Purpose: The aim of this scientific contribution is to show the potential that integral calculus has offered to the analysis of thermodynamic processes. Method: Application of Integral Calculus. In this context, the d...Purpose: The aim of this scientific contribution is to show the potential that integral calculus has offered to the analysis of thermodynamic processes. Method: Application of Integral Calculus. In this context, the document covers the theoretical principles of integral calculus, such as Theoretical framework and background, Geometric interpretation of the primitive, Primitive existence theorem. Results: Integral calculus and generalized thermodynamic models, and their applications in various thermodynamic analysis contacts such as the Generalized Enthalpy Model, the Generalized Entropy Model, and the Generalized Model applied to gas mixtures and the General Model to elaborate the properties table. Conclusion: The mathematical analysis developed in this document is very useful in engineering and applied physics environments, a fact that supports its common pedagogical practice in university institutions.展开更多
The effects of internal stresses and depolarization fields on the properties of epitaxial ferroelectric perovskite thin films are discussed by employing the dynamic Ginzbur~Landau equation （DCLE）. The numerical solu...The effects of internal stresses and depolarization fields on the properties of epitaxial ferroelectric perovskite thin films are discussed by employing the dynamic Ginzbur~Landau equation （DCLE）. The numerical solution for BaTiO3 film shows that internal stress and the depolarization field have the most effects on ferroelectric properties such as polarization, Curie temperature and susceptibility. With the increase of the thickness of the film, the polarization of epitaxia] ferroelectric thin film is enhanced rapidly under high internal compressively stress. With the thickness exceeding the critical thickness for dislocation formation, the polarization increases slowly and even weakens due to relaxed internal stresses and a weak electrical boundary condition. This indicates that the effects of mechanical and electrical boundary conditions both diminish for ferroelectric thick films. Consequently, our thermodynamic method is a full scale model that can predict the properties of ferroelectric perovskite films in a wide range of film thickness.展开更多
The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The ...The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The homotopy Levenberg-Marquardt algorithm was proposed to accurately solve nonlinear equations with singular Jacobian matrices,and is constructed by the Saha equation and Guldberg-Waage equation combined with mass conservation,the electric neutrality principle and Dalton’s partial pressure law,to solve the problem of dependence on the initial value in the process of iteration calculation.In this research,the equations at a higher temperature were solved and used as the auxiliary equations,and the homotopy control parameters’sequence of the homotopy equations was selected by equal ratios.For auxiliary equations,the iterative initial value was obtained by assuming that there were only the highestvalence atomic cations and electrons at this temperature,and the plasma equilibrium composition distribution with the required accuracy was ultimately solved under the current conditions employing the Levenberg-Marquardt algorithm.The control parameter sequence was arranged according to the geometric sequence and the homotopy step was gradually shortened to ensure continuity of the homotopy process.Finally,the equilibrium composition and thermodynamic properties of pure N_(2),Mg(30%)-CO_(2)(70%)and Mg(40%)-CO(50%)-N_(2)(10%)mixture plasma at atmospheric pressure were calculated and the calculation process of some specified temperatures was shown and analyzed.The calculation accuracy of equilibrium composition is higher than other findings in the literature.The results for the thermodynamic properties are in good agreement with data reported by the literature.展开更多
Ionic liquids combined with supercriticalfluid technology hold great promise as working solvents for developing compact processes.Ionic liquids,which are organic molten salts,typically have extremely low volatility and...Ionic liquids combined with supercriticalfluid technology hold great promise as working solvents for developing compact processes.Ionic liquids,which are organic molten salts,typically have extremely low volatility and high functionality,but possess high viscos-ities,surface tensions and low diffusion coefficients,which can limit their applicability.CO_(2),on the other hand,especially in its supercritical state,is a green solvent that can be used advantageously when combined with the ionic liquid to provide viscosity and