Introducing the concept “entropy” in the course of natural science at the specialized school
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Introducing the concept «entropy» in the course of natural science at the specialized school
Section 13. Physics
Dubitskaya Larisa Vladimirovna, GAOU VPO & quot-Moscow State Regional Social-Humanitarian Institute& quot-, candidate of pedagogical sciences, Associate Professor of the Department of & quot-Physics, theory and methods of teaching physics and Applied Computer science& quot-
E-mail: l. v. dubi@yandex. ru
Introducing the concept «entropy» in the course of natural science at the specialized school
Abstract: This article discusses the formation of the general scientific concept «entropy» at the masters and practicing teachers who can conduct the integrated natural sciences courses at a specialized school (profile school) in the future.
The analysis of academic literature leads to a conclusion that the process of introducing this concept at school is the most difficult. The analysis of the existing grants on natural sciences for school pupils has shown that this issue is receiving attention only in the book edited by I. Y. Aleksashina where material is presented from a physical point of view and does not have the integrative nature. In our view, the concept of entropy is much wider and applied in biology and chemistry.
Keywords: entropy, natural sciences, thermodynamics.
The attention to training of specialists in the field of nat-urally-scientific education has recently increased. This is due to the introduction of such disciplines as «Concepts of the modern natural science», «A naturally-scientific picture of the world», etc. in educational programs of higher education and the course «Natural sciences» in curricula of general secondary education. Therefore among profiles of training the masters of the Pedagogical education direction there is «Naturally-scientific education» This is the results of the fact that the social processes connected with production development, inquiries of the next stage of an advancement of science and technique, caring out nowadays, set new professional tasks for the higher school, make new requirements to vocational training of the modern school teacher, bachelors and masters of education. New tasks of their preparation are: formation of professional competences in the process of realization of naturally-scientific education at the students, teaching the integrated and elective courses. In this regard it is necessary to provide compliance of the subject training of the future teachers to tasks of the modern stage of reforming in the general secondary and higher education.
This article discusses the formation of the general scientific concept «entropy» at the masters and practicing teachers who can conduct the integrated natural sciences courses at a specialized school (profile school) in the future.
The analysis of academic literature leads to a conclusion that the process of introducing this concept at school is the most difficult. The analysis of the existing grants on natural sciences for school pupils has shown that this issue is receiving
attention only in the book edited by I. Y. Aleksashina where material is presented from a physical point of view and does not have the integrative nature. In our view, the concept of entropy is much wider and applied in biology and chemistry.
While studying thermodynamics first of all pupils have to learn that the person is an isothermal heat machine" [1, 187]. The mechanism of muscles action has not been fully understood, but the fact that their efficiency reaches 20−30% when the temperature difference between the human body and the environment is only 10−20 K, speaks of the impossibility of considering the body as an ordinary heat machine [1, 187].
The person receives energy at oxidation of food. So, for example one kilogram of oil gives 33 000 kJ., rice kilogram — 12 000 kJ., potatoes kilogram — 3 000 kJ. To maintain the normal activity the person needs on average 7 000−10 000 kJ. a day. It is established that only the 20−40% of all chemical energy is to perform an external work, and the rest part turns into an internal energy (that is why a person is heated doing exercises). Therefore, a person exchanges with a surrounding environment not only energy, but also substance, and the person is an open thermodynamic system. Up to this point the pupils knew only the isolated thermodynamic systems and the concept of a thermodynamic equilibrium. It should be noted that alive organisms tend to resist establishment of a thermodynamic equilibrium. Temperature of the human, a cat remains constant in rather big range of ambient temperatures. «Moreover, life creates also the additive regularity which is shown in a particular structure of
Section 13. Physics
alive organisms. Therefore, life is the least probable condition of a matter and it cannot exist the long time by itself» [1, 86].
Entropy is one of the main thermodynamic functions of a state. It defines opportunity, an orientation and a limit of all processes. «Introduction of entropy allowed generalizing conditions of occurrence of spontaneous and equilibrium processes and to formulate the second beginning of thermodynamics which, as well as the first one, is the postulate not contradicting practice» [2, 31]. Entropy is a thermodynamic function of a state- it possesses extensive characteristics, i. e. it depends on the system mass and has the same dimension, as a thermal capacity: J/mol. *K, however, it is the only thing they have in common. Then the reasons defining the role of entropy in spontaneous processes are discussed. According to the first beginning of thermodynamics the internal energy of the isolated system remains constant and cannot be the reason of spontaneous processes. In an isolated system the energy is redistributed as a result of its scattering. So, before puncturing a bicycle tire there was a particular order in an arrangement of gas molecules. After a puncture this order has broken as a result of the spontaneous expiration of air from a tire.
