The simplest equation of state that can be applied to calculate the thermodynamic properties of gases is the virial equation with the second coefficient B. The probability of applying the one-coefficient equation Z = ...The simplest equation of state that can be applied to calculate the thermodynamic properties of gases is the virial equation with the second coefficient B. The probability of applying the one-coefficient equation Z = exp(A/V) for the calculation of compressibility factor at critical temperature of gases and gas mixtures is investigated. It was verified that the one-coefficient equation of state can be applied to calculated the thermodynamic properties for both normal and strongly polar gases and gas mixtures.展开更多
We present a model of non-uniform granular gases in one-dimensional case, whose granularity distribution has the fractal characteristic. We have studied the nonequilibrium properties of the system by means of Monte Ca...We present a model of non-uniform granular gases in one-dimensional case, whose granularity distribution has the fractal characteristic. We have studied the nonequilibrium properties of the system by means of Monte Carlo method. When the typical relaxation time T of the Brownian process is greater than the mean collision time To, the energy evolution of the system exponentially decays, with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state in which the velocity distribution strongly deviates from the Gaussian one. Three other aspects have also been studied for the steady state: the visualized change of the particle density, the entropy of the system and the correlations in the velocity of particles. And the results of simulations indicate that the system has strong spatial clustering; Furthermore, the influence of the inelasticity and inhomogeneity on dynamic behaviors have also been extensively investigated, especially the dependence of the entropy and the correlations in the velocity of particles on the restitute coefficient e and the fractal dimension D.展开更多
The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple ba...The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.展开更多
We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the firs...We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the first time in this field. The thermomechanical states of the heat engine are in Nonequilibrium Irreversible States (NISs), and time-dependent thermodynamic work W(t), internal energy E(t), energy dissipation or entropy Q<sub>d</sub>(t), and temperature T(t), are precisely studied and computed in TMD. We also introduced the new formalism, Q(t)-picture of thermodynamic heat-energy flows, for consistent analyses of NISs. Thermal flows in a long-time uniform heat flow and in a short-time heat flow are numerically studied as examples. In addition to the analysis of time-dependent physical quantities, the TMD analysis suggests that the concept of force and acceleration in Newtonian mechanics should be modified. The acceleration is defined as a continuously differentiable function of Class C<sup>2</sup> in Newtonian mechanics, but the thermomechanical dynamics demands piecewise continuity for acceleration and thermal force, required from physical reasons caused by frictional variations and thermal fluctuations. The acceleration has no direct physical meaning associated with force in TMD. The physical implications are fundamental for the concept of the macroscopic phenomena in NISs composed of systems in thermal and mechanical motion.展开更多
The irreversible mechanism of heat engines is studied in terms of <em>thermodynamic consistency</em> and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible ...The irreversible mechanism of heat engines is studied in terms of <em>thermodynamic consistency</em> and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible thermodynamic systems. As an example, a water drinking bird (DB) known as one of the heat engines is specifically examined. The DB system suffices a rigorous experimental device for the theory of nonequilibrium irreversible thermodynamics. The DB nonlinear equation of motion proves explicitly that nonlinear differential equations with time-dependent coefficients must be classified as independent equations different from those of constant coefficients. The solutions of nonlinear differential equations with time-dependent coefficients can express emergent phenomena: nonequilibrium irreversible states. The <em>couplings</em> among mechanics, thermodynamics and time-evolution to nonequilibrium irreversible state are defined when the internal energy, thermodynamic work, temperature and entropy are integrated as a spontaneous thermodynamic process in the DB system. The physical meanings of the time-dependent entropy, <em>T</em>(<em>t</em>)d<em>S</em>(<em>t</em>), , internal energy, d<span style="white-space:nowrap;"><em>Ɛ</em></span>(<em>t</em>), and thermodynamic work, dW(<em>t</em>), are defined by the progress of time-dependent Gibbs relation to thermodynamic equilibrium. The thermomechanical dynamics (TMD) approach constitutes a method for the nonequilibrium irreversible thermodynamics and transport processes.展开更多
The classical molecular dynamics simulation has been used to study the equation of state of gas H<SUB>2</SUB>, D<SUB>2</SUB> and T<SUB>2</SUB>. It has also been investigated that th...The classical molecular dynamics simulation has been used to study the equation of state of gas H<SUB>2</SUB>, D<SUB>2</SUB> and T<SUB>2</SUB>. It has also been investigated that the isotope mass affects on the accuracy of equation of state. Our calculated results show that the classical effect is principal and the isotope mass effects on the equation of state are obvious for the much light gases. At the same time, some useful theoretical data of equation of state for these gases have been provided. It is found that the classical simulation is still effective to the quantum gas. However, the quantum mechanics simulation and the improvement of intermolecular interaction potential are necessary if more accurate computational results are expected.展开更多
The recently presented equation for nonequilibrium state of gases is hereextended to liquid,and thus an equation of thermal conductivity for normal liquid is de-rived.The equation is applied to both polar and nonpolar...The recently presented equation for nonequilibrium state of gases is hereextended to liquid,and thus an equation of thermal conductivity for normal liquid is de-rived.The equation is applied to both polar and nonpolar liquids,with the average error of608 experlmental values being 1.75% based upon 110 compounds of 29 types of structures.This method is far better than all the other methods published.展开更多
文摘The simplest equation of state that can be applied to calculate the thermodynamic properties of gases is the virial equation with the second coefficient B. The probability of applying the one-coefficient equation Z = exp(A/V) for the calculation of compressibility factor at critical temperature of gases and gas mixtures is investigated. It was verified that the one-coefficient equation of state can be applied to calculated the thermodynamic properties for both normal and strongly polar gases and gas mixtures.