surface tension reduction and to promote mass transfer.The solubility of CO_(2) in the ionic liquid is key to estimating the important physical properties that include partition coefficients,viscosities,densities,interfacial tensions,thermal conductivities and heat capacities needed in contactor design.In this work,we examine a subset of available high pressure pure component ionic liquid PVT data and high pressure CO_(2)-ionic liquid solubility data and report new correlations for CO_(2)-ionic liquid systems with equations of state that have some industrial applications including:(1)general,(2)fuel desulfurization,(3)CO_(2) capture,and(4)chiral separation.New measurements of solubility data for the CO_(2) and 1-butyl-3-methylimidazolium octyl sulfate,[bmim][OcSO4]system are reported and correlated.In the correlation of the CO_(2) ionic liquid phase behavior,the Peng-Robinson and the Sanchez-Lacombe equations of state were considered and are compared.It is shown that excellent correlation of CO_(2) solubility can be obtained with either equation and they share some common characteristics regarding inter-action parameters.In the Sanchez-Lacombe equation,parameters that are derived from the supercritical region were found to be important for obtaining good correlation of the CO_(2)-ionic liquid solubility data.展开更多
The thermodynamics of strange quark matter with density dependent bag constant are studied self-consistently in the framework of the general ensemble theory and the MIT bag model.In our treatment,an additional term is...The thermodynamics of strange quark matter with density dependent bag constant are studied self-consistently in the framework of the general ensemble theory and the MIT bag model.In our treatment,an additional term is found in the expression of pressure.With the additional term,the zero pressure locates exactly at the lowest energy state,indicating that our treatment is a self-consistently thermodynamic treatment.The self-consistent equations of state of strange quark matter in both the normal and color-flavor-locked phase are derived.They are both softer than the inconsistent ones.Strange stars in both the normal and color-flavor locked phase have smaller masses and radii in our treatment.It is also interesting to find that the energy density at a star surface in our treatment is much higher than that in the inconsistent treatment for both phases.Consequently,the surface properties and the corresponding observational properties of strange stars in our treatment are different from those in the inconsistent treatment.展开更多
文摘Purpose: The aim of this scientific contribution is to show the potential that integral calculus has offered to the analysis of thermodynamic processes. Method: Application of Integral Calculus. In this context, the document covers the theoretical principles of integral calculus, such as Theoretical framework and background, Geometric interpretation of the primitive, Primitive existence theorem. Results: Integral calculus and generalized thermodynamic models, and their applications in various thermodynamic analysis contacts such as the Generalized Enthalpy Model, the Generalized Entropy Model, and the Generalized Model applied to gas mixtures and the General Model to elaborate the properties table. Conclusion: The mathematical analysis developed in this document is very useful in engineering and applied physics environments, a fact that supports its common pedagogical practice in university institutions.
基金Project supported by the National Natural Science Foundation of China （Grant Nos. 10802070, 10972188, and 10902055）, Natural Science Foundation of Fujian Province of China （Grant No. 2011J01329）, and the Fundamental Research Funds for the Central Universities of China （Grant No. 2011121002）.
文摘The effects of internal stresses and depolarization fields on the properties of epitaxial ferroelectric perovskite thin films are discussed by employing the dynamic Ginzbur~Landau equation （DCLE）. The numerical solution for BaTiO3 film shows that internal stress and the depolarization field have the most effects on ferroelectric properties such as polarization, Curie temperature and susceptibility. With the increase of the thickness of the film, the polarization of epitaxia] ferroelectric thin film is enhanced rapidly under high internal compressively stress. With the thickness exceeding the critical thickness for dislocation formation, the polarization increases slowly and even weakens due to relaxed internal stresses and a weak electrical boundary condition. This indicates that the effects of mechanical and electrical boundary conditions both diminish for ferroelectric thick films. Consequently, our thermodynamic method is a full scale model that can predict the properties of ferroelectric perovskite films in a wide range of film thickness.