In everyday life, we have to cope with order and disorder constantly. The ordered systems are: matches in the box, the ions in the crystal and others. Here the samples of possible systems with a disorder: a crowd in the subway in «rush hour», an arrangement of molecules in liquids and gases, etc.
It is worth to remember that the entropy growth leading to increasing of a disorder is characterized for all systems, and for the isolated systems it defines a spontaneous process. If there would be no restriction on increasing of entropy in spontaneous processes only for the isolated systems, the mankind would be expected to plunge into chaos and disorder in the future. The reason is that in open systems the conduct of entropy essentially differs from its conduct in the isolated systems. How to define, in what direction this or that process will go and whether will go in general? Further, taking into consideration specifics of humanitarian profiles, we offer to expound this issue in its historical context. Students will be interested to learn that in 1854 the German scientist Clasius introduced the concept of entropy (from the Greek word Tponq — transformation). The prefix «en» is added to the Greek «trope», it turned out — an entropy. In 1909 professor ofJena University F. Auerbach called energy the queen of the world which transition is defined by the first beginning of thermodynamics, and its shadow -entropy which change reflects the essence of the second beginning of thermodynamics.
The concept of entropy is initially introduced within phenomenological thermodynamics and is connected with the analysis of thermal processes. Entropy, as well as energy, is a function of state, i. e. its size does not depend on how, by what processes the system came to this state- value of entropy is uniquely determinated by the parameters characterizing this state. Establishment of existence of a special function of state — entropy makes the first part of the second beginning of
thermodynamics. The second part claims: «At real (not ideal) processes an entropy of loop system increases».
In thermodynamics it is proved that given abstract formulation of the second beginning is physically equivalent to some other formulations seemed axiomatic. For the explanation of meaning of the second beginning we will define them here:
1. Heat cannot pass from system with a smaller temperature to system with a larger temperature by itself (R. Clasius’s formulation). «By itself» means that in the environment, surrounding the systems which are involved in the heat exchange, should not occur any changes, associated with this process.
2. It is impossible to get work permanently, only cooling a separate body below the temperature of the coldest part of a surrounding environment (V Kelvin’s formulation).
3. The perpetuum mobile of the second kind is impossible, i. e. periodically working car which would lift the load only due to the cooling of the thermal tank (V Ostvald’s formulation).
So, «the law of entropy increasing determines the flow of energy transformations: all of them in loop systems occur only in one direction. Real processes are always irreversible, they can only with a larger or smaller accuracy come nearer to ideally reversible processes» [2, 31].
Achievement by a loop system of the greatest possible entropy corresponds to approaching in it a temperature balance. The temperature differences characterizing separate parts of system disappear, and macroscopic processes become impossible. All energy inherent in system turns into energy of the unregulated, chaotic mooving of the micro-particles forming a system, and the inverse transition of heat to work is impossible. From this point entropy acts as the qualitative characteristic of energy showing its ability to transformations. Therefore, the more entropy, the less free energy and the more the total energy is depreciated though quantitatively it remains the same.
Based on the aforementioned, it is sometimes argued that entropy increase means degradation, energy depreciation. However similar comprehension is unilateral: it, in essence, states only the negative part of the second beginning of thermodynamics. Any loop system can evolve only in the direction of entropy increase, but real systems which we meet in nature (and especially in technique), are seldom loop. For open systems the second beginning first of all allows to discover the ways of the most effective use of energy and, consequently, acts not only as the law of depreciation of energy, but as the law of its optimum use. B. G. Kuznetsov absolutely fairly pays attention to this aspect of the issue: «It (the second beginning) indicates only those conditions under which entropy cannot decrease, and accordingly allows to find (and to create!) conditions under which entropy decreases» [6, 123].
