Методичні особливості вивчення статистичних розподілів Гіббса в курсі теоретичної фізики
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2013
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У статті проводиться короткий аналіз методичних особливостей вивчення статистичних розподілів Гіббса в курсі теоретичної фізики педагогічного університету, що має важливе значення в фундаментальній і професійній підготовці майбутнього вчителя фізики. Ефективному засвоєнню одного з ключових питань курсу сприятиме максимальна лаконічність математичного апарату, чіткість і послідовність викладу навчального матеріалу у відповідності з логікою його подання згідно наукових «першоджерел».
The article provides a brief analysis of approaches of teaching Gibbs’ statistical distributions in the course of theoretical physics in pedagogical university, which is important in basic and professional training of future teachers of physics. The process of professional preparation of future teachers of physics involves the study of fundamental physical theories, which include thermodynamics and statistical physics. The latter traditionally investigates various properties of macroscopic objects, i.e., those that consist of a huge number of particles. Application of statistical methods to macro systems historically contributed to the theoretical substantiation of the basic equations of thermodynamics and provided them with in-depth analysis. In our view, the efficient absorption of one of the key issues of the course of theoretical physics will promote maximum brevity of the mathematical apparatus, integrity and consistency of presentation of educational materials in accordance with the logic of their submission under scientific «primary sources». From a passive consumer of knowledge the student must turn into its active creator, because personal knowledge is really fundamental. In this sense special value gets organization of independent educational-cognitive work, which is directed at creativity and research. Of course, mastering of theoretical materials will be the most effective only together with the decision of the relevant tasks of the training course. Statistical methods are now widely used in solving various problems of physics, particularly in such cases as: 1) adiabatic isolated system with fixed energy; 2) isothermal system that exchanges energy with surrounding bodies with certain temperature; 3) system, which exchanges with surrounding bodies both energy and particles, that is, they are in thermal and diffusive contact. The first case leads to so called micro canonic distribution, the second case corresponds to the canonical distribution. The third case leads to the so-called big canonical distribution, which is a generalization of the first two. The author analyses well-known equations considering the fact that mathematical proof of the general expression of the canonical distribution in the academic literature is sufficiently detailed.
The article provides a brief analysis of approaches of teaching Gibbs’ statistical distributions in the course of theoretical physics in pedagogical university, which is important in basic and professional training of future teachers of physics. The process of professional preparation of future teachers of physics involves the study of fundamental physical theories, which include thermodynamics and statistical physics. The latter traditionally investigates various properties of macroscopic objects, i.e., those that consist of a huge number of particles. Application of statistical methods to macro systems historically contributed to the theoretical substantiation of the basic equations of thermodynamics and provided them with in-depth analysis. In our view, the efficient absorption of one of the key issues of the course of theoretical physics will promote maximum brevity of the mathematical apparatus, integrity and consistency of presentation of educational materials in accordance with the logic of their submission under scientific «primary sources». From a passive consumer of knowledge the student must turn into its active creator, because personal knowledge is really fundamental. In this sense special value gets organization of independent educational-cognitive work, which is directed at creativity and research. Of course, mastering of theoretical materials will be the most effective only together with the decision of the relevant tasks of the training course. Statistical methods are now widely used in solving various problems of physics, particularly in such cases as: 1) adiabatic isolated system with fixed energy; 2) isothermal system that exchanges energy with surrounding bodies with certain temperature; 3) system, which exchanges with surrounding bodies both energy and particles, that is, they are in thermal and diffusive contact. The first case leads to so called micro canonic distribution, the second case corresponds to the canonical distribution. The third case leads to the so-called big canonical distribution, which is a generalization of the first two. The author analyses well-known equations considering the fact that mathematical proof of the general expression of the canonical distribution in the academic literature is sufficiently detailed.
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макроскопічна система, статистичний ансамбль, ергодична гіпотеза, функція статистичного розподілу, статистична вага, статистичний інтеграл, хімічний потенціал, macroscopic system, statistical ensemble, ergodic hypothesis, function of the statistical distribution, statistical weight, statistical integral, chemical potential
Бібліографічний опис
Школа, О. В. Методичні особливості вивчення статистичних розподілів гіббса в курсі теоретичної фізики [Текст] / О. В. Школа // Педагогічні науки: теорія, історія, інноваційні технології : науковий журнал / Міністерство освіти і науки України, Сумський державний університет імені А. С. Макаренка ; редкол.: А. А. Сбруєва, Дж. Бішоп, О. В. Єременко та ін. – Суми : СумДПУ імені А. С. Макаренка, 2013. – №6 (32). – С. 412–424.