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ENERGY USEFUL AND UTILIZABLE

Physics. Research in physics.

Doctor of technical sciences, prof., Etkin VA

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Energy is useful and useless. The analytical expression for the first law of thermodynamics in the form (2) gave JK Maxwell the basis for determining energy as the sum of all the actions that a system can produce over the environment . A common measure of this action is, as you know, work. However, in the classical thermodynamics of closed systems, heat and work are qualitatively different ways of supplying energy [5]. It is generally believed that the work done on the system "can directly go on increasing any form of its energy, while heat is only for replenishing internal energy" [3]. Therefore, Maxwell's point of view, which relates heat exchange to a kind of "micro-work," has not become widespread. Meanwhile, it is here that the opportunity opens up to return to the original understanding of energy as a measure of the system's efficiency. For this it is necessary only to generalize the concept of work.

We give the most general definition of work as a quantitative measure of the process associated with the overcoming of any forces F. The forces have a different (i-th) nature and, accordingly, are divided into mechanical, thermal, chemical, electrical, magnetic, gravitational, etc. We shall denote them by . Distinguish between the forces of mass, volume, surface, etc. - depending on the quantitative measure of the object θi of its application, they are proportional (mass M, volume V, surface f, etc.). To the parameters Can also be attributed to the charge , The entropy S, the momentum Mv, etc. These parameters are extensive quantities, i.e. - the value of the parameter For a single particle of the k-th kind, which is the carrier of this form of energy (hereinafter, for brevity, energy carrier).

In general, the forces of the i-th nature act on any k-th particle, which forms a given hierarchical level of the structure of matter (nuclei, atoms, molecules, cells, etc.). Denoting this "elementary" force through , The resultant force , Acting on all particles of a given kind, we find the sum . These forces can be subdivided into external and internal, depending on whether they act between the particles of the system or between the system and the environment.

These general considerations are sufficient to establish the existence of two categories of work that differ in the presence or absence of the resultant overcoming forces. Let us consider the case when the elementary forces Cause displacement One sign of the objects of its application, i.e. The work has an orderly, directional character. In this case , And strength Have a resultant Even in homogeneous systems. This, for example, is the work of accelerating the system as a whole. The same ordered nature is the work on a heterogeneous system, when the forces Are applied to subsystems with the opposite sign of any property , For example, to positive and negative charges, to the north and south poles of magnetic dipoles, to electrons and holes in metals, to regions with a reduced and increased (in comparison with the average) etc. This kind of useful work is done with the polarization of dielectrics and magnets, the dissociation and ionization of gases, the stretching of the rod, the redistribution of charges, substances, impulses and entropy between parts of the initially homogeneous system. Breaking down for this case the sum Into two parts having the same sign of magnitudes and , We again obtain a nonzero resultant force . Work of this kind is usually called useful .

Another character gets the job when the object of the application of force Moves or is oriented chaotically. Imagine the power As a product of its module And the unit vector , Characterizing the direction of the force: . In this case So that the presence of the resultant depends both on the magnitude of the elementary forces , And from their direction. In the case of homogeneous systems (where Ubiquitously the same), taking them for the sign of the sum, we find that the presence of the resultant Depends solely on the direction of the elementary forces And with their chaotic orientation Is equal to zero. Forces , Oriented randomly, are usually called scattering forces, and the work against such forces is dissipative The accomplishment of this work causes the heating of the system, the destruction of matter and other phenomena. It is to this kind of work that the micro-work accompanying heat exchange should be attributed. Dissipative work is reminiscent of "Sisyphean labor" for raising boulders to a mountain, which immediately slid back, and in this sense is useless.

Resultant Will also be absent in the case when the forces Order, but the movements caused by them Are mutually compensated. Let us show, for example, that the work of a comprehensive expansion refers to the same category of impacts that do not have a resultant, as is reversible heat exchange. Considering the local pressure p as the force p acting on the surface element In the direction of the normal n, on the basis of the divergence theorem, we find that the resultant of the pressure forces in the absence of pressure gradients Is equal to zero:

Thus, the work of comprehensive expansion is not connected with overcoming the resultant pressure forces. To this category is the work of the uniform introduction of matter, charge, etc. into the system, since this does not disturb the internal equilibrium in the system. Since a homogeneous (internally equilibrium) system alone can not do useful work (see below), there is reason to call this work dissipative (useless). Note, however, that with respect to the "extended" system, which includes the environment - a source of matter or charge, this work is already useful, because it breaks the balance in it. Note also that in spite of the absence of the resultant force Sum of elementary strength modules When doing dissipative work has a finite value. In the future, this allows us to introduce the concept of a generalized potential . Such potentials are, in particular, the absolute temperature T and the pressure p, and Potentials.

Thus, we have the opportunity to distinguish between the useful And dissipative Work on whether the forces to be overcome have a resultant , Or not . A useful work done on a set of interacting (mutually moving) bodies or parts of the body necessarily violates the equilibrium in such a system, even if the processes are quasi-static (infinitely slow). It differs in that it leads to opposite in nature state changes in these subsystems: the appearance of opposite charges or poles, opposite in direction to the displacement of different parts of the body, an increase in temperature, pressure, concentration of any substances, etc. In some parts of the system, and lowering them - in others. However, this work is done against the same forces , As dissipative work.