Later the authors of the second beginning V Tomson (lord Kelvin) and R. Clasius spread it to the world in general and concluded about supposedly inevitable heat death of the world. Kelvin in his article «About the common tendency to mechanical dispersion which is shown in nature» wrote: «1. In the material world there is a common tendency to
Introducing the concept „entropy“ in the course of natural science at the specialized school
squandering of a mechanical energy now. 2. Recovery of a mechanical energy in its former amount without dispersion it in more than equivalent quantity cannot be carried out by means of any processes …» [6, 125]. R. Clasius extremely briefly stated the same thought in a formula: «Energy of the Universe is constant- entropy of the Universe aspires to a maximum».
So, all the processes in nature proceed eventually in the direction of entropy increase that means steady depreciation of energy, bound to its turning into heat, and alignment of temperatures as a result of thermal exchange. Sooner or later it inevitably leads to approach of an absolute temperature balance in the Universe and, therefore, to its thermal death. Though energy will remain quantitatively, but, using words of Engels, «it will disappear in a qualitative aspect».
Such position inevitably leads to an assumption of nonmaterial, super-physical factors. It was shown clearly by F. Engels: «A world watch at first has to be wound, and then they go, until it comes to a balanced state, and only the miracle can bring them out of this state and let it go again. The energy spent for winding the watch disappeared, at least in a qualitative sense, and can be restored only by a pushing from the outside. It means, that the push from the outside was necessary as well in the beginning.» [6, 126].
The following historical fact is interesting: On November 22, 1951 the Pope Pius XII made the sensational speech «proofs of God existence in the light of modern science data» in Pontifical Academy of Sciences. He saw one of the main arguments in favor of God existence in the second beginning of thermodynamics. «If. the scientist, having taken away the look from the real condition of the Universe, will turn back to the future, even to the farthest, he will have to recognize that the whole world, both a macro cosmos, and a micro cosmos, is growing old, and the matter at the end of its path will be in a state of dormant and stiffened volcano. Everything points to the fact that the material universe some time ago got a mighty initial rise, was filled with incredible amounts of energy reserves thanks to which it, developing at first quickly, then more and more slowly, achieved its present state» [6, 126].
The natural science which is unshakably standing on materialism foundations has never agreed with religious and idealistic interpretation of the second beginning. It was expressed very well by one of the largest physicists-chemists of the XX century V. Nernst: «The scientist-explore will never agree that at a certain moment of time the Universe was in a chaotic state from which then were formed … the dazzling suns and that eventually it will come to a state at which the formation of the worlds will be already impossible. In other words: the idea that all the events in the world began at a certain time and that all these processes will absolutely stop too in a particular day, is so improbable itself, so any theory, by perforce leading to such conclusions, has to be recognized incredible, and therefore imperfect» [6, 126]. One of the first people who deeply criticized the «theory» of the world thermal death was F. Engels. He pointed to incompatibility of this
«theory» with materialistic outlook. It contradicts the principle of indestructibility of movement and that is why it has to be rejected from the philosophical point of view. But its naturally-scientific refutation (and it is necessary because «theory» of thermal death is given for an inevitable conclusion from laws of natural sciences), certainly, can give only natural sciences [6, 127].
According to the second law of thermodynamics in nature in general and in each isolated system entropy always increases and as the quantity of entropy characterizes disorder degree, regularity always decreases. Therefore it has seemed for a long time that the spontaneous rush to a temperature balance contradicts to the process of structures formation in alive organisms. The first who tried to eliminate this contradiction was E. Schrodinger (1947). He noted that biological objects are not enclosed, and interact with an environment in which there are streams of energy and substance caused by inflow of sunlight. Functioning of an alive organism is a passing through itself parts of these streams and their transformation. Entropy of an open system is to a surrounding environment or as Schrodinger noticed, an organism «eats negative entropy». The existence of open systems with an increasing degree of order is not a paradox from the positions of atheist non-balanced physics. For Schrodinger the organism is «an aperiodic crystal», that is the high-ordered system, similar to a solid body, and deprived of periodicity in an arrangement of elements — cells, molecules, atoms. That is why the phenomena like self-organization are possible in inanimate nature in strongly non-balanced open systems.
Alive organisms constantly create regularity from a disorder. Physical and chemical balance, on which is based the performance of living systems, arises and is supported in them. In the process of individual development (ontogeny) of every living organism as well as in the process of evolution (phy-logeny), new structures are formed all the time, i. e., the state of higher regularity is reached. This apparent contradiction with the law of entropy increase is explained with the fact that organisms are not isolated, but open systems, permanently exchanging matter and energy with the environment. It allowed formulating definition of Life from the thermodynamic point of view by the following way: «Alive can be called such systems, which are capable of self-support and increase its very high degree of order in an environment with a lower degree of order» [1, 86]. Accordingly the metabolism as the most important function of living organisms from the point of view of thermodynamics is necessary to prevent the increasing of an entropy caused by irreversible processes in system.
