The thermodynamic quantities for the gases of massless particles with spin s = 1/2, 1, 3/2, 2 around static spherical black holes are investigated by using the brick-wall method. The appearance of the spin-dependent s...The thermodynamic quantities for the gases of massless particles with spin s = 1/2, 1, 3/2, 2 around static spherical black holes are investigated by using the brick-wall method. The appearance of the spin-dependent subleading terms is demonstrated and the terms are shown to contain not only the linear and quadratic terms of the spins but also a zero-power terra of the spins.展开更多
In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters...In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters satisfy the first law of thermodynamics,the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained.Then,we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes.It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position.We discuss the influence of the hair parameter and electric charge on the critical point.We also find that the isochoric heat capacity of the spacetime is not zero,which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes,which is zero.Using the Ehrenfest equations,we prove that the critical phase transition is a second order equilibrium phase transition.Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties.Our universe is an asymptotically dS spacetime,and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.展开更多
The entropy density, energy density, pressure and equation of state around the RNAdS black hole are calculated in the WKB approximation on the Teukolsky-type master equation. The appearance of spin-dependent terms is ...The entropy density, energy density, pressure and equation of state around the RNAdS black hole are calculated in the WKB approximation on the Teukolsky-type master equation. The appearance of spin-dependent terms is demonstrated. The existence of these terms shows that the black hole radiation is not exactly thermal radiation and the black hole entropy is not strictly proportional to the area of the event horizon.展开更多
In the present study,humic acid was used as an adsorbent for the investigation of the adsorption kinetics,isotherms,and thermo-dynamic parameters of hexavalent chromium from aqueous solution at varying pH,temperatures...In the present study,humic acid was used as an adsorbent for the investigation of the adsorption kinetics,isotherms,and thermo-dynamic parameters of hexavalent chromium from aqueous solution at varying pH,temperatures,and concentrations.Adsorption isotherms and equilibrium adsorption capacities were determined by the fittings of the experimental data to three well-known iso-therm models:Langmuir,Freundlich,and Redlich-Peterson.The results showed that the Langmuir and Redlich-Peterson models appear to fit the adsorption better than did the Freundlich adsorption model for the adsorption of chromium onto humic acid.The equilibrium constants were used to calculate thermodynamic parameters such as the change of free energy,enthalpy,and entropy.The derived adsorption constants (logaL) and their temperature dependencies from Langmuir isotherm have been used to calculate the corresponding thermodynamic quantities such as the free energy of adsorption,heat,and entropy of adsorption.The thermo-dynamic data indicate that Cr (VI) adsorption onto humic acid is entropically driven and characterized by physical adsorption.展开更多
The statistical counting method for the computer simulation of the thermodynamic quantities of polymer solution has been reviewed. The calculating results for a single athermal chain confirm the theory of the renorma...The statistical counting method for the computer simulation of the thermodynamic quantities of polymer solution has been reviewed. The calculating results for a single athermal chain confirm the theory of the renormalization group. The results for the athermal solution are consistent with the scaling law of the osmotic pressure with the exponent 2.25. The results for a single chain with the segmental interaction are in a good agreement with the exact results obtained by the direct counting method. The results for the polymer solution show us that the Flory-Huggins parameter is strongly dependent on both the polymer concentration and the interaction energy between segments. (Author abstract) 15 Refs.展开更多
For a black hole with two horizons, the effective entropy is assumed to be a linear combination of the two entropies of the outer and inner horizons. In terms of the effective thermodynamic quantities the effective Be...For a black hole with two horizons, the effective entropy is assumed to be a linear combination of the two entropies of the outer and inner horizons. In terms of the effective thermodynamic quantities the effective Bekenstein-Smarr formula and the effective first law of thermodynamics are derived.展开更多
In this study, the convertibility of disposable plastic waste injectors made of HDPE and PP plastics into valuable chemical products by thermal pyrolysis was investigated. While PP plastic wastes were decomposed in th...In this study, the convertibility of disposable plastic waste injectors made of HDPE and PP plastics into valuable chemical products by thermal pyrolysis was investigated. While PP plastic wastes were decomposed in the temperature range of 400°C - 445°C, HDPE plastic wastes were decomposed in the higher temperature range (430°C - 475°C). Although the physical appearance of the liquid products obtained in the thermal decomposition of PP plastic wastes are lighter in color and fluid, it has been observed that the liquid decomposition products of HDPE plastic wastes have a more dense and viscous structure. By using the first-order kinetic model, kinetic expressions for both plastic wastes were derived, reaction rate constants, k, and activation energy, E<sub>act</sub>, and thermodynamic quantities such as reaction enthalpy, △H<sup>≠</sup>, reaction entropy, △S<sup>≠</sup> ve and Gibbs free energy, △G<sup>≠</sup> were calculated. In the thermal pyrolysis of PP and HDPE plastic wastes, E<sub>act</sub>, △H<sup>≠</sup>, △G<sup>≠</sup>, △S<sup>≠</sup> values are 162.30 kJ/mol, 156.52 kJ/mol, 219.50 kJ/mol, -87.71 J/molK, and 201.80 kJ/mol, 195.77 kJ/mol, and 229.14 kJ/mol, -46.48 J/molK, respectively. These thermodynamic quantities calculated for both plastic wastes show that the pyrolytic decomposition studies carried out in an inert gas atmosphere have endothermic reaction behavior.展开更多
