Fig. 5.2. Entropy versus internal energy.

The state of equilibrium we are referring to (the point c in Fig. 5.2) obviously does not coincide with the state of equilibrium corresponding to the given value, Ut (the point a).

Since the system represents only a very small part of the whole supersystem, the processes taking place in it lead to relatively insignificant changes in the total energy and entropy. From Fig. 5.2 it thus follows that ASt < — {dSt(Ut)/dUt|8Amin = {dSt(Ut)/dUt|8Amax, where the derivative dUt/dSt is the equilibrium temperature of the supersystem, i.e. the temperature T0 of the environment. Thus,

This equality expresses how much the entropy of the closed supersystem differs from its maximum possible value if the system is not in equilibrium with its environment, where AU, AS, AV and DNi are, respectively, the differences between the energy, entropy, volume, the number of particles in the system and their values in the state of total thermodynamic equilibrium.

We can see that when we want to describe the behaviour and properties of an open system which is connected very closely with its surrounding environment (this is a typical definition of ecosystem), then the concept of maximum work considered above plays a very important role. For this reason this work has been honoured with a special term: exergy. Exergy (Ex) is defined as the amount of work (= entropy-free energy) a system can perform when it is brought into thermodynamic equilibrium with its environment, i.e. l^max l = Ex (J0rgensen et al., 1999). The state of the environment is usually named as the reference state. Note that exergy is, therefore, not a state variable. For instance, as a reference state we can select the same system but at thermodynamic equilibrium, i.e. such that all components are inorganic and at the highest oxidation state if sufficient oxygen is present (nitrogen as nitrate, sulphur as sulphate and so on). The reference state in this case n

SAmax = To DSt = To (St - Sfq ) = DU - To DS + pQ DV - £ M DNt

will correspond to the ecosystem without life forms and with all chemical energy utilised or as an "inorganic soup". This usually implies that we consider T = T0 and p = p0, which means that exergy becomes equal to the difference of Gibb's potential (free energy) of the system and the same system is at thermodynamic equilibrium. Notice also that exergy depends on intensive state variables of the environment.

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