entropy

4. The improved conception of irreversible thermodynamic processes

Studying in the previous items the models of thermodynamical systems, we permanently encountered the term ‘irreversibility of thermodynamic processes’ and saw, this irreversibility is conventionally related exceptionally to the thermal conduction, and there are excluded all physical processes causing the disbalance of the system, when previously disbalanced thermodynamical system was isolated from any external affections. We also encountered the fact that sometimes the system was isolated conventionally, with ignoring real physical processes accompanying the heat transfer, nothing to say of processes that do not accompany it. In particular, on the example of Pohl’s model we could see that he ignored the gas heating that preceded the work of gas and did not properly account the very process of plunger’s work that premises the difference of pressures, not only the pressure of expanding gas. And when we raise the issue, why thermodynamical processes in the systems are irreversible, the authors usually point namely those processes which they ignored in their modelling schemes. “Let some body be sliding on another body. Due to the friction, this motion will be gradually decelerating, finally the system will come to the state of thermal equilibrium and the motion will stop. The kinetic energy of moved body will go into the heat, i.e. into the kinetic energy of chaotic motion of molecules of both bodies” [4, p. 210]. However, just this dissipative process of friction causes the result – the energy of reciprocal motion going over to the thermal energy of molecules of these bodies.

All these features are reflected in the definitions of reversibility of thermodynamical processes. “All reversible processes are characterised by three indications: reversible processes admit (when necessary, through the related additional instrument) the reverse going, by way of simple change of the path direction; to restore the initial state, it needs no energy supply; the reversible process retains in no of participating bodies a long-lasting change of state” [8, p. 432]. As a corroborating example, Pohl describes the following experiment of quasi-static transformation of liquid in its saturated vapour. “We see in Fig. 3 a cylinder with the plunger.

Under the plunger there is the liquid, and between its surface and plunger – its saturated vapour. The plunger is loaded by a weight, and above the plunger the air has been pumped down from the cylinder. Choosing the weight, we can make the pressure practically equal to that of saturation. Then the plunger either very slowly rises up and all liquid turns into vapour (case A), or it very slowly lowers and all vapour turns into liquid (case C). In this case the environment serves as the keeper of heat. The heat absorption in evaporation, as well as the heat extraction in condensation, goes here quasi-statically and so is reversible. A however small change of temperature is sufficient to direct the process to some or other trend” [8, p. 432]. As we can see from the description of this experiment, there occurs an opposite pattern. To turn the liquid into vapour and vice versa as our wish, we have to apply the external force, which in this case is the Earth gravity force, and to supply a definite quantity of heat from the exterior source. Should R.W. Pohl try to carry such experiment out in the Earth orbit, in weightless state, he would have to apply instead the weight a special device affecting the studied volume as the external forces. Understanding it, the author agrees, the volume is not isolated, and dependently on the process, the exterior medium is a stock either a source of turns in the studied cylinder. From the outwards it is very like the situation with inventors of perpetual mobile who usually disregard the gravity, thinking it to be something natural – thus, irrelevant to the concepts of force and work.

But possibly, in this case also, Pohl’s definition and example are not fully correct? Let us analyse other definitions of reversibility. “Reversible process is the process in which the system passes from one state to another, with which we can compare a really possible reverse transition that sequentially repeats in the inverse order all intermediate states of the considered process” [14, p. 469]. And “natural processes usually do not satisfy this condition and are irreversible, only some of them at idealised conditions can be thought reversible” [ibidem]. As we see, this definition in fact reiterates that Pohl’s but is well less particular. Pohl clearly said, the reversibility is achieved through the interaction with surrounding medium, while this second definition only vaguely states the fact that the processes are not fully reversible. This does not lift the doubt in full reversibility at Pohl’s conditions.