In order to finally see the unity of the nature of the forces overcome when performing useful and dissipative work, it is useful to represent the energy U as a function of a certain number of coordinates of a state of vector nature Is the radius vector of the center of magnitude In the chosen frame of reference [7]. These parameters were called by us earlier "distribution moments" (entropy, kx substances, volume, charge, pulse, etc.) [7]. The number of such independent coordinates determines the number of energy forms that the system possesses. In this case, the energy U as a function of the state has the form And its total differential is given by:

Presenting In the form of a sum , Whose terms are found under the conditions of Instead of (8) we can write:

Taking into account that the derivatives Represent respectively the generalized potentials And strength In their usual (Newtonian) understanding, we arrive at the basic equation of thermodynamics of nonequilibrium systems in the form of an identity [7]:

Where the terms of the first sum under reversible conditions characterize the "useless" work (external heat transfer Work of comprehensive compression - Energy mass exchange , The work of charging an electric charge (Φ is the electric potential), etc.), and the terms of the second sum are useful external work of the i-th kind, performed by the system:

Thus, the members of the first and second sums (10) are two independent categories of work connected with the overcoming of forces of the same i-th nature. The qualitative difference between these processes is that as a result of committing useful work the system deviates from internal equilibrium and acquires the ability to convert energy from one form to another (including thermal one). Thus, the main feature of useful work is that it is a quantitative measure of the energy conversion process [7].

Unlike it, the dissipative work Causes the same in nature and magnitude of changes in the state (parameters ) In different parts of the system (uniform increase or decrease of temperatures (entropy), pressures (densities), masses (concentrations), etc.). The same analytical form of representation has the work of introducing electric charge, heat of friction, heat of phase transitions and homogeneous chemical reactions. Although every elementary act of doing dissipative work still has a vector character, causing an elementary displacement Of each k-th particle separately , The resultant force Is absent in this case. This brings the input work together with the work against frictional forces (scattering). Their common feature is the process scalarization , i.e. The loss of the work process of its directed nature with the transition from the microlevel to the macro level. At the same time for the system as a whole:

The main distinguishing feature of dissipative work is that it does not disturb the equilibrium in the system, and therefore does not affect its ability to subsequently perform useful external or internal work. Therefore, it can be defined as a quantitative measure of the energy transfer process (energy transfer without changing its shape). Since the dissipative work at the microlevel is directional in character and does not differ from useful work, heat exchange can be attributed to a kind of "micro work".

As we see, the presence or absence of the resultant Has a profound physical meaning, pointing out that the essence of the matter is not in the form of supplying energy to the system, but in the form of its perception by the system. In particular, it is possible to disrupt the internal thermal equilibrium in the system by cooling part of the system by heat exchange. However, as a result of this, the system will acquire the ability to perform useful work, because it will include a heat source and a heat receiver. As a result, we increased the efficiency of the system, reducing its energy.

Thus, we come to the need to distinguish in the composition of the energy of the system its useful (transformable, efficient, non-equilibrium) part, and the useless (inescapable, inoperative, equilibrium) part. It would be expedient to call for brevity the first (in the absence of more suitable terms) inertia (From Greek - internal, - action), which means "internal ability to act", and the second (after Rant) anergy .

Select the inertia As a function of the state can be determined from the known fields of the potential of the inhomogeneous system By the difference between the "medium-energy" value of this potential And its weight average value :

As a function of the state of inertia Has a number of advantages. First of all, it is a more general concept than external energy, since it differs from zero for isolated (closed) systems. Further, unlike the free energy of Gibbs or Helmholtz, energy is a more informative function of efficiency, since its loss - Can be found for each specific process (as the product of the driving force of the process To change its coordinates ):

Finally, unlike exergy, the inertia of the environment is different from zero, if the latter is not in internal equilibrium. This allows us to evaluate the performance of the environment itself, in particular, an excited physical vacuum. For an inhomogeneous system, the ratio of the energy to the energy of the system Characterizes the degree of transformability of energy in it and can serve as a measure of its orderliness as a whole. This makes it possible to reflect, with the help of inertia, qualitative changes in energy in isolated systems, where the inertia is lowered as a result of internal dissipative work and, as a consequence, devaluation of energy1. Thanks to this, the first and second principles of thermodynamics can be combined into one simple and understandable statement: "When spontaneous processes take place in isolated systems, the operable part of its energy (inertia) becomes inoperable (anergy); While their amount remains. "

If the considered system is energy-transforming (carries out the energy conversion), the inertia allows us to introduce the concept of the inertial As the ratio of inertia at the output of the unit To the inertia applied to its input :

This indicator of the perfection of energy converters is applicable to thermal and non-thermal, open and closed cyclic and non-cyclic, direct and reverse machines.

All this makes the inertia a very flexible and convenient tool for the thermodynamic analysis of nonequilibrium systems.

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Author: Doctor of technical sciences, prof., Etkin VA
PS The material is protected.
Date of publication on August 15, 2004