Isochoric Heat Capacity Measurements for Light and Heavy Water Near the Critical Point

The isochoric heat capacity was measured for D₂O at a fixed density of 356.075 kg·m^–3 and for H₂O at 309.905 kg·m^–3. The measurements cover the range of temperatures from 623 to 661 K. The measurements were made with a high-temperature, high-pressure, adiabatic calorimeter with a nearly constant inner volume. The uncertainty of the temperature is 10 mK, while the uncertainty of the heat capacity is estimated to be 2 to 3%. Measurements were made in both the two-phase and the one-phase regions. The calorimeter instrumentation also enables measurements of PVT and the temperature derivative (P/T)_V along each measured isochore. A detailed discussion is presented on the experimental temperature behavior of C_V in the one- and two-phase regions, including the coexistence curve near the critical point. A quasi-static thermogram method was applied to determine values of temperature at saturation T_S() on measured isochores. The uncertainty of the phase-transition temperature measurements is about ±0.02 K. The measured C_V data for D₂O and H₂O are compared with values predicted from a recent developed parametric crossover equation of state and IAPWS-95 formulation.     

Isochoric Heat Capacity Measurements for 0.5 H2O+0.5 D2O Mixture in the Critical Region

The isochoric heat capacity C _V of an equimolar H₂O+D₂O mixture was measured in the temperature range from 391 to 655 K, at near-critical liquid and vapor densities between 274.05 and 385.36 kgm^–3. A high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter was used. The measurements were performed in the one- and two-phase regions including the coexistence curve. The uncertainty of the heat-capacity measurement is estimated to be ±2%. The liquid and vapor one- and two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from the experimental data for each measured isochore. The critical temperature and the critical density for the equimolar H₂O+D₂O mixture were obtained from isochoric heat capacity measurements using the method of quasi-static thermograms. The measurements were compared with a crossover equation of state for H₂O+D₂O mixtures. The near-critical isochoric heat capacity behavior for the 0.5 H₂O+0.5 D₂O mixture was studied using the principle of isomorphism of critical phenomena. The experimental isochoric heat capacity data for the 0.5 H₂O+0.5 D₂O mixture exhibit a weak singularity, like that of both pure components. The reliability of the experimental method was confirmed with measurements on pure light water, for which the isochoric heat capacity was measured on the critical isochore (321.96 kgm^–3) in both the one- and two-phase regions. The result for the phase-transition temperature (the critical temperature, T _{C, this work}=647.104±0.003 K) agreed, within experimental uncertainty, with the critical temperature (T _{C, IAPWS}=647.096 K) adopted by IAPWS.     

Two-Phase Isochoric Heat Capacity Measurements for Nitrogen Tetroxide in the Critical Region and Yang–Yang Relation

The two-phase isochoric heat capacity of nitrogen tetroxide was measured in the temperature range from 261.74 K to the critical temperature (431.072 K) at densities between 201.21 and 1426.5 kg·m^–3 using a high-temperature and high-pressure adiabatic calorimeter. The measurements were performed in the two-phase region for 26 isochores (15 liquid and 11 vapor densities) including the coexistence curve and critical region. Uncertainties of the measurements are estimated to be 2%. The original temperatures and C _V data were converted to the ITS-90. The liquid and vapor two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from experimental data for each measured isochore. From measured (T _S, _S, C _V2, C _V2) data, the values of second temperature derivatives of vapor-pressure d ² P _S/dT ² and chemical potential d ² /dT ² were derived using the Yang–Yang relation. The results were compared with values calculated from other vapor-pressure equations. The values of saturated densities and critical parameters derived in calorimetric experiments were compared with literature data. The unusual temperature behavior of d ² P _S/dT ² and d ² /dT ² was found at low temperatures around 351 K and near the critical point.     

