Topic
Triple point
About: Triple point is a research topic. Over the lifetime, 2191 publications have been published within this topic receiving 57423 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this article, the authors present a new equation of state in the form of a fundamental equation explicit in the Helmholtz free energy, which is able to represent even the most accurate data to within their experimental uncertainty.
Abstract: This work reviews the available data on thermodynamic properties of carbon dioxide and presents a new equation of state in the form of a fundamental equation explicit in the Helmholtz free energy. The function for the residual part of the Helmholtz free energy was fitted to selected data of the following properties: (a) thermal properties of the single‐phase region (pρT) and (b) of the liquid‐vapor saturation curve (p s, ρ′, ρ″) including the Maxwell criterion, (c) speed of soundw and (d) specific isobaric heat capacityc p of the single phase region and of the saturation curve, (e) specific isochoric heat capacityc v , (f) specific enthalpyh, (g) specific internal energyu, and (h) Joule–Thomson coefficient μ. By applying modern strategies for the optimization of the mathematical form of the equation of state and for the simultaneous nonlinear fit to the data of all these properties, the resulting formulation is able to represent even the most accurate data to within their experimental uncertainty. In the technically most important region up to pressures of 30 MPa and up to temperatures of 523 K, the estimated uncertainty of the equation ranges from ±0.03% to ±0.05% in the density, ±0.03% to ±1% in the speed of sound, and ±0.15% to ±1.5% in the isobaric heat capacity. Special interest has been focused on the description of the critical region and the extrapolation behavior of the formulation. Without a complex coupling to a scaled equation of state, the new formulation yields a reasonable description even of the caloric properties in the immediate vicinity of the critical point. At least for the basic properties such as pressure, fugacity, and enthalpy, the equation can be extrapolated up to the limits of the chemical stability of carbon dioxide. Independent equations for the vapor pressure and for the pressure on the sublimation and melting curve, for the saturated liquid and vapor densities, and for the isobaric ideal gas heat capacity are also included. Property tables calculated from the equation of state are given in the appendix.
4,591 citations
TL;DR: Using self-consistent field theory, microphases of diblock copolymers are examined and a stable gyroid phase is found which occurs between the lamellar and hexagonal ones and terminates at a triple point.
Abstract: Using self-consistent field theory, we examine microphases of diblock copolymers and find, in addition to lamellar, hexagonal, and cubic phases, a stable gyroid phase which occurs between the lamellar and hexagonal ones. It terminates at a triple point, with a lamellar to hexagonal transition occurring in the weak-segregation limit. Other phases of experimental interest are studied, and we describe the regions in which they are most nearly stable.
1,419 citations
TL;DR: In this paper, a new formulation for the thermodynamic properties of nitrogen has been developed, which is valid from the triple point temperature to temperatures of 1000 K and up to pressures of 2200 MPa.
Abstract: A new formulation for the thermodynamic properties of nitrogen has been developed. Many new data sets have become available, including high accuracy data from single and dual-sinker apparatuses which improve the accuracy of the representation of the pρT surface of gaseous, liquid, and supercritical nitrogen, including the saturation states. New measurements of the speed of sound from spherical resonators yield accurate information on caloric properties in gaseous and supercritical nitrogen. Isochoric heat capacity and enthalpy data have also been published. Sophisticated procedures for the optimization of the mathematical structure of equations of state and special functional forms for an improved representation of data in the critical region were used. Constraints regarding the structure of the equation ensure reasonable results up to extreme conditions of temperature and pressure. For calibration applications, the new reference equation is supplemented by a simple but also accurate formulation, valid only for supercritical nitrogen between 250 and 350 K at pressures up to 30 MPa. The uncertainty in density of the new reference equation of state ranges from 0.02% at pressures less than 30 MPa up to 0.6% at very high pressures, except in the range from 270 to 350 K at pressures less than 12 MPa where the uncertainty in density is 0.01%. The equation is valid from the triple point temperature to temperatures of 1000 K and up to pressures of 2200 MPa. From 1000 to 1800 K, the equation was validated with data of limited accuracy. The extrapolation behavior beyond 1800 K is reasonable up to the limits of chemical stability of nitrogen, as indicated by comparison to experimental shock tube data.
816 citations
TL;DR: The TIP4P/2005 model is able to accurately describe the surface tension of water over the whole range of temperatures from the triple point to the critical temperature, and the test area is an appropriate methodological choice for the calculation of thesurface tension.
Abstract: We consider the calculation of the surface tension from simulations of several models of water, such as the traditional TIP3P, SPC, SPC/E, and TIP4P models, and the new generation of TIP4P-like models including the TIP4P/Ew, TIP4P/Ice, and TIP4P/2005. We employ a thermodynamic route proposed by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)] to determine the surface tension that involves the estimate of the change in free energy associated with a small change in the interfacial area at constant volume. The values of the surface tension computed from this test-area method are found to be fully consistent with those obtained from the standard mechanical route, which is based on the evaluation of the components of the pressure tensor. We find that most models do not reproduce quantitatively the experimental values of the surface tension of water. The best description of the surface tension is given by those models that provide a better description of the vapor-liquid coexistence curve. The values of the surface tension for the SPC/E and TIP4P/Ew models are found to be in reasonably good agreement with the experimental values. From the present investigation, we conclude that the TIP4P/2005 model is able to accurately describe the surface tension of water over the whole range of temperatures from the triple point to the critical temperature. We also conclude that the test area is an appropriate methodological choice for the calculation of the surface tension not only for simple fluids, but also for complex molecular polar fluids, as is the case of water.
810 citations
TL;DR: In this paper, a thermodynamic study of the liquid-solid phase transformations in porous materials provides the relationships between the size of the pores in which solidification takes place and the temperature of the triple point of the divided liquid, on the one hand, and between this temperature and the apparent solidification energy on the other hand.
763 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 12 |
| 2024 | 23 |
| 2023 | 33 |
| 2022 | 89 |
| 2021 | 42 |
| 2020 | 50 |