Dr Audrius Bagdanavicius

The meaning of the word efficiency is so obvious to us that we do not even bother to think about what the actual definition is.

In the Oxford English Dictionary one of the many definitions of efficiency is “the ratio of useful work performed to the total energy expended or heat taken in”. For an engineer this definition is synonymous with energy efficiency. But although the definition of efficiency is generally accepted it is slightly misleading.

For example, the efficiency of a boiler (the energy conversion device used for conversion of chemical fuel energy into heat) is the ratio of useful heat (not work!) obtained and energy expended. Therefore allowing for this, the definition of efficiency could be stated as “the ratio of useful work performed or heat obtained to the total energy expended or heat taken in”.

In energy engineering the concept of energy efficiency is frequently used to evaluate and compare various energy conversion systems and devices. Despite the apparent usefulness of this concept it has several drawbacks. For instance, how does one compare heat generators such as gas boilers, heat pumps and CHP?

Let’s say that an average energy efficiency of a gas boiler, heat pump and CHP is 85%; 300% (COP = 3) and 85% respectively. Clearly, gas boiler and CHP efficiencies are below 100%. However, for the heat pump the efficiency is 3 times higher than the maximum expected value of 100%. This approach violates the First Law of Thermodynamics, which states that energy is conserved and cannot be generated or destroyed. Therefore, we have to accept that the traditional concept of energy efficiency for heat pumps is distorted.

For heat pumps only one energy input stream – electricity (for electrically driven heat pumps) – is taken into account. The other energy input stream – thermal energy from the air (for air source heat pump) or ground (for ground source heat pump) is simply ignored. Thus, the energy efficiency of a heat pump is currently calculated by simply manipulating data. To avoid confusion the term Coefficient of Performance (COP) is used instead of efficiency to assess the performance of heat pumps. But this does not help solve the issue.

As energy efficiencies of different energy conversion technologies are sometimes incomparable, other methods to evaluate energy systems should be used. To overcome the confusion due to the different interpretations of energy efficiency, the concept of exergy was suggested more than fifty years ago.

The concept of exergy is based on the assumption that the “quality” of various forms of energy is different at different temperatures. It has been generally agreed that mechanical work and electricity are energy forms of the highest quality. This means that their energies and exergies are equal and their exergies do not depend on temperatures.

However, the “value of energy” (exergy) of thermal energy (heat) depends on the temperature (it also depends on the pressure, but for the sake of simplicity we can omit this component) of the hot substance and the environment. For example, it can be shown that 1 kWh of electrical energy is more useful than 1 kWh of thermal energy.

From 1 kWh of electrical energy 1 kWh of thermal energy could be obtained in theory. However, only 0.17 kWh of electricity can be recovered from 1 kWh of thermal energy, assuming that the source of thermal energy is hot water in a tank at +80°C at ambient temperature +20°C. Thus, the exergy of the hot water at given conditions is 0.17 kWh and the exergy efficiency of the water heating process using electrical energy is only 17%. f the temperature of the hot water is +25°C theoretically only 0.017 kWh of electrical energy could be generated at the same ambient temperature. Therefore, the exergy efficiency of water heating process using electrical energy is only 1.7%.

The fundamental difference between energy and exergy is that exergy can be destroyed. Therefore, every time when one form of energy is converted to another form of energy the “value of energy” (exergy) degrades. This degradation of exergy can be calculated and compared. As in the previous example, if 1 kWh of electrical energy is used to heat the water tank from ambient temperature +20°C to +80°C, the final exergy of the hot water in the tank is 0.17 kWh. This means that 0.83 kWh of exergy is destroyed during the heating process, because high value electricity has been used to generate low value heat.

Using the concept of exergy different energy systems can be evaluated and compared. The exergy efficiency is defined similarly as energy efficiency. It is the ratio of exergy output to the exergy input. Typical exergy efficiencies of a gas boiler, heat pump and CHP (at ambient temperature 0°C and water temperature 65-75°C) are 18%, 45% and 46% respectively. In this case the efficiency of heat pump is comparable with the efficiency of other energy conversion technologies.

The exergy of the input stream supplied from the air or ground to the heat pump is equal to 0, because using the exergy concept this stream has no value (remember using the energy analysis this stream is deliberately omitted). Thus, using exergy analysis there is no need to manipulate data. It is also obvious that gas boilers are not as efficient as heat pumps or CHP, because it uses high value chemical energy of fuel to produce low value heat.

Exergy efficiency analysis is methodologically more robust compared with energy efficiency analysis. Its rigorous approach allows us to assess and compare different energy systems. However, both methods should be used. Energy analysis provides an initial glimpse of technology efficiencies, whereas exergy analysis should be used as a tool for more detail investigation of the imperfections of energy conversion systems.

Dr Audrius Bagdanavicius is a Research Fellow at the University of Cardiff’s Institute of Energy.