Isochoric Heat Capacity of Heavy Water at Subcritical and Supercritical Conditions

The heat capacity of heavy water was measured in the temperature range from 294 to 746 K and at densities between 52 and 1105 kg·m^–3 using a high-temperature, high-pressure adiabatic calorimeter. The measurements were performed at 14 liquid and 9 vapor densities between 52 and 1105 kg·m^–3. Uncertainties of the measurements are estimated to be within 3% for vapor isochores and 1.5% for the liquid isochores. In the region of the immediate vicinity of the critical point (0.97T/T _c1.03 and 0.75/_c1.25), the uncertainty is 4.5%. The original C _V data were corrected and converted to the new ITS-90 temperature scale. A parametric crossover equation of state was used to represent the isochoric heat capacity measurements of heavy water in the extended critical region, 0.8T/T _c1.5 and 0.35/_c1.65. The liquid and vapor one- and two-phase isochoric heat capacities, temperatures, and saturation densities were extracted from experimental data for each measured isochore. Most of the experimental data are compared with the Hill equation of state, and the overall statistics of deviations between experimental data and the equation of state are given.     

Isochoric Heat Capacity of CO2 + n-Decane Mixtures in the Critical Region

The isochoric heat capacity of two binary (CO₂+n-decane) mixtures (0.095 and 0.178 mole fraction of n-decane) have been measured with a high- temperature, high-pressure, nearly constant volume adiabatic calorimeter. Measurements were made at nineteen near-critical liquid and vapor densities between 87 and 658 kg·m⁻³ for the composition of 0.095 mole fraction n-decane and at nine densities between 83 and 458 kg·m⁻³ for the composition of 0.178 mole fraction n-decane. The range of temperatures was 295 to 568 K. These temperature and density ranges include near- and supercritical regions. The measurements were performed in both one- and two-phase regions including the vapor + liquid coexistence curve. The uncertainty of the heat- capacity measurements is estimated to be 2% (coverage factor k=2). The uncertainty in temperature is 15 mK, and that for density measurements is 0.06%. The liquid and vapor one- and two-phase isochoric heat capacities, temperatures (T _S), and densities (ρ_S) at saturation were measured by using the well-established method of quasi-static thermograms for each filling density. The critical temperatures (T _C), the critical densities (ρ_C), and the critical pressure (P _C) for the CO₂+n-decane mixtures were extracted from the isochoric heat-capacity measurements on the coexistence curve. The observed isochoric heat capacity along the critical isochore of the CO₂+n-decane mixture exhibits a renormalization of the critical behavior of C _{V X} typical for mixtures. The values of the characteristic parameters (K ₁, K ₂), temperatures (τ₁ ,τ₂), and the characteristic density differences were estimated for the CO₂+n-decane mixture by using the critical-curve data and the theory of critical phenomena in binary mixtures. The ranges of conditions were defined on the T-x plane for the critical isochore and the ρ-x plane for the critical isotherm, for which we observed renormalization of the critical behavior for the isochoric heat capacity.     

Isochoric Heat-Capacity Measurements for Pure Methanol in the Near-Critical and Supercritical Regions

Isochoric heat-capacity measurements for pure methanol are presented as a function of temperature at fixed densities between 136 and 750 kg·m⁻³. The measurements cover a range of temperatures from 300 to 556 K. The coverage includes the one- and two-phase regions, the coexistence curve, the near-critical, and the supercritical regions. A high-temperature, high-pressure, adiabatic, and nearly constant-volume calorimeter was used for the measurements. Uncertainties of the heat-capacity measurements are estimated to be 2–3% depending on the experimental density and temperature. Temperatures at saturation, T _S(ρ), for each measured density (isochore) were measured using a quasi-static thermogram technique. The uncertainty of the phase-transition temperature measurements is 0.02 K. The critical temperature and the critical density for pure methanol were extracted from the saturated data (T _S,ρ_S) near the critical point. For one near-critical isochore (398.92 kg·m⁻³), the measurements were performed in both cooling and heating regimes to estimate the effect of thermal decomposition (chemical reaction) on the heat capacity and phase-transition properties of methanol. The measured values of C _V and saturated densities (T _S,ρ_S) for methanol were compared with values calculated from various multiparametric equations of state (EOS) (IUPAC, Bender-type, polynomial-type, and nonanalytical-type), scaling-type (crossover) EOS, and various correlations. The measured C _V data have been analyzed and interpreted in terms of extended scaling equations for the selected thermodynamic paths (critical isochore and coexistence curve) to accurately calculate the values of the asymptotical critical amplitudes ( and B ₀).     