The entropy density, energy density, pressure, and equation of state of an ideal relativistic gas around the Schwarzschild-anti-de Sitter black hole with a global monopole are investigated by using the brick-wall meth...The entropy density, energy density, pressure, and equation of state of an ideal relativistic gas around the Schwarzschild-anti-de Sitter black hole with a global monopole are investigated by using the brick-wall method. It is shown that the sub-leading term with spin-dependence exists and that the corrected expression for any spin field is very different from that for scalar field. The usual result that these thermodynamical quantities take the same forms as those in fiat spacetime holds only for the leading term.展开更多
We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite en...We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility, and the persistent currents are also studied by using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.展开更多
Using the divergence term appearing in the Lagrangian of the teleparallel equivalent of general relativity （TEGR）, we calculate the thermodynamic quantities of four tetrads＇ spacetime reproducing Lense-Thirring （L...Using the divergence term appearing in the Lagrangian of the teleparallel equivalent of general relativity （TEGR）, we calculate the thermodynamic quantities of four tetrads＇ spacetime reproducing Lense-Thirring （LT） metric. We also investigate the first law of thermodynamics and the quantum statistical relation.展开更多
We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black h...We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system,we derive effective thermodynamic quantities of the system according to the first law of thermodynamics,and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α.It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system,and along with electric charge has an effect on the phase structure of the system,which is obvious,especially as the effective temperature is below the critical temperature.The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.展开更多
Generic axiomatic-nonextensive statistics introduces two asymptotic properties,to each of which a scaling function is assigned.The first and second scaling properties are characterized by the exponents c and d,respect...Generic axiomatic-nonextensive statistics introduces two asymptotic properties,to each of which a scaling function is assigned.The first and second scaling properties are characterized by the exponents c and d,respectively.In the thermodynamic limit,a grand-canonical ensemble can be formulated.The thermodynamic properties of a relativistic ideal gas of hadron resonances are studied,analytically.It is found that this generic statistics satisfies the requirements of the equilibrium thermodynamics.Essential aspects of the thermodynamic self-consistency are clarified.Analytical expressions are proposed for the statistical fits of various transverse momentum distributions measured in most-central collisions at different collision energies and colliding systems.Estimations for the freezeout temperature（T_（ch）） and the baryon chemical potential（μ_b） and the exponents c and d are determined.The earlier are found compatible with the parameters deduced from Boltzmann-Gibbs（BG） statistics（extensive）,while the latter refer to generic nonextensivities.The resulting equivalence class（c,d） is associated with stretched exponentials,where Lambert function reaches its asymptotic stability.In some measurements,the resulting nonextensive entropy is linearly composed on extensive entropies.Apart from power-scaling,the particle ratios and yields are excellent quantities to highlighting whether the particle production takes place（non）extensively.Various particle ratios and yields measured by the STAR experiment in central collisions at 200,62.4 and 7.7 GeV are fitted with this novel approach.We found that both c and d 〈 1,i.e.referring to neither BG-nor Tsallis-type statistics,but to（c,d）-entropy,where Lambert functions exponentially rise.The freezeout temperature and baryon chemical potential are found comparable with the ones deduced from BG statistics（extensive）.We conclude that the particle production at STAR energies is likely a nonextensive process but not necessarily BG or Tsallis type.展开更多
Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,t...Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,their thermodynamical properties nearby the critical point have attracted considerable attention.However,there exists little work on the thermodynamic properties of the de Sitter(dS)spacetime with black holes.In this paper,based on the effective thermodynamical quantities and the method of the Maxwell's equal-area law,we explore the phase equilibrium for the de Sitter spacetime with the charged black holes and the cloud of string and quintessence(i.e.,C-dSSQ spacetime).The boundaries of the two-phase coexistence region in both P_(eff)−T_(eff)and T_(eff)−S diagrams are obtained.The coexistent curve and the latent heat of phase transition for this system are also investigated.Furthermore,we analyze the effect of parameters(the state parameterωand the ratio of two horizon radii x=r+/r_(c))on the two-phase coexistence region boundary.The results indicate that the phase transition in C-dSSQ spacetime is analogous to that in a van der Waals fluid(vdw)system,which is determined by the electrical potential at the horizon.These results are helpful for understanding the basic properties of black holes and are also of great value for the establishment of quantum gravity.展开更多
文摘The thermodynamic quantities for the gases of massless particles with spin s = 1/2, 1, 3/2, 2 around static spherical black holes are investigated by using the brick-wall method. The appearance of the spin-dependent subleading terms is demonstrated and the terms are shown to contain not only the linear and quadratic terms of the spins but also a zero-power terra of the spins.
