Physical Openness

An energy balance equation for ecosystems might be written as follows in accordance with the principle of energy conservation:

Here Ecap is external energy captured per unit of time. A part of the incoming energy, solar radiation being the main source for the ecosystems on earth, is captured and a part is reflected unused, determining the albedo of the globe. The more biological structure an ecosystem possesses the more of the incoming energy it is able to capture, i.e. the lower the albedo. The structure acts as an umbrella capturing the incoming solar radiation.

In ecosystem steady states, the formation of biological compounds (anabolism) is in approximate balance with their decomposition (catabolism). That is, in energy terms:

The energy captured can in principle be any form of energy (electromagnetic, chemical, kinetic, etc.), but for the ecosystems on earth the short-wave energy of solar radiation (electromagnetic energy) plays the major role. The energy captured per unit of time is, however, according to Equation 2.2 used to pay the maintenance cost per unit of time including evapotranspiration and respiration. The overall result of these processes requires that Ecap to be greater than 0, which entails openness (or at least non-isolation).

The following reaction chain summarizes the consequences of energy openness (Jorgensen et al., 1999): source: solar radiation —■ anabolism (charge phase): incorporation of high-quality energy, with entrained work capacity (and information), into complex bio-molecular structures, entailing antientropic system movement away from equilibrium — catabolism (discharge phase): deterioration of structure involving release of chemical bond energy and its degradation to lower states of usefulness for work (heat) — sink: dissipation of degraded (low work capacity and high entropy) energy as heat to the environment (and, from earth, to deep space), involving entropy generation and return toward thermodynamic equilibrium. This is how the energy cascade of the planet is usually described. Another way might be to express it in terms of gradient creation and destruction. The high-quality entering energy creates a gradient with baseline background energy. This enables work to be done in which the energy is degradiented and dissipated to space. On arrival there (at approximately 280 K) it locally re-gradients this new environment (at 3 K) but then rapidly disperses into the vacuum of the cosmos at large.

This same chain can also be expressed in terms of matter: source: geochemical substrates relatively close to thermodynamic equilibrium — anabolism: inorganic chemicals are molded into complex organic molecules (with low probability, it means that the equilibrium constant for the formation process is very low, low entropy, and high distance from thermodynamic equilibrium) — catabolism: synthesized organic matter is ultimately decomposed into simple inorganic molecules again; the distance from thermodynamic equilibrium decreases, and entropy increases — cycling: the inorganic molecules, returned to near-equilibrium states, become available in the nearly closed material ecosphere of earth for repetition of the matter charge-discharge cycle.

Input environments of ecosystems serve as sources of high-quality energy whose high contents of work and information and low entropy raise the organizational states of matter far from equilibrium. Output environments, in contrast, are sinks for energy and matter lower in work capacity, higher in entropy, and closer to equilibrium. This is one possibility. On the other hand, since output environments also contain equilibrium-avoiding entities (organisms), their energy quality on a local basis might be just as great as that of organisms in input environments. Since, output environments feedback to become portions of input environments living systems operating in the ecosphere, which is energetically non-isolated but materially nearly closed, must seek an adaptive balance between these two aspects of their environmental relations in order to sustain their continued existence. That is, the charge-discharge cycle of the planet wraps output environments around to input environments, which homogenizes gradients and forces gradient-building (anabolic) biological activity.

The expression high-quality energy is used above to indicate that energy can either be applied to do work or it is what is sometimes called "anergy", i.e. energy that cannot do work. The ability to do work can be expressed by:

Work = an extensive variables X a difference in intensive variables

For instance

where m is the mass, g the gravity, h the height, and (h1 - h2) the difference in height (see Table 2.1).

The concept exergy was introduced by Rant (1953) to express the work capacity of a system relative to its environment (see details presented in Wall, 1977; Szargut et al., 1988). It was particularly useful when the efficiencies of a power plant or the energy transfer should be expressed. We have therefore:

Qevap + Qresp in Equations 2.1 and 2.2 represents anergy because it is heat at the temperature of the environment. The temperature of the ecosystem would currently increase, if the ecosystem was not open at both ends, so to say. The heat is exported to the environment. The openness, or actually non-isolation, of ecosystems makes it possible for the systems to capture energy for photosynthesis but also to export the generated heat to maintain an acceptable temperature for the life processes.

