This description of exergy development in ecosystems makes it pertinent to assess the exergy of ecosystems. It is not possible to measure exergy directly—but it is possible to compute. If we presume a reference environment that represents the same 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 in the system (no gradients), the situation illustrated in Figure 1.2 is valid. As the chemical energy embodied in the organic components and the biological structure contribute 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, which we will name eco-exergy to distinguish from the technological exergy defined above, as coming entirely from the chemical energy:
This represents the non-flow chemical exergy. It is determined by the difference in chemical potential (/j,c — ^co) 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. We can measure the concentrations in the ecosystem, but the concentrations in the reference state (thermodynamic c
Ecosystem at temperature T and pressure p
Ecosystem at temperature T and pressure p
WORK CAPACITY = ECO-EXERGY =
where m, is the amount of compo-inent i and ^, is the chemical potential of component i in the ecosystem Hlo is the corresponding chemical potential at thermodynamic equilibrium
Reference system: the same system at the same temperature and pressure but at thermodynamic equilibrium
Figure 1.2 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, but as an inorganic soup with no life, biological structure, information or organic molecules.
equilibrium) can be based on the usual use of chemical equilibrium constants. If we have the process:
Component A $ inorganic decomposition products (1.15)
It has a chemical equilibrium constant, K:
K = [inorganic decomposition products] / [Component A] (1.16)
The concentration of component A at thermodynamic equilibrium is difficult to find, but we can find it from the probability of forming A from the inorganic components.
Eco-exergy is a concept close to Gibb's free energy (De Wit, 2005); but opposite to Gibb's free energy, eco-exergy has a different reference state from case to case (from ecosystem to ecosystem) and it can furthermore be used far from thermodynamic equilibrium, while Gibb's free energy in accordance to its exact thermodynamic definition is only a state function close to thermodynamic equilibrium.
We find by these calculations the eco-exergy of the system compared with the same system at the same temperature and pressure but in the form of an inorganic soup without any life, biological structure, information or organic molecules. As ^c — ^co can be found from the definition of the chemical potential replacing activities by concentrations, we get the following expressions for the exergy:
where R is the gas constant (8.317 J/K moles = 0.08207 l atm/Kmoles), T is the temperature of the system, while Ci is the concentration of the ith component expressed in a suitable unit, for example for phytoplankton in a lake, Ci could be expressed as mg/l or as mg/l of a focal nutrient. Ci,o is the concentration of the ith component at thermodynamic equilibrium and n is the number of components. Ci,o is of course a very small concentration (except for i = 0, which is considered to cover the inorganic compounds), corresponding to a very low probability of forming complex organic compounds spontaneously in an inorganic soup at thermodynamic equilibrium. Ci,o is even lower for the various organisms, because the probability of forming the organisms is very low with their embodied information which implies that the genetic code should be correct.
By using this particular exergy based on the same system at thermodynamic equilibrium as reference, the eco-exergy becomes dependent only on the chemical potential of the numerous biochemical components that are characteristic for life. It is consistent with Boltzmann's statement that life is struggle for free energy.
The total eco-exergy of an ecosystem cannot be calculated exactly, as we cannot measure the concentrations of all the components or determine all possible contributions to the eco-exergy of an ecosystem. If we calculate the eco-exergy of a fox, for instance, the above-shown calculations will only give the contributions coming from the biomass and the information embodied in the genes, but what is the contribution from the blood pressure, the sexual hormones and so on? These properties are at least partially covered by the genes, but is that the entire story? We can calculate the contributions from the dominant components, for instance, by the use of a model or measurements that covers the most essential components for a focal problem. The difference in eco-exergy by comparison of two different possible structures (species composition) is decisive here. Moreover, eco-exergy computations give always only relative values, as the eco-exergy is calculated relatively to the reference system.
Notice that the definition of eco-exergy is very close to free energy. Eco-exergy is, however, a difference in free energy between the system and the same system at thermodynamic equilibrium. The reference system used is different for every ecosystem according to the definition of eco-exergy. In addition, free energy is not a state function far from thermodynamic equilibrium. Consider, for instance, the immediate loss of free energy (or let us use the term eco-exergy as already proposed to make the use of the concepts more clear) when an organism dies. A microsecond before the death the information can be used and after the death the information is worthless and should therefore not be included in the calculation of eco-exergy.
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