Each alive organism and each cell is a thermodynamic open system which continuously turns the chemical energy enclosed in organic matters into energy ofworking processes, and, eventually, gives it to the environment in the form of heat. As a result of this exchange of substance and energy with a surrounding environment and alive system there is no thermodynamic balance. «Living system is never in balance and all the time the work is done against the balance due to its free energy
Section 13. Physics
which is established under these external conditions» — Bauer «The general law of biology» (1935). At temperatures characterized an alive organism, its structures are labile and exposed to the continuous disintegration. For compensation of this disintegration «internal work» in the form of synthesis processes has to be made. In other words, working processes are processes with negative entropy (negentropy processes) as they counteract an entropy increase, connected with disintegration of structures, create regularity with the help of chemical energy and a low entropy of the absorbed high-molecular organic matters (heterotrophic organisms) or by means of electromagnetic energy and a low entropy of the absorbed sunlight (autotrophic green plants) [4, 141].
Thus, it is proved by science that non-balanced alive systems submit to the same general laws of thermodynamics to which other non-balanced, but lifeless systems submit, that is why for the characteristic of living organisms the corresponding thermodynamic functions and first of all such as energy and entropy are applicable.
A living organism is an extremely ordered system with low entropy. Existence of a living organism means the continuous resistance to the disordering factors and, in particular, to the factors causing diseases. It may seem that the living organism does not submit to requirements of the second beginning.
This is certainly not the case. It is necessary to consider that any alive organism is the not loop system staying in a significant misbalance. This system interacts with the environment actively, for example in the feeding process living organisms consume high-molecular compounds. Decrease of entropy occurs during synthesis of high-molecular compounds from the low-molecular ones [1, 87]. It is known, for example, that the food has lower entropy, than waste. And at energy exchange there is splitting of glucose into a carbon dioxide and water which is characterized by entropy increase.
The person does not simply live. He works, creates and, therefore, reduces entropy energetically. All this is possible only thanks to the fact that «…a person receives necessary quantity of a negentropy (information) from an environment by two different channels. The first one is bound to teaching process. The second one is connected with the physiological processes of an exchange happening in system (the human + environment)» [4, 141].
The next step would be to present a modern point ofview on this issue. We use in our article materials from L. V. Tarasov’s book  because we consider that here is the most understandable statement for the students of humanitarian cycle.
«A man understood long ago: initially there was a chaos, various ordered structures, living creatures and, at last, he himself was formed of it eventually. The modern science assigns this part to casual processes- in fact the role of God plays his Majesty the Case».
«Process of emergence an order out of chaos is not a result of intervention of God, but a result of self-organization of a matter on the basis of a random search» [5, 204]. In the process of self-organization of a matter the initial chaos of the
fundamental particles formed after the Big Bang gradually was organized at first in atomic nuclei and atoms, and later in substance of stars and planets. This process led to emergence of life on Earth, to appearance of the more and more composite species. At first sight, the evolution in wildlife, which is followed according Darwin by the complication of species, contradicts the second beginning of thermodynamics according to which the matter should eventually degrade (an entropy has to increase). «According to the theory of Darwin at first there are spontaneous fluctuations of species then selection comes into force and irreversible biological evolution begins. Like in Boltzmann’s theory, happenstance leads to irreversibility. However the result of evolution at Darwin turns out to be different, than at Boltzmann. Boltzmann’s interpretation entails forgetting the initial conditions, „destruction“ of initial structures whereas Darin’s evolution is associated with selforganization, with steadily increasing complexity» [3, 182].
You can try to get around this contradiction by pointing out that Darwinian evolution is bound to the space and local decrease in entropy due to even more significant increase of entropy in the remaining space. In such explanation there is a particular reason as entropy decrease in the process of creative activity of a human is followed, as we know, by entropy increase as result of growth in waste production, and the formation of combustion products, etc.