Exergy as it is defined technologically cannot be used to express the work capacity of an ecosystem, because the reference (the environment) is the adjacent ecosystem. The Eco-exergy expresses, therefore, the work capacity of an ecosystem compared with the same system as a dead and completely homogeneous system without gradients. See Box 2.1 for definition and documentation of "eco-exergy."

Eco-exergy expresses the development of an ecosystem by its work capacity (see Box 2.1). We can measure the concentrations in the ecosystem, but the concentrations in the reference state (thermodynamic equilibrium; see Box 2.1) can be based on the usual use of chemical equilibrium constants. If we have the process:

Component A o inorganic decomposition products (2.6)

it has a chemical equilibrium constant, K:

K = [inorganic decomposition products] / [component A] (2.7)

The concentration of component A at thermodynamic equilibrium is difficult to find (see the discussion in Chapter 6), but we can, based on the composition of A, find the concentration of component A at thermodynamic equilibrium from the probability of forming A from the inorganic components.

Box 2.1 Eco-exergy, definition

Eco-exergy was introduced in the 1970s (Jorgensen and Mejer, 1977, 1979; Mejer, 1979; Jorgensen, 1982) to express the development of ecosystems by increase of the work capacity. If we presume a reference environment that represents the system (ecosystem) at thermodynamic equilibrium, which means that all the components are inorganic at the highest possible oxidation state if sufficient oxygen is present (as much free energy as possible is utilized to do work) and homogeneously distributed at random in the system (no gradients), the situation illustrated in Figure 2.1 is valid. As the chemical energy embodied in the organic components and the biological structure contributes far most to the exergy content of the system, there seems to be no reason to assume a (minor) temperature and pressure difference between the system and the reference environment. Under these circumstances we can calculate the exergy content of the system as coming entirely from the chemical energy:

where /xc and nco are the chemical potentials and N in the number of chemical compounds.

This represents the non-flow chemical exergy. It is determined by the difference in chemical potential (^c-^m) between the ecosystem and the same system at thermodynamic equilibrium. This difference is determined by the concentrations of the considered components in the system and in the reference state (thermodynamic equilibrium), as it is the case for all chemical processes.

Ecosystem at temperature T and pressure p

Ecosystem at temperature T and pressure p

WORK CAPACITY = ECO-EXERGY = i=n

where mi is the amount of component i and Mi is the chemical potential of component i in the ecosystem Mio is the corresponding chemical potential at thermodynamic equilibrium

Reference system: the same system at the same temperature and pressure but at thermody-mic equilibrium

Reference system: the same system at the same temperature and pressure but at thermody-mic equilibrium

Figure 2.1 The exergy content of the system is calculated in the text for the system relative to a reference environment of the same system at the same temperature and pressure at thermodynamic equilibrium, it means as an inorganic soup with no life, biological structure, information, gradients, and organic molecules.

Eco-exergy is a function of the reference state which is different from ecosystem to ecosystem. Eco-exergy expresses, therefore, the work capacity relative to the same system but at thermodynamic equilibrium. Eco-exergy can furthermore, with the definition given, be applied far from thermodynamic equilibrium. It should be mentioned that eco-exergy cannot be measured, as the total internal energy content of a body or system cannot be measured. Even a small ecosystem contains many microorganisms and it is, therefore, hardly possible by determination of the weight of all components of an ecosystem to assess the eco-exergy of an ecosystem. The eco-exergy of a model of an ecosystem can, however, be calculated as it will be shown in Chapter 6.

We find by these calculations the exergy of the system compared with the same system at the same temperature and pressure but in form of an inorganic soup without any life, biological structure, information, or organic molecules. As (^c-uco) can be found from the definition of the chemical potential replacing activities by concentrations, we get the following expressions for the exergy:

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