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Isochoric process

About: Isochoric process is a research topic. Over the lifetime, 1762 publications have been published within this topic receiving 37129 citations.


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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.

3,942 citations

Journal ArticleDOI
TL;DR: In this article, a regular solution-type thermodynamic model for twelve-component silicate liquids in the system SiO2-TiO 2-Al 2O3-Fe2O 3-Cr2O3 -FeO-MgO-CaO-Na2O-K 2O-P2O5-H2O is calibrated.
Abstract: A revised regular solution-type thermodynamic model for twelve-component silicate liquids in the system SiO2-TiO2-Al2O3-Fe2O3-Cr2O3-FeO-MgO-CaO-Na2O-K2O-P2O5-H2O is calibrated. The model is referenced to previously published standard state thermodynamic properties and is derived from a set of internally consistent thermodynamic models for solid solutions of the igneous rock forming minerals, including: (Mg,Fe2+,Ca)-olivines, (Na,Mg,Fe2+,Ca)M2 (Mg,Fe2+, Ti, Fe3+, Al)M1 (Fe3+, Al,Si)2TETO6-pyroxenes, (Na,Ca,K)-feldspars, (Mg,Fe2+) (Fe3+, Al, Cr)2O4-(Mg,Fe2+)2 TiO4 spinels and (Fe2+, Mg, Mn2+)TiO3-Fe2O3 rhombohedral oxides. The calibration utilizes over 2,500 experimentally determined compositions of silicate liquids coexisting at known temperatures, pressures and oxygen fugacities with apatite ±feldspar ±leucite ±olivine ±pyroxene ±quartz ±rhombohedral oxides ±spinel ±whitlockite ±water. The model is applicable to natural magmatic compositions (both hydrous and anhydrous), ranging from potash ankaratrites to rhyolites, over the temperature (T) range 900°–1700°C and pressures (P) up to 4 GPa. The model is implemented as a software package (MELTS) which may be used to simulate igneous processes such as (1) equilibrium or fractional crystallization, (2) isothermal, isenthalpic or isochoric assimilation, and (3) degassing of volatiles. Phase equilibria are predicted using the MELTS package by specifying bulk composition of the system and either (1) T and P, (2) enthalpy (H) and P, (3) entropy (S) and P, or (4) T and volume (V). Phase relations in systems open to oxygen are determined by directly specifying the fo2 or the T-P-fo2 (or equivalently H-P-fo2, S-P-fo2, T-V-fo2) evolution path. Calculations are performed by constrained minimization of the appropriate thermodynamic potential. Compositions and proportions of solids and liquids in the equilibrium assemblage are computed.

2,614 citations

Journal ArticleDOI
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 for thermodynamic properties of methane which were available up to the middle of 1991 and presents a new strategy for optimizing the structure of empirical thermodynamic correlation equations.
Abstract: This work reviews the data on thermodynamic properties of methane which were available up to the middle of 1991 and presents a new equation of state in the form of a fundamental equation explicit in the Helmholtz free energy. A new strategy for optimizing the structure of empirical thermodynamic correlation equations was used to determine the functional form of the equation. The Helmholtz function containing 40 fitted coefficients was fitted to selected experimental data of the following properties: (a) thermal properties of the single phase (pρT) and (b) of the liquid‐vapor saturation curve (psρ’ρ‘) including the Maxwell criterion, (c) speed of sound w, (d) isochoric heat capacity cv, (e) isobaric heat capacity cp, (f) difference of enthalph Δh, and (g) second virial coefficient B. Independent equations are also included for the vapor pressure, the saturated liquid and vapor densities, the isobaric ideal gas heat capacity and the melting pressure as functions of temperature. Tables for the thermodynamic ...

928 citations

Journal ArticleDOI
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.

697 citations

Journal ArticleDOI
TL;DR: The role of Maxwell's demon is discussed and it is found that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine.
Abstract: In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwell's demon in quantum thermodynamic cycles. We find that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine.

601 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202365
2022140
202190
202092
201993
201883