Equation of State and Thermodynamic Properties of Pure D2O and D2O + H2O Mixtures in and Beyond the Critical Region

A parametric crossover model is adapted to represent the thermodynamic properties of pure D₂O in the extended critical region. The crossover equation of state for D₂O incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of D₂O + H₂O mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure D₂O and for the D₂O + H₂O mixture. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8T _c(x)T1.5T _c(x) and densities 0.35_c(x)1.65_c(x).     

Thermodynamic Properties of Methanol in the Critical and Supercritical Regions

The isochoric heat capacity of pure methanol in the temperature range from 482 to 533 K, at near-critical densities between 274.87 and 331.59 kg· m⁻³, has been measured by using a high-temperature and high-pressure nearly constant volume adiabatic calorimeter. The measurements were performed in the single- and two-phase regions including along the coexistence curve. Uncertainties of the isochoric heat capacity measurements are estimated to be within 2%. The single- and two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from experimental data for each measured isochore. The critical temperature (T_c = 512.78±0.02K) and the critical density (ρ_c = 277.49±2 kg · m⁻³) for pure methanol were derived from the isochoric heat-capacity measurements by using the well-established method of quasi-static thermograms. The results of the C_VVT measurements together with recent new experimental PVT data for pure methanol were used to develop a thermodynamically self-consistent Helmholtz free-energy parametric crossover model, CREOS97-04. The accuracy of the crossover model was confirmed by a comprehensive comparison with available experimental data for pure methanol and values calculated with various multiparameter equations of state and correlations. In the critical and supercritical regions at 0.98T_c≤ T ≤ 1.5T_c and in the density range 0.35ρ_c ≤ ρ leq 1.65 ρ_c, CREOS97-04 represents all available experimental thermodynamic data for pure methanol to within their experimental uncertainties.     

Decay rate of critical fluctuations in steam and in dilute steam-NaCl mixtures

The decay rate of critical fluctuations in steam and in a steam-NaCl mixture has been investigated experimentally with the aid of photon correlation spectroscopy. For pure steam, the measurements have been performed along seven isochores [(¦– _c¦)/_c<0.09] as a function of the temperatureT for (T–T_t)<1 K. The results have been compared with the values predicted by the renormalization-group theory written as a modification of the classical mode coupling theory. The agreement between experiment and theory is satisfactory along the critical isochore, but larger deviations are noted for _c when approching the transition temperatureT _t. The decay rate of a 0.1% (molar) dilute mixture of NaCl in H₂O has been measured along some near-critical isochores as a function of temperature. Its behavior, which is very different from that observed for pure steam, is dicussed.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

An experimental study of the thermodynamic properties of 1,1-difluoroethane

Experimental vapor pressures andP--T data of an important alternative refrigerant, 1, 1-difluoroethane (HFC-152a), have been measured by means of a constant-volume method coupled with expansion procedures. SixtyP--T data were measured along eight isochores in a range of temperaturesT from 330 to 440 K, at pressuresP from 1.6 to 9.3 MPa, and at densities from 51 to 811 kg·m^–3. Forty-six vapor pressures were also measured at temperatures from 320 K to the critical temperature. The uncertainties of the temperature and pressure measurements are within ±7mK and ±2kPa, respectively, while the uncertainty of the density values is within ±0.1%. The purity of the sample used is 99.9 wt%. On the basis of the measurements along each isochore, five saturation points were determined and the critical pressure was determined by correlating the vapor-pressure measurements. The second and third virial coefficients for temperatures from 360 to 440 K have also been determined.     