Here it is necessary to take into account the fundamental difference between loop and open systems. Increase of entropy happens in a loop system- only the system isolated from world around can come into balance state corresponding to «thermal death». But in the wildlife, properly speaking, there are no loop systems- such systems are always some idealization, artificiality.
It is necessary to distinguish two types of processes. The processes in loop systems conducting to establishment of a temperature balance are followed by disorder increase- they go in the direction from an order to chaos. Processes in especially non-balanced open systems can go in the opposite direction — from chaos to an order. This is the process of self-organization.
Self-organization is considered in details in the above-cited book by I. Prigogin and I. Stengers. Authors emphasize: «Nowadays we know that far from equilibrium there can spontaneously generate new types of structures. In strongly nonequilibrium conditions transition from a disorder, thermal chaos to an order can be made» [3, 54]. They called the new types of structures arising in the process of self-organization, dissipative structures.
Further: «…Irreversible processes are an order source. Closely related with the openness of the system and the happenstance, irreversible processes generate high levels of organization. That is why one of the leitmotifs of the present book is a new and unusual interpretation of the second law of thermodynamics, proposed by the authors. According to Prigozhin and Stengers, entropy is not simply unceasing sliding of system to the state deprived of any organization.
Introducing the concept „entropy“ in the course of natural science at the specialized school
Under certain conditions entropy becomes the progenitress of an order» [3, 25].
The word «synergetic» comes from Greek «together» and «act». This term is applied in physiology rather long ago: muscle groups that work together to make a movement, are called synergists. Use of this term as the name of the recent scientific trend was offered by the German scientist G. Haken quite recently. He suggested calling a synergetic area of science the one which is engaged in studying of effects of self-organization in physical, chemical, biological and other systems. In other words, the synergetic is a science about selforganization in non-balanced open systems of various origin, a science about laws of the birth of an order from chaos. At present time such science does not exist yet, it only still starts developing. Then Tarasov L. V reviews some examples which will be pertinent at a performing of this material.
The first example is cloudiness. Everybody who flew by plane over clouds, could observe their regular, very ordered structure more than once. It is possible to observe the almost exact rectangular and hexagon cells of clouds, the regular shaft, straight «streets». All this geometrical order was formed of chaos of molecular movements, various outbreaks in the air atmosphere and a layer of the water steams caused by the irregularity of their warming up leading to an intensive convection.
The second example is Benar’s instability (this phenomenon was discovered by G. Benar in 1900). It is absolutely easy to reproduce the phenomenon. It is necessary to pour a layer of a mineral oil about 5 mm. thick in an usual frying pan, having added to oil (in order the effect was visible more distinctly) little aluminum shavings. Then it is necessary to put the pan on fire. In the beginning, while temperature difference between the bottom of a pan and a surface of oil is still small, the warmth brought from below will extend up due to thermal conductivity. At further heating the convection will begin: heated oil
will rise, and cold oil will fall down. The spatial distribution of these two opposing streams after a while will organize itself — there is an ordered structure from hexagon convection cells — Benar’s cells. In the center of each cell oil rises up, and at the edges falls down. «Benar's instability is a very impressive phenomenon. Convective flow of fluid generates the composite space organization of system. Millions of molecules move in coordination, forming convective cells in the form of the exact hexagons of some certain size» [3, 196].
The third example is a chemical watch. We imagine a chemical action in this way: in different directions in space molecules of reagents move and collide with each other randomly. It seems that in such picture self-organization is impossible. But it is not so. Under certain conditions some chemical reactions are followed by periodic changes (in time and in space) of concentration of reagents. Eventually one reagent is replaced by another, then again it is restored and then again disappears. All this occurs through particular time periods. It is a periodic chemical process — chemical watch.
Let us notice that lately it is found more and more such processes- they are called auto wave. It is curious that heart beating, as it turned out, is supported by the whole complex of oscillating chemical reactions. Often used free comparison of healthy heart with watch gets today a specific meaning — it is a chemical watch.
It is possible to find many similar examples within any school subject.
In conclusion we will note that the content of training of masters of pedagogical education on the naturally scientific profile cannot be considered developed and satisfactory as there is only a standard of a new generation, and the main educational program is not completely formed yet. The material offered in the article can be included in the program of students training, as one of its elements.
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3. Prigozhin I., Stengers I. An order from chaos/Trasl. From English. — M.: Progress, 1986- 6 ed. — M.: LKI/UPSS, 2008.
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