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 (Figure 1). 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 chemical compounds, and by the intensive state variables, T, p, , , ,..., where T is the temperature, p the pressure, and m symbolizes the chemical potential of the components 1,2,3, The system is coupled to a reservoir or reference state by a shaft, together forming a closed system. The reservoir (the environment) is characterized by the intensive state variables To, po, , poCi, ,..., and as
Toward thermodynamic equilibrium with the environment
Figure 1 Definition of exergy is shown. The work is symbolized by the gain in potential energy of the weight.
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 toward 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 (i.e., work energy) must be transferred through the shaft only.
According to the definition of exergy, Ex, we have
(when we only consider the three energy forms: heat, spatial energy (displacement work), and chemical energy; see any textbook in thermodynamics), and correspondingly
we get the following expression for exergy, when in this case kinetic energy, potential energy, electrical energy, radiation energy, and magnetic energy are excluded we have
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.
This definition of exergy is used in engineering to express the efficiency of power plants. The energy efficiency of power plants is of course 100%, according to the first law of thermodynamics, while the interesting efficiency is the exergy efficiency: how much of the chemical energy (exergy) in the applied fossil fuel if fossil fuel is the energy source is converted to useful work (exergy)? What is not converted to exergy in form of electricity is lost as heat to the environment at the temperature of the environment - it contains therefore no work potential.
Notice that the exergy of the system is dependent on the intensive state variables of the reservoir. Notice 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). So, the formulation of the second law of thermodynamic 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.
The efficiency of concern is the ratio of useful energy (work) to total energy which always is less than 100% for real processes, which always are irreversible. This efficiency expresses that a part of the energy cannot be utilized as work and that all processes are irreversible because exergy is lost by all energy transfer processes as heat to the environment.
Exergy efficiency, defined as work performed divided by the total exergy available, is also of interest, particularly in technology. It expresses how much of the work capacity we are able to utilize.
All transfers of energy imply that exergy is lost because energy is transformed to heat at the temperature of the environment. It has therefore been of interest to set up for all environmental systems an exergy balance in addition to an energy balance. Our concern is exergy loss because it means that 'first class energy' which can do work is converted to 'second class energy' (heat at the temperature of the environment) which cannot do work. So, the particular properties of heat and temperature are 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 the next section).
Exergy or rather the loss of exergy as heat, which means production of entropy, seems more useful to apply than entropy to describe the irreversibility of real processes. 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 to our usual description of reality. In addition entropy is not clearly defined for 'far from thermodynamic equilibrium systems', particularly for living systems. Moreover, it should be mentioned that the self-organizing abilities of systems depend strongly on the temperature. Exergy takes the temperature into consideration as the definition shows, while entropy does not. It implies that exergy at 0 K is 0 and at minimum. 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.
Information contains exergy. Boltzmann showed that the free energy of information (it means exergy) that we actually possess (in contrast to the information we need to describe the system) is kT 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 ones and k is Boltzmann's constant 1.3803 x 10~23J/(molecules deg). It implies that one bit of information has the exergy equal to kT ln2. Transformation of information from one system to another is often almost an entropy-free energy transfer. If the two systems have different temperatures, then 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. Also, in this case, it is obviously more convenient to apply exergy than entropy.
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