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:
Modifications 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.
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.