. Below is a simple diagram of the stages of a heat pump:

Figure 1: Heat pump components and flow of refrigerant

Figure 2: Heat pump components and flow of refrigerant

As the refrigerant passes through this system, it undergoes a predictable series of variations in pressure and volume, which drive the overall heat transfer. This cyclical change in pressure in volume can be visualized approximately as a reversed Carnot cycle.


Figure 3: Heat Pump Cycle (left) alongside Reversed Carnot Cycle (right)

Let’s break down each stage, starting with the evaporator. This step (labeled evaporation in the pressure-volume (PV) diagram above) involves the refrigerant taking on heat from its surroundings. In the case of a heat pump, the refrigerant at this stage is at a low temperature, lower than the temperature of the air surrounding. The second law of thermodynamics tells us that heat will spontaneously transfer from an area of greater heat, the surrounding air, to an area of lesser heat, the refrigerant. This heat transfer will cause the refrigerant to boil, changing it from a liquid to a gaseous state. Due to the high latent heat of the refrigerant, this process takes up a great deal of energy, which can be modeled with the equation q = m(ΔHvap), where q, m, and Hvap represent heat, mass, and latent heat of vaporization, respectively.

The gas undergoes an increase in pressure by means of mechanical work at the compressor. The ideal gas law, PV=nRT, tells us that at a constant volume, the temperature of a gas varies directly with its pressure, that is, an increase in pressure yields an increase in temperature and a decrease in pressure yields a decrease in temperature. For this reason, this pressurized gas becomes heated to a certain temperature, which is then transported further down the line towards the condenser.

At the condenser, the gas passes through heat conductive piping along through the condenser. The condenser is a vessel filled with liquid at a lower temperature than the gas. As we recall from the second law of thermodynamics, the heat will transfer from an area of greater heat, the gas, to an area of lesser heat, the cooler liquid. A great deal of heat is extracted at this stage, so much so that the gas refrigerant is condensed into a liquid. The evaporator stage greatly increased the heat of the refrigerant by a liquid to gas phase change, and this is stage represents the reverse of that; a gas to liquid phase change occurs. Thus, the change in heat can be modeled as -q = m(ΔHvap). This high pressure, cooled liquid now must pass through the final stage, the expansion valve.

At the expansion valve, the pressure on the liquid is relieved, returning it to a low pressure, low temperature state. At this point, the liquid refrigerant is once again capable of taking in heat from the outside air and repeating the process again.

Personal Viewpoints:

Heat pumps, utilize what is essentially the Carnot cycle to move heat from a cold to hot reservoir. This process is extremely efficient, and it has greater energy efficiency than other heaters (e.g. space heaters). In the future, we must develop better refrigerants that do not interfere with ozone in the atmosphere to fight its depletion over time.


Boundless. “Heat Pumps and Refrigerators.” Boundless Physics Boundless, 26 May. 2016. Retrieved 12 Dec. 2016 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/thermodynamics-14/the-second-law-of-thermodynamics-118/heat-pumps-and-refrigerators-414-8447/

“Heat Pump Systems.” Heat Pump Systems | Department of Energy. U.S. Department of Energy, 24 Sept. 2005. Web. 11 Dec. 2016.

Environmental Impacts of Heat Pumps

The environmental impacts of heat pump systems (air to air, water, geothermal) can be summarized in two categories; total emissions of CO2 and the environmental safety of refrigerants used.

Environmental Aspects of Operation

Too fully account for the total emissions of heat pumps evaluation of the system and the energy required to operate the system must be takin into account. A report from the European Union has tackled this problem and created an equation that evaluates such aspects of a heat pump and produces a value in total mass of CO2 produced. This equation is called the Total Equivalent Warming Impact (TEWI) (below).


When looking at an example of a geothermal heat pump, it’s clear the most emission intensive component is not the pump itself but the production of electricity to run the pump.


The total TEWI value can be greatly reduced by the source of the electricity running the pump; thus, a solar powered heat pump has very low carbon emissions. Below is an example of European countries and their production of CO2 based on electricity generation. Norway has the smallest emissions because the majority of electricity production is from renewables.


Overall the operation of a heat pump is a low emission process that can greatly reduce carbon emissions, but ultimately depends on the source of the electricity powering the pump.

Environmental Aspects of Refrigerants         

Once the emissions of the pump are taken into account for environmental sustainability the refrigerant used in the system must also be assessed. The refrigerants must have certain thermodynamic requirements to efficiently operate a heat pump and this requirement leads to the use of flammable and toxic refrigerants. The type of refrigerant is determined by the specific requirements of the heat pump namely industrial vs household systems. The most common refrigerant was R-22 (HCFC) or Freon until is ozone depleting effects were realized. Currently this refrigerant is being phased out for a non-ozone depleting option R-410A (HFC) which is more efficient. Although efficient, R-410A is still a powerful greenhouse gas that if let unchecked is estimated to contribute 10% to the greenhouse effect (NOAA). Thus mitigating any leaks is extremely important. The largest contributers to refrigerant loss are leaks during operation lifetime and dismantling/demolition. The use of refrigerants is necessary for the operation of heat pumps but the properties required promote the use of potentially dangerous chemicals. Ideally we will phase out harmful refrigerants but science and technology needs to produce an environmentally sound, affordable, efficient replacement.


*1  http://ec.europa.eu/environment/ecolabel/about_ecolabel/reports/hp_tech_env_impact_      aug2005.pdf

*2  https://www.eia.gov/tools/faqs/faq.cfm?id=427&t=3

*3  https://www.epa.gov/ods-phaseout

*4 http://research.noaa.gov/News/NewsArchive/LatestNews/TabId/684/ArtMID/1768/Articl     eID/11414/HFC-greenhouse-gases-a-tale-of-two-or-more-futures.aspx