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1

Stan równowagi trwałej układu termodynamicznego : Entropia

Litke B.

Problemy Nauk Stosowanych

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2016

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T. 5

73--84

PL

Wstęp i cele: W pracy opisano stan równowagi trwałej układu termodynamicznego. Przestawiono pewnik równowagi, zerową zasadę termodynamiki, entropię. Omówiono entropię gazu doskonałego i półdoskonałego oraz entropię systemu termodynamicznego. Opisano przemiany nieodwracalne układów wymieniających ciepło przy skończonej różnicy temperatur, ciepło tarcia oraz samorzutne mieszanie się różnych gazów. Materiał i metody: Materiał stanowią źródła z literatury z zakresu termodynamiki. W pracy zastosowano metodę analizy teoretycznej. Wyniki: Rezultatem analizy jest opracowanie i podanie wzorów opisujących entropię dla układów otwartych i zamkniętych, entropię dla gazów doskonałych i półdoskonałych oraz entropię dla system termodynamicznego. Ponadto opracowano wzory dla entropii przy przemianach nieodwracalnych układów wymieniających ciepło i entropii przy samorzutnym mieszaniu się gazów. Wniosek: W równaniu dla układów otwartych w stanie ustalonym można zastąpić ciepło entropią i temperaturą. Wartość ciepła przemiany, tak jak i pracy, zależy nie tylko od stanów początkowego i końcowego, ale również od drogi przemiany. Zmiana entropii w przypadku przemiany odwracalnej, jest równa zero, a dla przemiany nieodwracalnej - większa od zera.

EN

Introduction and aim: This paper describes the state of permanent equilibrium thermodynamic system. It has been shown an axiom of balance, zero law of thermodynamics, entropy. Some entropy of an ideal and semi-perfect gas and the entropy of the thermodynamic system have been discussed in the paper. The transformation of irreversible heat-exchange systems at finite temperature difference, heat friction and spontaneous mixing of different gases have been described in the considerations. Material and methods: Material covers some sources based on the literature in the field of thermodynamics. The method of theoretical analysis has been shown in the paper. Results: The result of the analysis is the elaboration and presenting some formulas which describe the entropy for open systems and closed, entropy for ideal gases and semi-perfect and thermodynamic entropy of the system. In addition, have been developed some formulas for the entropy for changes of irreversible heat exchange systems and the entropy for the spontaneous mixing of the gases. Conclusion: In the equation for open systems in steady state you can replace the heat by entropy and temperature. The value of the heat of transformation, like a work, depends not only on the initial and final states but also on the pathway of changes. Entropy transformation for the reversible changes, is equal to zero, and for irreversible changes - greater than zero.

2

Discrete modeling of the three species syn-ecosystem with unlimited resources

Prasad B. H.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 2

85--93

EN

In this paper, the three species syn-ecosystem is comprised of a commensal (S1), two hosts S2 and S3, i.e. S2 and S3 both benefit S1 without getting themselves affected either positively or adversely. Further, S2 is a commensal of S3, S3 is a host of both S1, S2 and all the three species have unlimited resources. The basic equations for this model constitute as three first order non-linear coupled ordinary difference equations. All possible equilibrium states are identified based on the model equations at two stages and criteria for their stability are discussed. Further, the numerical solutions are computed for specific values of the various parameters and the initial conditions.

3

Steady state of solid-grain interfaces during simulated CPT

Butlanska J., Arroyo M., Gens A.

Studia Geotechnica et Mechanica

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2013

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Vol. 35, nr 4

13--22

EN

It has recently been shown (Arroyo et al. [1]) that 3D DEM models are able to reproduce with reasonable accuracy the macroscopic response of CPT performed in calibration chambers filled with sand. However, the cost of each simulation is an important factor. Hence, to achieve manageable simulation times the discrete material representing the sand was scaled up to sizes that were more typical of gravel than sand. A side effect of the scaled-up discrete material size employed in the model was an increased fluctuation of the macro-response that can be filtered away to observe a macroscopic steady-state cone resistance. That observation is the starting point of this communication, where a series of simulations in which the size ratio between penetrometer and particles is varied are systematically analyzed. A micromechanical analysis of the penetrometer–particle interaction is performed. These curves reveal that a steady state is arrived also at the particle–cone contact level. The properties of this dynamic interface are independent of the initial density of the granular material.

