# What Is Exergy

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Previously in this chapter, we have used the term "work capacity'' to express the ability of a part of the total energy to perform work in contrast to the heat energy at the temperature of the environment, that is without work capacity. The classical thermodynamics is using the G-function to cover the work capacity; but when we are dealing with very far from thermodynamic systems, we cannot any longer use state variables that are independent of the pathway. Furthermore, we need in different situations different reference states. Therefore, we have to define a work capacity that can be used also for very far from thermodynamic equilibrium systems (Szargut et al., 1988).

Exergy is defined as the amount of work (=entropy-free energy) a system can perform when it is brought into thermodynamic equilibrium with its environment (J0rgensen et al., 1999). Figure 1.1 illustrates the definition. The considered system is characterized by the extensive state variables S, U, V, N1, N2, N3 , where S is the entropy, U is the energy, V is the volume and Ni, N2, N3 are moles of various

Towards thermodynamic equilibrium with the environment

Figure 1.1 Definition of exergy is shown.

chemical compounds, and by the intensive state variables, T, p, ^c3 ••• • The system is coupled to a reservoir, a reference state, by a shaft. The system and the reservoir are forming a closed system. The reservoir (the environment) is characterized by the intensive state variables To, po, ^c1o, ^c2o, ^c3o and as the system is small compared with the reservoir, the intensive state variables of the reservoir will not be changed by interactions between the system and the reservoir. The system develops towards thermodynamic equilibrium with the reservoir and is simultaneously able to release entropy-free energy to the reservoir. During this process the volume of the system is constant as the entropy-free energy must be transferred through the shaft only.

The entropy is also constant as the process is an entropy-free energy transfer from the system to the reservoir, but the intensive state variables of the system become equal to the values for the reservoir. The total transfer of entropy-free energy in this case is the exergy of the system. It is seen from this definition that exergy is dependent on the state of the total system (=system + reservoir) and not dependent entirely on the state of the system. Exergy is therefore not a state variable. In accordance with the first law of thermodynamics, the increase of energy in the reservoir, DU, is

where Uo is the energy content of the system after the transfer of work to the reservoir has taken place. According to the definition of exergy, Ex, we have

(when we consider only heat, spatial energy (displacement work) and chemical energy, see any textbook in thermodynamics), and correspondingly for Uo:

c we get the following expression for exergy, excluding of course in this case kinetic energy, potential energy, electrical energy, radiation energy and magnetic energy:

Notice that the above-shown equation also emphasizes that exergy is dependent on the state of the environment (the reservoir = the reference state), as the exergy of the system is dependent on the intensive state variables of the reservoir. Notice furthermore that exergy is not conserved—only if entropy-free energy is transferred, which implies that the transfer is reversible. All processes in reality are, however, irreversible, which means that exergy is lost (and entropy is produced). Loss of exergy and production of entropy are two different descriptions of the same reality, namely that all processes are irreversible, and we unfortunately always have some loss of energy forms which can do work to energy forms which cannot do work (heat at the temperature of the environment) (see also J0rgensen, 2002). So, the formulation of the second law of thermodynamics by use of exergy is

All real processes are irreversible which implies that exergy inevitably is lost.

Exergy is not conserved, while energy of course is conserved by all processes according to the first law of thermodynamics. It is therefore wrong to discuss, an energy efficiency of an energy transfer, because it will always be 100%, while the exergy efficiency is of interest, because it will express the ratio of useful energy to total energy which always is less than 100% for real processes. All transfers of energy imply that exergy is lost because energy is transformed to heat at the temperature of the environment.

It is therefore of interest to set up for all environmental systems an exergy balance in addition to an energy balance. Our concern is loss of exergy, because that means that ''first class energy'' which can do work is lost as ''second class energy'' (heat at the temperature of the environment) which cannot do work. So, the particular properties of heat and that temperature is a measure of the movement of molecules, given limitations in our possibilities to utilize energy to do work. Due to these limitations, we have to distinguish between exergy which can do work and anergy which cannot do work, and all real processes imply inevitably a loss of exergy as anergy (see also next section).

Exergy seems more useful to apply than entropy to describe the irreversibility of real processes, as it has the same unit as energy and is an energy form, while the definition of entropy is more difficult to relate to the concepts associated to our usual description of the reality. In addition, entropy is not clearly defined for ''far from thermodynamic equilibrium systems'', particularly for living systems (see, for instance, Tiezzi, 2003). Moreover, it should be mentioned that the self-organizing abilities of systems are strongly dependent on the temperature, as it is discussed in J0rgensen et al. (1999). Exergy takes the temperature into consideration as the definition shows, while entropy doesn't. It implies that exergy at 0K is 0 and at minimum. The negative entropy is not expressing the ability of the system to do work (we may call it ''the creativity'' of the system as creativity requires work), but exergy becomes a good measure of ''the creativity'', which is increasing proportional with the temperature. Furthermore, exergy facilitates the differentiation between low-entropy energy and high-entropy energy, as exergy is entropy-free energy.

Finally, notice that information contains exergy. Boltzmann (1905) showed that the free energy of the information that we actually possess (in contrast to the information we need to describe the system) is k x T x ln I, where I is the information we have about the state of the system, for instance, that the configuration is 1 out of W possible (i.e., that

W = I) and k is Boltzmann's constant = 1.3803 x 10—23 (J/molecules x deg). It implies that one bit of information has the exergy equal to kTln2. Transformation of information from one system to another is often almost an entropy-free energy transfer. If the two systems have different temperatures, the entropy lost by one system is not equal to the entropy gained by the other system, while the exergy lost by the first system is equal to the exergy transferred and equal to the exergy gained by the other system, provided that the transformation is not accompanied by any loss of exergy. In this case, it is obviously more convenient to apply exergy than entropy.

Exergy of the system measures the contrast—it is the difference in free energy if there is no difference in pressure and temperature, as may be assumed for an ecosystem or an environmental system and its environment—against the surrounding environment. If the system is in equilibrium with the surrounding environment ,the technological exergy is of course zero. The only way to move systems away from equilibrium is to perform work on them. Therefore, it is reasonable to use the available work, that is the exergy, as a measure of the distance from thermodynamic equilibrium. As we know that ecosystems due to the through-flow of energy have the tendency to move away from thermodynamic equilibrium, loosing entropy or gaining exergy and information, we can put forward the following proposition of relevance for ecosystems.

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