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Exergy is not conserved unless 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, 2001b). So the formulation of the Second Law, using exergy is: All real processes are irreversible which implies that eXergy is inevitably lost. EXergy is not conserved; while energy, of course, is conserved by all processes according to the First Law. It is therefore wrong (as already mentioned briefly) to speak of the energy efficiency of an energy transfer because it will always be 100%; rather, the exergy efficiency is of interest because it expresses the ratio of useful energy to total energy, which is always less than 100% for real processes. All transfers of energy imply that exergy is lost because energy is transformed into heat at the temperature of the environment.

It is, therefore, of interest for all environmental systems to set up an exergy balance in addition to an energy balance. Our concern is loss of exergy, because here "first class energy" which can do work is lost and replaced by "second class energy" (heat at the temperature of the environment) which cannot do work. So, as presented in Chapter 3, the particular properties of heat and of temperature are a measure of the movement of molecules, and give limitations in our possibilities to utilise energy to do work. Due to these limitations, we have to distinguish between exergy, which can do work, and energy, which cannot do work. The latter may be called anergy (see, for instance, Cerbe and Hoffmann, 1996). Therefore, the energy can be represented as a sum of two items:

In accordance with the Second Law, anergy is always positive for any process.

It seems more useful to apply exergy 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 concepts associated with our usual description of reality. In addition, entropy is not clearly defined for systems "far from thermodynamic equilibrium", particularly for living systems (see, for instance, Tiezzi, 2003). Moreover, it should be mentioned that the self-organising abilities of systems are strongly dependent on temperature, as discussed in J0rgensen et al. (1999). Exergy takes the temperature into consideration as the definition shows, while entropy does not. The negative entropy is as discussed in Chapters 2 and 3, i.e. it does not express 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 increasingly proportional with the temperature. Furthermore, exergy facilitates the differentiation between low-entropy energy and high-entropy energy, as exergy is entropy-free energy. These expressions were not properly defined in Chapter 3.

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.

The exergy of the system measures the contrast—i.e. 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—with the surrounding environment. If the system is in equilibrium with the surrounding environment the exergy is, of course, zero.

Since the only way to move systems away from equilibrium is to perform work on them, and since the available work in a system is a measure of the ability to do it, we have to distinguish between the system and its environment or thermodynamic equilibrium, alias, for instance, an inorganic soup. Therefore it is reasonable to use the available work, i.e. 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 losing entropy or gaining exergy and information, we can put forward the following proposition of relevance for ecosystems: Ecosystems attempt to develop towards a higher level of exergy.

It is interesting in this context to draw a parallel with the discussion of the development of entropy for the entire Universe. The classic thermodynamic interpretations of the Second Law of Thermodynamics predict that the Universe will develop towards "the heat death", where the entire Universe will have the same temperature, no changes will take place and a final overall thermodynamic equilibrium will be the result. This prediction is based upon the steady increase of the entropy according to the Second Law of Thermodynamics: the thermodynamic equilibrium is the attractor. It can, however, be shown (see Frautschi, 1988; J0rgensen, 2002b) that we are moving away from the thermodynamic equilibrium at a high rate due to the expansion of the Universe.

Due to the incoming energy of solar radiation an ecosystem is able to move away from thermodynamic equilibrium—i.e. the system evolves and obtains more information and organisation.

The ecosystem must produce entropy for maintenance, but the low-entropy energy flowing through the system may be able to more than cover this production of disorder, resulting in an increased order or information of the ecosystem.

One of the main concepts in the thermodynamics of an open system is the decomposition of the total production of entropy into two items: the rate of entropy exchange between the system and its environment and the internal entropy production by the system: dS/dt = deS/dt + diS/dt. An analogous relation can be written for the time derivative of exergy d(Ex) de(Ex) di(Ex)

dt dt

where, in fact, the real process of the system evolution can be represented as the composition of two processes: the first is a forced movement from thermodynamic equilibrium when the exergy increases, de(Ex)/dt > 0, and the second when the system spontaneously moves to thermodynamic equilibrium. In the course of the latter the exergy decreases, di (Ex)/dt < 0, i.e. it is lost. The loss of exergy is a result of such spontaneous irreversible processes within the system as diffusion, heat conduction, turbulence and chemical reactions (as presented in Chapter 3). Eq. (2.2) shows among other things that systems can only maintain a non-equilibrium steady state by compensating the loss of exergy with a positive exergy inflow. Such an inflow induces order into the system. In ecosystems the ultimate exergy inflow comes from solar radiation, and the order induced is, for example, biochemical molecular order. If di(Ex)/dt > Ide(Ex)/dtl (the exergy loss within the system), the system has surplus exergy input, which may be utilised to construct further order in the system, or as Prigogine (1980) calls it: dissipative structure. The system will thereby move further away from the thermodynamic equilibrium. Evolution shows that this situation has been valid for the ecosphere on a long-term basis. In spring and summer, ecosystems are in the typical situation that de(Ex)/dt exceeds Idi(Ex)/dtl. If di(Ex)/dt < Ide(Ex)/dtl, the system cannot maintain the order already achieved, but will move closer to the thermodynamic equilibrium, i.e. it will lose order. This may be the situation for ecosystems during autumn and winter or due to environmental disturbances.

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