# Heat Pump Efficiency

Normally when we think of efficiency, we think of a percentage, i.e. of the energy we put into an appliance, only some of it provides a useful output and some is wasted. Thus we talk about a boiler being 90% efficient – because only 90% of the fuel energy input ends up as useful output heat, with the rest being lost via the flue or via radiant and convective losses from the boiler.

By contrast, heat pumps seemingly undertake the impossible: you get more heating out than the energy you put in. This is possible because we are using energy to move heat – rather than converting the energy directly to heat. As a result the apparent efficiency in terms of heat output is greater than 100%. This is shown in Figure 2.

Figure 2. The heat pump cycle.

The ratio of electrical energy input to heat output is called the coefficient of performance or COP; the higher the COP, the more efficient the heat pump. For the heat pump in Figure 2, the COP is 4 units of heat output divided by one unit of electricity input, i.e. a COP of 4.

The COP can be maximised by careful design of the heat pump (efficient compressor, fans) and the use of a thermodynamically appropriate refrigerant.

The key external factor affecting both the COP and capacity of a heat pump is the temperature difference between the evaporator and the condenser. The narrower this temperature difference, the easier it is to transfer the heat and so the more heat we can transfer for every unit of energy input. This means that in a space heating application, for instance, the heat pump will be very efficient at mild temperatures but less efficient when it’s really cold.

This article series is kindly contributed by Dr Paul Bannister, a thought leader and public speaker on energy and energy efficiency issues in Australia. For other articles by Dr Paul Bannister, please refer to our news section

Nerd Space: Maximum efficiency of a heat pump

Heat pumps have so many counterintuitive features – an apparent efficiency greater than one, transferring heat from a cold object to a hot object – because they are playing with the second law of thermodynamics. Most sensible people don’t want to spend much time thinking about the second law of thermodynamics, and it is generally the preserve of bespectacled, crazy-haired physicists (like the author). For those interested, the maximum efficiency of a conventional heat pump is described using the Carnot efficiency equation:

COPmax = Tcond (K)
Tcond (K) – Tevap (K)

It can be seen from the format of the equation that the larger the temperature difference is between evaporator and condenser, the lower the maximum COP. If we take an evaporator at 10°C (283K) and a condenser at 60°C (333K) the theoretical maximum COP is 6.7, which is well ahead of anything we are achieving today, so there is clearly scope for the technology to become even more efficient in the future.