Fundamental Equations Of State Research Articles

Determination of Hydrogen’s Thermophysical Properties Using a Statistical Thermodynamic Method

Accurate determination of the thermophysical properties of hydrogen is a crucial issue in hydrogen system design. By developing computational programs, a statistical thermodynamic model based on fundamental equations of state was implemented to determine hydrogen’s thermophysical properties, including the ortho-hydrogen fraction in equilibrium hydrogen, para-ortho hydrogen conversion heat, isobaric heat capacities and enthalpies. The deviations of calculated para-hydrogen enthalpies from REFPROP data were within 2.22%, ranging from 20 K to 300K at 0.1 MPa, and within 2.32% between 100 K and 1500 K at pressures from 0.1 MPa to 20 MPa. To quantitatively assess the convenience of the statistical thermodynamic method, the running speeds of programs with different methods for determining hydrogen’s thermophysical properties were compared. The time required for statistical thermodynamic calculation was 7.95% that required for treading REFPROP data when the performance of the variable density multilayer insulation combined with a one vapor-cooled shield and para-ortho hydrogen conversion was calculated. The programs developed based on the statistical thermodynamic method can be used to determine the thermophysical properties of hydrogen or other fluids.

Evaluation of Liquid Heat Capacity of Latest Low Global Warming Hydrofluoroolefins (HFOs): A Comparison of a Cubic Equation of State, Fundamental Equations of State, and a Corresponding State Equation

Isobaric heat capacity is one of the key thermophysical properties for working fluids in thermal systems and plays an important role in the development of equation of state. Due to the lack of experimental data for promising hydrofluoroolefins (HFOs), we carried out theoretical predictions for condensed liquid phase with three different methods: traditional cubic equation of state (CEOS), fundamental equations of state (FEOS) explicit in Helmholtz free energy and a corresponding state equation (CSE). Both CEOS and CSE are generalized models that only need several characteristic parameters to conduct calculation, while FEOS are specific models in which the structure and parameters are regressed from experimental data of one certain fluid. Liquid heat capacity data of 9 HFOs were calculated, including well-known R1234yf, R1234ze(E), and latest prospective R1123, R1216, R1243zf, R1234ze(Z), R1336mzz(Z), R1141, and R1125zc. A critical comparison was carried out between different calculation methods. The comparison showed that both CSE and FEOS predicted available experimental data well with AADs % less than the reported experimental uncertainties. For refrigerants without experimental heat capacity, CSE and FEOS showed good agreements with AADs % less than 3.6 %. The selected CEOS always provided relatively larger predictions than experiments or the other two methods. Despite that, calculated data of CEOS showed a strong linear relation with the other two methods, which suggested that there might be a potential linear modification or correlation for CEOS in improving its heat capacity calculations. Furthermore, when there were no experimental data available, CSE used in this study could be a useful preliminary evaluation tool for the liquid heat capacity of hydrofluoroolefins, considering its accuracy and easy application characteristics.

Measurement of the isobar heat capacity of fluids in the critical area by the method of flowing adiabatic calorimeter

With regard to the problem of refining the fundamental equations of state of hydrocarbons, the methodological and design features of the experimental measurement of the isobaric heat capacity in the critical region by the method of a flow adiabatic calorimeter are considered. The pressure measurement system has been improved by introducing a differential manometer into the measuring circuit, which made it possible not only to increase the accuracy of pressure determination, but also to implement a universal scheme of calorimetric experiment. The use of a universal scheme of the calorimetric experiment allows one to determine two values of the isobaric heat capacity at pressures that differ by the value of the pressure loss in the calorimeter. Such an approach in the critical region is relevant, since it makes it possible to quite simply and reliably determine the value of the derivative of the heat capacity with respect to pressure, which is used to estimate not only the error in assigning the value of heat capacity to pressure, but also the equilibrium conditions of the experiment in a flow-through calorimeter. The technique of determining and making a correction for the inhomogeneity of the supply wires of the differential thermocouple, for the throttling of the flow of matter in the calorimeter is considered. Correct relations are obtained for determining the average temperature of the measurement experiment for various methods of measuring the temperature and temperature difference in a flow-through calorimeter. The results of experimental measurements of the isobaric heat capacity of n-pentane in the critical region, obtained using the universal scheme of the calorimetric experiment, for n-pentane were measured on an isobar of 3.400 MPa (critical pressure 3.355 MPa), which is the closest to the critical point at practice of flow calorimetry

Thermodynamic Properties of Dodecamethylpentasiloxane, Tetradecamethylhexasiloxane, and Decamethylcyclopentasiloxane