基金supported by the National Key Research and Development Program of China(No.2017YFA0700300)the Fundamental Research Funds for the Central Universities(No.N2025032)the Liaoning Provincial Natural Science Foundation(No.2020-MS-362)。
文摘The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The homotopy Levenberg-Marquardt algorithm was proposed to accurately solve nonlinear equations with singular Jacobian matrices,and is constructed by the Saha equation and Guldberg-Waage equation combined with mass conservation,the electric neutrality principle and Dalton’s partial pressure law,to solve the problem of dependence on the initial value in the process of iteration calculation.In this research,the equations at a higher temperature were solved and used as the auxiliary equations,and the homotopy control parameters’sequence of the homotopy equations was selected by equal ratios.For auxiliary equations,the iterative initial value was obtained by assuming that there were only the highestvalence atomic cations and electrons at this temperature,and the plasma equilibrium composition distribution with the required accuracy was ultimately solved under the current conditions employing the Levenberg-Marquardt algorithm.The control parameter sequence was arranged according to the geometric sequence and the homotopy step was gradually shortened to ensure continuity of the homotopy process.Finally,the equilibrium composition and thermodynamic properties of pure N_(2),Mg(30%)-CO_(2)(70%)and Mg(40%)-CO(50%)-N_(2)(10%)mixture plasma at atmospheric pressure were calculated and the calculation process of some specified temperatures was shown and analyzed.The calculation accuracy of equilibrium composition is higher than other findings in the literature.The results for the thermodynamic properties are in good agreement with data reported by the literature.
基金support of the Monbukagakusho,the Ministry of Education,Culture,Sports,Science and Technology and also that of the Global Education Center of Excellence(GCOE).
文摘Ionic liquids combined with supercriticalfluid technology hold great promise as working solvents for developing compact processes.Ionic liquids,which are organic molten salts,typically have extremely low volatility and high functionality,but possess high viscos-ities,surface tensions and low diffusion coefficients,which can limit their applicability.CO_(2),on the other hand,especially in its supercritical state,is a green solvent that can be used advantageously when combined with the ionic liquid to provide viscosity and surface tension reduction and to promote mass transfer.The solubility of CO_(2) in the ionic liquid is key to estimating the important physical properties that include partition coefficients,viscosities,densities,interfacial tensions,thermal conductivities and heat capacities needed in contactor design.In this work,we examine a subset of available high pressure pure component ionic liquid PVT data and high pressure CO_(2)-ionic liquid solubility data and report new correlations for CO_(2)-ionic liquid systems with equations of state that have some industrial applications including:(1)general,(2)fuel desulfurization,(3)CO_(2) capture,and(4)chiral separation.New measurements of solubility data for the CO_(2) and 1-butyl-3-methylimidazolium octyl sulfate,[bmim][OcSO4]system are reported and correlated.In the correlation of the CO_(2) ionic liquid phase behavior,the Peng-Robinson and the Sanchez-Lacombe equations of state were considered and are compared.It is shown that excellent correlation of CO_(2) solubility can be obtained with either equation and they share some common characteristics regarding inter-action parameters.In the Sanchez-Lacombe equation,parameters that are derived from the supercritical region were found to be important for obtaining good correlation of the CO_(2)-ionic liquid solubility data.
基金Supported by the National Natural Science Foundation of China (Grant Nos.10275029 and 10675024)the National Fundamental Fund Project Subsidiary Funds of Personnel Training (Grant No.J0730311)
文摘The thermodynamics of strange quark matter with density dependent bag constant are studied self-consistently in the framework of the general ensemble theory and the MIT bag model.In our treatment,an additional term is found in the expression of pressure.With the additional term,the zero pressure locates exactly at the lowest energy state,indicating that our treatment is a self-consistently thermodynamic treatment.The self-consistent equations of state of strange quark matter in both the normal and color-flavor-locked phase are derived.They are both softer than the inconsistent ones.Strange stars in both the normal and color-flavor locked phase have smaller masses and radii in our treatment.It is also interesting to find that the energy density at a star surface in our treatment is much higher than that in the inconsistent treatment for both phases.Consequently,the surface properties and the corresponding observational properties of strange stars in our treatment are different from those in the inconsistent treatment.
