Heat Pumps

Lord Kelvin ( Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907).

Heat pumps are a well established, but generally poorly understood technology. Simply put these are devices that access a heat reservoir at relatively low temperature and deliver heat at a higher temperature. They can be thought of as heat engines working in reverse. The principles were first formulated by Sadi Carnot who published a pamphlet in 1824 in which he investigated the process by which heat engines, such as the steam engine, produce power. This work was refined by William Thomson ( later Lord Kelvin) who gave his name to the absolute temperature scale.

In a heat engine. heat is supplied to a boiler which raises temperature and pressure of the working fluid and transfers it to a turbine which does useful work ( usually rotating a shaft connected to an alternator) to produce electricity. After expansion the working fluid passes to a condenser which rejects heat to the environment, condensing the fluid, which is then pumped back into the boiler to evaporate. In the diagram, we show the boiler and condensers as heat exchangers.

Carnot Efficiency

The remarkable findings of Sadi Carnot is that there is a maximum efficiency that any sort of heat engine can achieve, and this efficiency is dependent on the high and low temperatures between which the engine operates, but not on the substance, such as air or steam, that produces the motive power. Of course in practical engines the actual efficiency depends on numerous mechanical details, but the theoretical maximum efficiency is the so called Carnot Efficiency. Carnot described this a function of temperature is was Lord Kelvin who later gave a form to the function based on the absolute temperature scale.

For a heat engine the Carnot Efficiency for an ideal engine is given by the formula on the right. The temperature must be expressed in kelvin which is relative to absolute zero. So for an steam engine working with boiler that produces steam at say 120C (393K) and exhausts to a condenser ambient say 15C (288K) The Carnot efficiency would be 36%. Of course the actual efficiency of a real steam engine would be much less than ( typically 12%) this as not all heat in the fire can be transferred to steam ( a lot goes up the stack) as the heat transfer area is limited. Similarly the working fluid is not fully condensed in the piston expansion, nor is any real condenser capable of taking all the working fluid to ambient temperatures. The Carnot efficiency is however an physical limit on the efficiency of a ideal engine working between these temperatures.

The diagram of the heat pump is essentially the same cycle in reverse in reverse (with the names of the components changed to reflect their changed function). Low grade heat is used to boil a fluid in the evaporator ( which evaporates at the low temperature and pressure of the evaporator allowing heat to flow from the environment to the working fluid). This fluid is then compressed. The compressor can be electrically driven by a motor or mechanically driven. The higher pressure fluid passes to a higher temperature condensor where the heat is extracted and the fluid condenses. The condensed fluid passes through an expansion valve to the low temperature evaporator which takes heat in.

The conceptual difficulty in the heat pump is that our experience is that heat flows by is own accord from a hot reservoir to a cold one. Taking heat from a low temperature reservoir to produce heat at a higher temperature seems counter intuitive. However the heat pump is not something for nothing. It takes in energy in the form of work in to drive the compressor. It should be obvious that the exit temperature on the evaporator heat exchanger is lower than the inlet temperature. Similarly the heat out from the condenser is higher than the heat in on the secondary side.

The whole point the heat pump is that the energy of the heat produced is more than the input work and the effect is to take low grade heat from the environment and transform it into a higher grade heat. The term for this is the coefficient of performance or COP. This COP also follows the Carnot efficiency in that it only depends on the absolute temperature of the two reservoirs. The smaller the temperature difference ( ie the amount of temperature uplift required) the higher the coefficient of performance will be).

Thus for a heat pump taking heat from the environment at say 5C ( 278K) and delivering heat into the building at say 29C ( 302K) would have a maximum theoretical Carnot efficiency of 12.5.

In practice real heat pumps would operate around 20-50% of the theoretical maximum. In this case a COP of 2.4 – 6.2. That is, with sufficient heat transfer rates in the evaporator and the condensor the COP could be up to about 6.2 . Delivering 6 kW of heat for 1 kw of power. This formula also shows why for heat pumps the temperature of the heat source and the delivered temperature is so critical. Why for example it is not a good idea to replace a gas boiler with a heat pump without changing the delivery temperatures. Assume for example that the gas boiler provides a flow temperature of 60C (333K) and the heat pump is air source with an outside temperature of -5C (268K) . Then the max possible Carnot Efficiency will be 5.12 and the actual nearer 1.2. This is because for any real device ther needs to to a temperature drop on the secondary side of the evaporator so the limit will be the exist temperature. If this is below freezing then the evaporator could ice up ( Exactly as happens in your freezer which is a heat pump pulling heat from inside the freezer to the outside.) many heat pumps will switch to resistance heating ( COP1) when the outside temperature is low.

Actual performance is quoted as SCOP or Seasonal Coefficient of performance as the input temperature often has seasonal component, particularly for air source devices where the external air temperature falls.

There are this two determining factors about the effectiveness of heat pumps. The temperature of eh heat source and the desired temperature of of the outlet from the condenser. For higher delivery temperatures then forms of hybrid can be used. For example heat pumps are not very effective at producing water at say 60C for Domestic Hot Water but much better at producing low grade heat for space heating. So a hybrid system that uses electricity or gas only for the high temperature output while using the heatpump for low temperature may be more effective that using the heat pump as a direct replacement for a gas boiler doing both Space heating and DHW.


A key advantage of heat pumps is that they can also be used to provide cooling. By simple changing the direction of flow through the compressor the roles of the heat exchangers are reversed and the heat pump will act as a refrigerator transferring heat from inside the building to outside. In this instance the wanted commodity is the low temperature, so the Carnot efficiency becomes as shown on the right.

The theoretical efficiency for operating in cooling mode also depends on the temperature of the two reservoirs. Thus for example, if the cooling required is 5C , 278K and heat is rejected to a heat sharing network at say 25 C (298K), the cooling COP would be 13.9. Similarly real machines will be operating at less than 50% of this ideal machine maximum so will be at a COP less than 7.0. Clearly for efficient cooling the smaller the temp difference between wanted cooling and reject temperature the higher the efficiency.