# What Is Exergy?

Exergy is a thermodynamic concept, used for many years within engineering analyses of chemical and mechnical processes and systems. Officially, exergy is defined as:

The maximum useful work which can be extracted from a system as it reversibly comes into equilibrium with its environment.

In other words, it is the capacity of energy to do physical work. To explain the concept, we’ll use four basic principles:

#### 1. Exergy is a measure of energy quality

Energy comes in many different forms, all of a different inherent quality. ‘Quality’ can refer to a number of attributes – ease of transport, energy density, environmental impact, etc. – but we refer here to its most fundamental form, which encapsulates the ability to perform physical work, i.e. to overcome a resistance to make an object move. This is important when considering thermal energy (heat), which is intrinsically of a lower quality than other forms of energy (such as electricity or mechanical motion). This is because for a given amount of heat, a portion – depending upon its temperature – will constitute the low-grade waste heat which cannot then be recovered and made to do physical work (for example, in a heat engine).

Fig. 1: Whereas one can theoretically recover all of the heat energy from a device such as an electric heater, very little of this low-quality energy can be subsequently made to do work (e.g. in moving an object). Thus the device is said to have a low exergy output. Source: Sousa et. al. (2016, submitted).

For example, 100 Joules (100J) of heat would correspond to less exergy than would 100J of electricity. Exactly how much exergy is present within 100J of heat would depends upon the temperature, pressure, chemical composition, etc., of the system, as well as its surroundings (see point 3). However, 100J of electrical energy corresponds exactly to 100J of exergy.

#### 2. Unlike energy, exergy can be, and is, destroyed, in every transformation process.

The first law of thermodynamics dictates that in any transformation process, energy is always conserved. In any real process, this translates into a certain amount of input energy being converted to low-temperature waste heat. The sum of the waste heat and useful energy output will always equal the input energy (see fig. 1).

Exergy, on the other hand, takes its basis in the second law of thermodynamics, which in one form states that every transformation process involves the loss of some measure of quality of the system. This measure is represented by exergy; taking the same units as energy (e.g. Joules), exergy corresponds to the portion of an energy flow which can be made to do useful work in a subsequent conversion process. Thus, it is partially destroyed in every process. Destruction, in this sense, refers to an irreversible process of entropy creation, though it’s sufficient to say that this corresponds to the low-temperature waste heat generated.

#### 3. Exergy is defined relative to a system’s environment.

Exergy is a property of all material and energy flows, and depends upon characteristics such as temperature, chemical composition and electric potential relative to an external environment. In other words, it is the contrast between a thermodynamic system and its environment that defines the amount of exergy available; the greater the difference between the two (in temperature, or in gravitational/electrical/chemical potential), the greater the exergy of the system.

Fig. 2: Demonstration of the relative nature of exergy – in a hydroelectric dam, exergy cannot be extracted from one body of water until it is at a higher point relative to another (thus having more gravitational potential energy). In the case that both are at an equal height, both bodies possess energy, but as a whole there is no exergy within the system. Source: André Serrenho.

This can be illustrated by considering, for example, a hydro power plant. What necessitates the large height difference in water level between the two sides? Both bodies of water independently have considerable gravitational potential energy, but this can’t be exploited until there is a potential difference between the two bodies. In the case where the two levels are even, the system has zero exergy. By lowering one level relative to another using a dam, the higher body gains more gravitational potential energy relative to the lower, and in turn a significant amount of easily exploitable exergy.

#### 4. Exergy efficiency illustrates the how far the efficiency of a conversion process is from its theoretical maximum.

Energy efficiency can be measured in a number of ways, though in physical terms so-called ‘first law efficiency’, or the ratio

Efficiency (η) = Useful energy output / Total energy input,

is often used to demonstrate the relationship between ‘benefits’ and ‘costs’, in energy terms, of a conversion process. Despite its pervasive use, this measure of efficiency has a number of limitations. For one, certain applications such as heat pumps and refrigerators can and do regularly have first-law efficiencies which exceed 100%. Moreover, the measure doesn’t indicate to what extent the quality of energy is affected during a conversion process.

Take an electric heater, for example, in which nearly all electric power is converted to heat. The first-law efficiency of such an appliance is thus close to 100%, giving the impression that it is one of the most efficient appliances available. Yet this obscures the fact that extremely high-quality electrical energy is being transformed to low-quality thermal energy. The confusion highlighted here is addressed by using the so-called exergy, or ‘second-law’ efficiency:

Efficiency (ε) = Minimum energy input / Actual energy input.

This measure provides a more accurate description of how energy is being used. It can also be expressed as:

ε = Exergy output / exergy input.

In other words, the theoretical ‘minimum’ exergy requirement of a device represents the best possible performance in reality. In the above example of an electric heater, there exists significant scope for using less energy input to achieve the same amount of output. If instead a heat pump were installed, then the same amount of heat could be transferred to a space at the cost of significantly less electricity – thus the exergy efficiency of a heat pump is much greater than that of an electric heater.

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