基金the National Natural Science Foundation of China(12075143)。
文摘In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters satisfy the first law of thermodynamics,the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained.Then,we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes.It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position.We discuss the influence of the hair parameter and electric charge on the critical point.We also find that the isochoric heat capacity of the spacetime is not zero,which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes,which is zero.Using the Ehrenfest equations,we prove that the critical phase transition is a second order equilibrium phase transition.Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties.Our universe is an asymptotically dS spacetime,and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.
基金Project supported by the National Natural Science Foundation of China （Grant No 10375051）.
文摘The entropy density, energy density, pressure and equation of state around the RNAdS black hole are calculated in the WKB approximation on the Teukolsky-type master equation. The appearance of spin-dependent terms is demonstrated. The existence of these terms shows that the black hole radiation is not exactly thermal radiation and the black hole entropy is not strictly proportional to the area of the event horizon.
基金supported by the National Key Technologies R&D Program in the 10th Five-year Plan (2004BA901A15)the Key Program of National Natural Science Foundation of China (Grant No.90702001)
文摘In the present study,humic acid was used as an adsorbent for the investigation of the adsorption kinetics,isotherms,and thermo-dynamic parameters of hexavalent chromium from aqueous solution at varying pH,temperatures,and concentrations.Adsorption isotherms and equilibrium adsorption capacities were determined by the fittings of the experimental data to three well-known iso-therm models:Langmuir,Freundlich,and Redlich-Peterson.The results showed that the Langmuir and Redlich-Peterson models appear to fit the adsorption better than did the Freundlich adsorption model for the adsorption of chromium onto humic acid.The equilibrium constants were used to calculate thermodynamic parameters such as the change of free energy,enthalpy,and entropy.The derived adsorption constants (logaL) and their temperature dependencies from Langmuir isotherm have been used to calculate the corresponding thermodynamic quantities such as the free energy of adsorption,heat,and entropy of adsorption.The thermo-dynamic data indicate that Cr (VI) adsorption onto humic acid is entropically driven and characterized by physical adsorption.
基金This work was supported by the National Key Project for Fundamental Research"Macromolecular Condensed State",The State Science and Technology Commission of China
文摘The statistical counting method for the computer simulation of the thermodynamic quantities of polymer solution has been reviewed. The calculating results for a single athermal chain confirm the theory of the renormalization group. The results for the athermal solution are consistent with the scaling law of the osmotic pressure with the exponent 2.25. The results for a single chain with the segmental interaction are in a good agreement with the exact results obtained by the direct counting method. The results for the polymer solution show us that the Flory-Huggins parameter is strongly dependent on both the polymer concentration and the interaction energy between segments. (Author abstract) 15 Refs.
文摘For a black hole with two horizons, the effective entropy is assumed to be a linear combination of the two entropies of the outer and inner horizons. In terms of the effective thermodynamic quantities the effective Bekenstein-Smarr formula and the effective first law of thermodynamics are derived.
文摘In this study, the convertibility of disposable plastic waste injectors made of HDPE and PP plastics into valuable chemical products by thermal pyrolysis was investigated. While PP plastic wastes were decomposed in the temperature range of 400°C - 445°C, HDPE plastic wastes were decomposed in the higher temperature range (430°C - 475°C). Although the physical appearance of the liquid products obtained in the thermal decomposition of PP plastic wastes are lighter in color and fluid, it has been observed that the liquid decomposition products of HDPE plastic wastes have a more dense and viscous structure. By using the first-order kinetic model, kinetic expressions for both plastic wastes were derived, reaction rate constants, k, and activation energy, E<sub>act</sub>, and thermodynamic quantities such as reaction enthalpy, △H<sup>≠</sup>, reaction entropy, △S<sup>≠</sup> ve and Gibbs free energy, △G<sup>≠</sup> were calculated. In the thermal pyrolysis of PP and HDPE plastic wastes, E<sub>act</sub>, △H<sup>≠</sup>, △G<sup>≠</sup>, △S<sup>≠</sup> values are 162.30 kJ/mol, 156.52 kJ/mol, 219.50 kJ/mol, -87.71 J/molK, and 201.80 kJ/mol, 195.77 kJ/mol, and 229.14 kJ/mol, -46.48 J/molK, respectively. These thermodynamic quantities calculated for both plastic wastes show that the pyrolytic decomposition studies carried out in an inert gas atmosphere have endothermic reaction behavior.