基金The project supported by National Natural Science of China under Grant No. 10675408 and Natural Science Foundation of Xianning College under Grant No. KZ0627
文摘We present a model of non-uniform granular gases in one-dimensional case, whose granularity distribution has the fractal characteristic. We have studied the nonequilibrium properties of the system by means of Monte Carlo method. When the typical relaxation time T of the Brownian process is greater than the mean collision time To, the energy evolution of the system exponentially decays, with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state in which the velocity distribution strongly deviates from the Gaussian one. Three other aspects have also been studied for the steady state: the visualized change of the particle density, the entropy of the system and the correlations in the velocity of particles. And the results of simulations indicate that the system has strong spatial clustering; Furthermore, the influence of the inelasticity and inhomogeneity on dynamic behaviors have also been extensively investigated, especially the dependence of the entropy and the correlations in the velocity of particles on the restitute coefficient e and the fractal dimension D.
文摘The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.
文摘We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the first time in this field. The thermomechanical states of the heat engine are in Nonequilibrium Irreversible States (NISs), and time-dependent thermodynamic work W(t), internal energy E(t), energy dissipation or entropy Q<sub>d</sub>(t), and temperature T(t), are precisely studied and computed in TMD. We also introduced the new formalism, Q(t)-picture of thermodynamic heat-energy flows, for consistent analyses of NISs. Thermal flows in a long-time uniform heat flow and in a short-time heat flow are numerically studied as examples. In addition to the analysis of time-dependent physical quantities, the TMD analysis suggests that the concept of force and acceleration in Newtonian mechanics should be modified. The acceleration is defined as a continuously differentiable function of Class C<sup>2</sup> in Newtonian mechanics, but the thermomechanical dynamics demands piecewise continuity for acceleration and thermal force, required from physical reasons caused by frictional variations and thermal fluctuations. The acceleration has no direct physical meaning associated with force in TMD. The physical implications are fundamental for the concept of the macroscopic phenomena in NISs composed of systems in thermal and mechanical motion.
文摘The irreversible mechanism of heat engines is studied in terms of <em>thermodynamic consistency</em> and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible thermodynamic systems. As an example, a water drinking bird (DB) known as one of the heat engines is specifically examined. The DB system suffices a rigorous experimental device for the theory of nonequilibrium irreversible thermodynamics. The DB nonlinear equation of motion proves explicitly that nonlinear differential equations with time-dependent coefficients must be classified as independent equations different from those of constant coefficients. The solutions of nonlinear differential equations with time-dependent coefficients can express emergent phenomena: nonequilibrium irreversible states. The <em>couplings</em> among mechanics, thermodynamics and time-evolution to nonequilibrium irreversible state are defined when the internal energy, thermodynamic work, temperature and entropy are integrated as a spontaneous thermodynamic process in the DB system. The physical meanings of the time-dependent entropy, <em>T</em>(<em>t</em>)d<em>S</em>(<em>t</em>), , internal energy, d<span style="white-space:nowrap;"><em>Ɛ</em></span>(<em>t</em>), and thermodynamic work, dW(<em>t</em>), are defined by the progress of time-dependent Gibbs relation to thermodynamic equilibrium. The thermomechanical dynamics (TMD) approach constitutes a method for the nonequilibrium irreversible thermodynamics and transport processes.
文摘The classical molecular dynamics simulation has been used to study the equation of state of gas H<SUB>2</SUB>, D<SUB>2</SUB> and T<SUB>2</SUB>. It has also been investigated that the isotope mass affects on the accuracy of equation of state. Our calculated results show that the classical effect is principal and the isotope mass effects on the equation of state are obvious for the much light gases. At the same time, some useful theoretical data of equation of state for these gases have been provided. It is found that the classical simulation is still effective to the quantum gas. However, the quantum mechanics simulation and the improvement of intermolecular interaction potential are necessary if more accurate computational results are expected.
基金Project supported by Jilin Provincial Applied Basic Research Funds.
文摘The recently presented equation for nonequilibrium state of gases is hereextended to liquid,and thus an equation of thermal conductivity for normal liquid is de-rived.The equation is applied to both polar and nonpolar liquids,with the average error of608 experlmental values being 1.75% based upon 110 compounds of 29 types of structures.This method is far better than all the other methods published.