Siloxanes are widely used in the chemical industry and in process and power engineering. For example, they are used as working fluids of organic Rankine cycle power plants since 20 years ago. For the process design and optimization, thermodynamic properties, such as enthalpy, entropy, speed of sound, density, and vapor–liquid equilibrium, are required. While the properties of short-chained siloxanes, such as hexamethyldisiloxane (MM) or octamethylcyclotetrasiloxane (D₄), have already been investigated comprehensively, information on thermophysical properties of higher order siloxanes is limited. Therefore, measurements on density and speed of sound in the liquid state of dodecamethylpentasiloxane (MD₃M), tetradecamethylhexasiloxane (MD₄M), and decamethylcyclopentasiloxane (D₅) are presented here. On the basis of these measurements and other experimental data from the literature, new fundamental equations of state were developed for these three fluids. The equations are based on the Helmholtz energy and, thus, allow for the calculation of any thermodynamic state property by means of derivatives with respect to the natural variables, namely temperature and density. The obtained models also feature a correct extrapolation behavior in regions where no data are available in order to ensure the applicability of the equations to mixture models in the future. On the basis of the present equations of state and recently published equations for other siloxanes, the possibility of the siloxanes belonging to the group of Bethe–Zel’dovich–Thompson fluids is also investigated.

The Widom line for supercritical fluids

We review the different approaches to establish the boundary between the liquid and the quasi-gas fluid above the critical point. Some experimental data by inelastic X-ray scattering demonstrates different dynamical regimes: gas-like and liquid-like reminiscent of the subcritical domains. Theoretical models based on the Lennard-Jones and square well interparticle potentials together with phenomenological Van der Waals model confirm similar picture for the Widom line in supercritical domain. To minimize uncertainty experimental data we calculated extrema of response functions via fundamental equations of state. The shift of critical points under influences of impurities and nanoparticle adding is analyzed.

Comparative study of the Grüneisen parameter for 28 pure fluids.

The Grüneisen parameter γG is widely used for studying thermal properties of solids at high pressure and also has received increasing interest in different applications of non-ideal fluid dynamics. Because there is a lack of systematic studies of the Grüneisen parameter in the entire fluid region, this study aims to fill this gap. Grüneisen parameter data from molecular modelling and simulation are reported for 28 pure fluids and are compared with results calculated from fundamental equations of state that are based on extensive experimental data sets. We show that the Grüneisen parameter follows a general density-temperature trend and characterize the fluid systems by specifying a span of minimum and maximum values of γG. Exceptions to this trend can be found for water.

Speed of sound measurements of liquid C1–C4 alkanols

Speed of sound measurements were made in methanol, ethanol, propan-1-ol, and butan-1-ol in the temperature range from (253.15 to 353.15)K at pressures up to 30MPa by use of a pulse-echo method with a double path type sensor. The expanded overall uncertainty (k=2) in speed of sound measurements are estimated to be 0.026% for methanol, 0.03% for ethanol, 0.013% for propan-1-ol and 0.01% for butan-1-ol. A double polynomial equation for the speed of sound with inputs of temperature and pressure has been fitted from the experimental results. These were compared with available literature sources and fundamental equations of state, showing good agreement among them to comparable alcohol purities and experimental uncertainties.

Measurements of the Speed of Sound in Propene in the Liquid and Supercritical Regions

This paper reports comprehensive and accurate measurements of the speed of sound in pure propene in the liquid and supercritical regions. The data have been measured by a double-path-length pulse-echo technique and cover the temperature range from 240 K to 420 K with pressures up to 100 MPa. The measurement uncertainties amount to 3 mK for temperature, 0.01 % for pressures below 10 MPa, 0.005 % for pressures between 10 MPa and 100 MPa, and 0.015 % for speed of sound. The high accuracy of the measurements is demonstrated by comparisons with literature data and three fundamental equations of state.

流体の熱力学状態方程式

Thermodynamic properties such as density, heat capacities, speed of sound, enthalpy, entropy, and other properties, can be calculated from a single thermodynamic equation of state in the case of pure fluids. Equation of state representing Helmholtz free energy provides those property values accurately in wide gaseous, liquid, and supercritical phases even at high temperatures and pressures by only differential procedures, which is sometimes called as fundamental equation of state. For many important fluids like water, air, carbon dioxide, ammonia, methane, isobutane, methanol, and hydrofluorocarbons (HFCs), the fundamental equations of state have already been established. This article introduces these fundamental equations of state and the background of them. Some latest aspects obtained in our group on thermodynamic equations of state are also introduced.

Deformation and fracture of materials under impulsive loads

1. Calculations of the behavior of materials under impulsive loads are based on fundamental equations of state. These equations link loading and deformation processes with the critical conditions of the fracture of local regions of the material. 2. Dynamic tests of specimens may be recommended for obtaining experimental data that will make it possible to construct the fundamental equations of state with an allowance for the strain rate and loading history. Here, reliable results can be obtained under conditions of high-rate loading only in tests conducted at a constant strain rate. 3. There are very few experimental studies of the behavior of materials with high-rate deformation under conditions of a complex stress state as well as studies of complex loading conditions and loading paths in a stress (strain) space. This makes the development of appropriate experimental methods and the conducting of pertinent studies more urgent. 4. It is necessary to develop experimental methods to investigate the laws of crack initiation and growth in a material in the propagation of intensive loading waves and to determine dynamic criteria of the local fracture of materials.

Testing fundamental equations of state for practical applicability

Testing fundamental equations of state for practical applicability