基金The project supported by the Natural Science Foundation of Zhanjiang Normal College under Grant No.L0612
文摘The entropy density, energy density, pressure, and equation of state of an ideal relativistic gas around the Schwarzschild-anti-de Sitter black hole with a global monopole are investigated by using the brick-wall method. It is shown that the sub-leading term with spin-dependence exists and that the corrected expression for any spin field is very different from that for scalar field. The usual result that these thermodynamical quantities take the same forms as those in fiat spacetime holds only for the leading term.
文摘We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility, and the persistent currents are also studied by using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.
文摘Using the divergence term appearing in the Lagrangian of the teleparallel equivalent of general relativity （TEGR）, we calculate the thermodynamic quantities of four tetrads＇ spacetime reproducing Lense-Thirring （LT） metric. We also investigate the first law of thermodynamics and the quantum statistical relation.
基金supported by NSFC under Grant No.11705107by the doctoral Sustentation Fund of Shanxi Datong University(2015-B-10).
文摘We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system,we derive effective thermodynamic quantities of the system according to the first law of thermodynamics,and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α.It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system,and along with electric charge has an effect on the phase structure of the system,which is obvious,especially as the effective temperature is below the critical temperature.The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.
文摘Generic axiomatic-nonextensive statistics introduces two asymptotic properties,to each of which a scaling function is assigned.The first and second scaling properties are characterized by the exponents c and d,respectively.In the thermodynamic limit,a grand-canonical ensemble can be formulated.The thermodynamic properties of a relativistic ideal gas of hadron resonances are studied,analytically.It is found that this generic statistics satisfies the requirements of the equilibrium thermodynamics.Essential aspects of the thermodynamic self-consistency are clarified.Analytical expressions are proposed for the statistical fits of various transverse momentum distributions measured in most-central collisions at different collision energies and colliding systems.Estimations for the freezeout temperature（T_（ch）） and the baryon chemical potential（μ_b） and the exponents c and d are determined.The earlier are found compatible with the parameters deduced from Boltzmann-Gibbs（BG） statistics（extensive）,while the latter refer to generic nonextensivities.The resulting equivalence class（c,d） is associated with stretched exponentials,where Lambert function reaches its asymptotic stability.In some measurements,the resulting nonextensive entropy is linearly composed on extensive entropies.Apart from power-scaling,the particle ratios and yields are excellent quantities to highlighting whether the particle production takes place（non）extensively.Various particle ratios and yields measured by the STAR experiment in central collisions at 200,62.4 and 7.7 GeV are fitted with this novel approach.We found that both c and d 〈 1,i.e.referring to neither BG-nor Tsallis-type statistics,but to（c,d）-entropy,where Lambert functions exponentially rise.The freezeout temperature and baryon chemical potential are found comparable with the ones deduced from BG statistics（extensive）.We conclude that the particle production at STAR energies is likely a nonextensive process but not necessarily BG or Tsallis type.
基金Supported by the Natural Science Foundation of China(11705106,12075143)the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province(2020L0471,2020L0472)+2 种基金the Science Technology Plan Project of Datong City,China(2020153)the Science Foundation of Shanxi Datong University(2022Q1,2015Q6,2022Q2)the Teaching Reform Project of Shanxi Datong University(XJG2022234)。
文摘Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,their thermodynamical properties nearby the critical point have attracted considerable attention.However,there exists little work on the thermodynamic properties of the de Sitter(dS)spacetime with black holes.In this paper,based on the effective thermodynamical quantities and the method of the Maxwell's equal-area law,we explore the phase equilibrium for the de Sitter spacetime with the charged black holes and the cloud of string and quintessence(i.e.,C-dSSQ spacetime).The boundaries of the two-phase coexistence region in both P_(eff)−T_(eff)and T_(eff)−S diagrams are obtained.The coexistent curve and the latent heat of phase transition for this system are also investigated.Furthermore,we analyze the effect of parameters(the state parameterωand the ratio of two horizon radii x=r+/r_(c))on the two-phase coexistence region boundary.The results indicate that the phase transition in C-dSSQ spacetime is analogous to that in a van der Waals fluid(vdw)system,which is determined by the electrical potential at the horizon.These results are helpful for understanding the basic properties of black holes and are also of great value for the establishment of quantum gravity.