And Sedov’s formulation adds nothing new: “The process going from some state A to the state B is called reversible, if for each intermediate state all equations for infinitesimal increments of parameters are true, too, when the signs of these increments are changed to opposite. Thus, if some sequence of states arranges in the space of states a reversible process, the system can go through this space both forth and back” [9, p. 210]. Proceeding from this definition, all above irreversible processes are in fact reversible. Actually, if we study the gas expanding into a void space and think this process irreversible, we can study in the same way the gas compression, thinking this process also irreversible. Well, lifting the load, we never will turn the system to its initial position, because of inevitable energy loss. The same, studying the phase transition, we spend some heat in the liquid-to-vapour change, but in studying the reverse transition, we return this heat accurate to the loss. Sedov factually corroborates it on his example of reversible process. “The study shows, sometimes we practically can think reversible even a fast process of gas particles effusion from the jet engine nozzle in which the gas particle during the time about one thousandth part of a second passes from the state of practically rest with the pressure about 70 atmospheres in the jet engine combustion chamber to the state of motion with the speed about 3000 m/s and almost zero pressure in the free space” [9, p. 211]. This Sedov’s example, as opposite to the above Landau’s example of spontaneous gas expansion, differs only in the following. In the first case the pressure source is in the very combustion chamber, while in Landau’s example the gas was compressed before experimenting. This is not the matter of principle, as it depends not on the phenomenology of process as such but on the experimenter’s personal decision to account or not the full amount of experimental parameters.

This also is reflected in the definitions of irreversible processes, as in accordance with the definition, “the irreversible processes are such processes that can spontaneously occur only in one direction. Processes of diffusion, thermal conductance, viscous flows, gas expansion to a void etc. relate to them” [15, p. 413]. And “in closed-loop systems, the entropy growth accompanies the irreversible processes; in open systems the entropy in irreversible processes can remain constant and even decrease, but the value of entropy producing is positive in all cases” [ibidem]. The same, “Irreversible processes are opposite to those reversible. There relate to them first of all diffusion, throttling, exterior and interior friction, plastic deformation of bodies, thermal conductance with infinitesimal difference of temperatures, heat transfer through the radiation and, finally, all chemical reactions that occur not infinitely slow. Irreversible processes are characterised by three indications.

1. All irreversible processes as such go only in one direction. …

2. In all irreversible processes the work is spent …

3. In closed-loop systems, the irreversible processes cause the long-term change of state” [8, p. 433–434].

As we see, not only the processes related immediately to the energy dissipation – such as thermal conductance and friction, but also diffusion and gas expansion are attributed to those irreversible. And at the same time these authors interpret these processes as reversible. In particular, we can suggest a simple and visual experiment concerning to diffusion. Take two gases much different in their molecular weight and put them into a large vessel divided into two equal parts by a partition. When opening the partition, we will see the diffusion, but it will be not so one-directed as it is usually described. After a long time the gases will not mix, as supposed, but will separate again: the heavy gas will be located in the bottom, and light gas – above it. The diffusion will take place in some boundary layer. Yes, it relates to affection of the external gravity field, but at the same time, as we could see above, all reversible processes are accompanied with the external work done. Only by changing the direction of heat supply or by doing the work, we can change the direction of process.

At the same time, there in the nature really exist the processes of one direction – such as thermal conductance, thermal radiation, however these processes are local and cause the dissipation of thermal energy. But the process of gravity compression of substance as such, separated from the dynamic balance, also can be related to irreversible processes, as we cannot provide in this process a spontaneous expansion of a gas cloud to its initial size. And, as we could see, the entropy produced in gravity compression is negative; this also puts in doubt both conventional opinion of inevitably growing entropy and entropy calculation, which we will try to clear below.

Concerning only the irreversibility of processes caused by dissipation, we can surely say, the entropy of these systems will be negative, not positive, as it is thought conventionally. Actually, if the irreversibility of processes is caused namely by the energy loss in circular process due to the dissipation into environment, such systems cannot be automatically thought isolated; in other words, all irreversible processes related to the energy loss are open. “In case of irreversible circular process we have

has not a definite value” [16, p. 310]. Although this last Rossel’s conclusion of indefinite entropy value in such circular processes is not so much correct and connected rather with a wish, despite the discrepancy, to prove the entropy growth, while it obviously falls. Later he by his own hand will write the entropy of the system for the direct and inverse branches of cycle. And the very fact that the entropy is determined for both branches says, for the cycle on the whole the entropy is determined and really has a negative, not positive value.

To finish the issue of reversible and irreversible processes, we can say, basing on this analysis, that if we consider the ideal systems without energy loss, the reversibility of processes can be defined in two meanings.