4

Effective energy integral functionals for thin films in the Orlicz-Sobolev space setting

Laskowski W., Nguyen H. T.

Demonstratio Mathematica

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2013

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Vol. 46, nr 3

585--604

EN

We consider an elastic thin film as a bounded open subset ω of R2. First, the effective energy functional for the thin film ω is obtained, by Γ-convergence and 3D-2D dimension reduction techniques applied to the sequence of re-scaled total energy integral functionals of the elastic cylinders (…) as the thickness ε goes to 0. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function for the elastic cylinders has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type and to satisfy the conditions (…) and (…) (that is equivalent to the reflexivity of Orlicz and Orlicz–Sobolev spaces generated by M). These results extend results of H. Le Dret and A. Raoult for the case M(t) = (…) for some (…).

5

The modeling of vacuum steel refining in the RH degassing unit based on thermodynamic analysis of the system

Drożdż P., Falkus J.

Archives of Metallurgy and Materials

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2007

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Vol. 52, iss. 4

585-591

EN

Determining the state of equilibrium in steel refining processes plays an important role in view of process intensification possibilities, fuller process control and the related economic effects. The main objective of this paper is to analyze the states of equilibrium in heterogeneous systems for vacuum degassing of steel in the RH degassing unit. The kinetic model of the RH process was based on a metal bath mixing model in which account is taken of the gas-metal equilibrium of the boundary layer of the metal bath in the vacuum chamber. This objective can be attained by using a software package containing suitable thermodynamic data bases and computing software integrated with it. The computer applications used to solve the problem include FactSage and ChemSheet. This paper will contribute to explaining some of the processes taking place during steel refining in the RH degassing unit.

PL

Określenie stanu równowagi w procesach pozapiecowej rafinacji stali odgrywa istotną rolę, ze względu na możliwość intensyfikacji procesu, jego pełniejszą kontrolę oraz związane z tym efekty ekonomiczne. Podstawowym celem pracy jest analiza stanów równowagi w układach wielofazowych dotyczących procesu próżniowego odgazowania stali w urządzeniu RH. Kinetyczny model procesu RH został oparty o model mieszania kąpieli metalowej, w którym uwzględniony jest fakt osiągnięcia stanu równowagi gaz-metal dla granicznej warstwy kąpieli metalowej w komorze. Realizacja celu pracy jest możliwa dzięki zastosowaniu pakietu komputerowego zawierającego odpowiednie bazy danych termodynamicznych oraz zintegrowane z nimi komputerowe programy obliczeniowe. Programem komputerowym zastosowanym jako narzędzie do rozwiązania postawionego problemu jest FactSageTM i ChemSheet. Praca stanowi wkład w wyjaśnienie niektórych procesów zachodzących podczas rafinacji stali w urządzeniu RH.

6

Charakterystyka stanów równowagi atmosfery w okresie IV-X 2002 roku dla Ursynowa-SGGW

Rozbicka K.

Przegląd Naukowy Inżynieria i Kształtowanie Środowiska

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2003

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Vol. 12, No. 1

105--113

EN

The paper presents atmospheric stability description by the use Richardson number (Ri). The calculation was done for two types o f weather: sunny days (24h) and cloudy days (24h). In accordance with Oke (1987) stability static was divided as follows: unstable stability a-fully forced convection, b-mixed convection, c-free convection; d-neutral stability; stable stability e-fully forced convection, f-damped forced convection, g-no convection. Richardson number accomplish negative value, which stands unstable static conditions (a, b) for more cases of day-time period both sunny and cloudy days. Stable static conditions, particularly f characterized by positive value of Ri appear for cloudless nights most frequently. A large diversity of static conditions was observed for night-time period with cloudy weather. The most frequent static conditions in considered period is stable (maximum in October), then unstable (maximum in summertime months).