In the narrow meaning of particular processes in local isolated systems, with disregarded pre-history and energy loss because of imperfect isolation of the system, most processes thought now irreversible are just such. For example, in a local thermodynamical system, really, we cannot return the gas expanded into a void space to its initial volume without applying an additional external work. But this irreversibility is conventional and limited by the frames of particular experiment. It would be absolutely incorrect to extend the results of experiment onto some global physical systems. Because, as we said above, all such experiments would be impossible, if not prematurely breaking the equilibrium of system on the account of same external forces and sources. In fact, all such local irreversible processes we can attribute to the phenomena providing the system’s return from the excited state to the equilibrium. And the phenomena that provide the system’s excitation do not relate to this kind of processes, as usually they have a global scale. One of such global processes is a spontaneous compression of gas clouds in the astronomical scale.

In the broad sense we can speak of processes irreversibility, minding only three kinds of processes. These are heat transfer, heat radiation and spontaneous gravity compression. These three processes provide the main diversity of forms of energy transformation in the universe, including chemical, nuclear, thermonuclear etc. Each of these processes is irreversible because, according to the laws of mechanics, is unable to transmit the energy from the low- to high-energy bodies. This means, we are unable to change the direction of heat transfer, of EM waves propagation – and this means, we are unable to reverse the body’s radiation. And finally, we are unable to change the direction of spontaneous gravity compression, because, as opposite to the electric interaction, it has only one sign – the body-to-body attraction. This last does not mean a little that we are unable to create the conditions for anti-gravity. But these conditions will be local, and they will not correspond to spontaneous processes. To create them, we will have to use an additional energy exciting the local forces that will compensate the gravity attraction.

Basically, only two processes of three listed can occur, as heat conductance and heat radiation have, in their essence, common nature and we can classify them as dissipative phenomena – i.e. phenomena providing the averaging of the energy in space. And the gravity compression relates to the phenomena localising the energy. These two phenomena provide the energy balance in the universe.

An additional important point in this conclusion is, the source energy cannot be concentrated locally, as the gravity forces are too weak to affect locally. So in local reference frames they are usually ignored. At the same time, all local sources of energy can originate only on the basis of global sources, with use of phenomena related to the energy dissipation. In this way all sources used in local isolated thermodynamical systems factually facilitate the energy dissipation of the main source. And the dissipative phenomena are revealed both globally and locally, violating the thermoisolation in the local systems and making the experimenters compensating the loss for friction and radiation on the account of external energy source. So in analysing of thermodynamical state of the system, their part is highly important. But dissipative phenomena, as we already said, reveal themselves also globally through stellar and cluster radiation, affecting the near clouds of gas and exciting them. At the same time the dissipative phenomena facilitate new fluctuations in the interstellar medium that cause the birth of new sites of origin of the energy localisation. But not only dissipative processes facilitate the origin of new energy sources. This system differs from the conventional idea of thermodynamic equilibrium as follows. In this case neither dissipative processes are able to change the sign of gravitational interaction of the matter nor the gravitational interaction is able to block dissipative processes. These processes go independently of each other and thermodynamically opposing each other. They can affect each other only through other phenomena. Thus, when compressed, the substance is heated and this prevents the further compression, and effective thermoisolating shell that is formed around the star’s nucleus as the energy source lowers to some extent the intensity of heat removal from the source. But their mutual affection is limited to this level. The gravity forces are unable to affect the dissipation, the same as dissipative processes are unable to prevent gravitational compression whose conditions of occurrence are only the density and volume of material substance in some region of space. Thereupon, the thermodynamical equilibrium in the full meaning of this word cannot be achieved, there is possible only a permanent continuous opposite process that balances the thermodynamical system as the whole and never brings the system to the unlimited in time thermodynamical equilibrium in the global or in local scale. So we may not consider the opposing affection of these phenomena as some fluctuation. For it, the system would have to be in a stable asymptotic equilibrium. But just this equilibrium is impossible, as the gravity compression needs no external source of energy. Heterogeneities can only facilitate the process but are not its definitive conditions. When the spontaneous compression originates, the heating of gas medium is inevitable, and this energises the mechanism of energy dissipation which does not prevent the gravity compression but is in strong relation with this process, causing in a long evolution of star the full dissipation of the source energy.

Because of the said, the part of entropy becomes basically other. It is important for us to grasp this part, in order to estimate the real descriptive function of this parameter both in the local and global meaning of thermodynamical processes.

V.6 No 1	21
Some improvements to the definition of entropy of macrosystem