Thermal diffusivity of fluids in a broad region around the critical point

Dynamic light scattering is a suitable method for the investigation of transport properties such as the thermal diffusivity of optically transparent fluids. The main advantages of the method are its quickness, the fact of the thermodynamic state of equilibrium of the sample (gradients are not required), and the relatively simple evaluation of data without the necessity of calibration. However, an insufficient production of intensity of scattered light may be a limiting effect. For that reason the vicinity of the gas-liquid critical point represents the classical range of application. In this paper, it is shown that by means of an appropriate choice of experimental apparatus, measurements are also feasible in an extended range of states. Broad regions around critical points of three pure fluids (sulfur hexafluoride, SF₆; ethane, C₂H₆; nitrous oxide, N₂O) over temperature ranges ¦T-T _c¦ of 0.02 to 50 K and density ranges (/_c) of 0.2 to 2 were investigated. In this region the thermal diffusivity shows great variations with temperature and density and cannot be described by means of ideal-gas behavior or relations for liquids. The measurements were carried out along the coexistence curve for both phases, along the critical isochore and along some isotherms with TT _c. The measured or calculated density, pressure, and thermal diffusivity data as well as some correlations are presented.     

Precise measurements of critical parameters of sulfur hexafluoride by laser interferometry

A laser interferometry has been applied, in the present study, for determination of the critical temperature and critical exponents of sulfur hexafluoride (SF₆). By means of laser holographic technique by real-time method, a series of Fraunhofer diffraction patterns due to the density fluctuation of the sample fluid in the very vicinity of the critical point has been successively photographed and analyzed. A dual-thermostat system which was designed and constructed for the present purpose has made the sample temperature constant within 15 K for several days. We have obtained 107 data for ( _L– _v)/ _c along the vapor-liquid coexistence curve in the reduced temperature range 10^–6¦T ^*¦7×10^–5 and additional 34 data for the isothermal compressibility in the single phase region. By analyzing these measurements with the aid of the simple power law, the critical temperature and the critical exponents of SF₆ have been determined as T _c=318.708±0.001 K, =0.350±0.004, and =1.24±0.02, respectively.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Isochoric p–ρ–T and Heat Capacity Cv Measurements for Ternary Refrigerant Mixtures Containing Difluoromethane (R32), Pentafluoroethane (R125), and 1,1,1,2-Tetrafluoroethane (R134a) from 200 to 400 K at Pressures to 35 MPa

The p––T relationships and constant volume heat capacity C _v were measured for ternary refrigerant mixtures by isochoric methods with gravimetric determinations of the amount of substance. Temperatures ranged from 200 to 400 K for p––T and from 203 to 345 K for C _v, while for both data types pressures extended to 35 MPa. Measurements of p––T were carried out on compressed gas and liquid samples with the following mole fraction compositions: 0.3337 R32+0.3333 R125+0.3330 R134a and 0.3808 R32+0.1798 R125+0.4394 R134a. Measurements of C _v were carried out on liquid samples for the same two compositions. Published p––T data are in good agreement with this study. For the p––T apparatus, the uncertainty is 0.03 K for temperature and is 0.01% for pressure at p>3 MPa and 0.05% at p<3 MPa. The principal source of uncertainty is the cell volume (28.5 cm³), with a standard uncertainty of 0.003 cm³. When all components of experimental uncertainty are considered, the expanded relative uncertainty (with a coverage factor k=2 and, thus, a two-standard deviation estimate) of the density measurements is estimated to be 0.05%. For the C _v calorimeter, the uncertainty of the temperature rise is 0.002 K and for the change-of-volume work it is 0.2%; the latter is the principal source of uncertainty. When all components of experimental uncertainty are considered, the expanded relative uncertainty of the heat capacity measurements is estimated to be 0.7%.     

Magnetic hysteresis of the zero-resistance critical temperature of high-Tc granular superconductors

We have found a notorious hysteretic behavior in the dependence of the zero-resistance critical temperature obtained through resistivity () versus temperature (T) measurements with applied field (H _e ) in High-T _c granular superconductors. This behavior is explained semi-quantitatively based on the analogy between the present observation and a similar hysteresis found in the field dependence of the transport critical current in these materials.     

Viscosity of steam in the critical region

The shear viscosity of fluids exhibits an anomalous enhancement in the close vicinity of the critical point. A detailed experimental study of the viscosity of steam in the critical region has been reported by Rivkin and collaborators. A reanalysis of the experimental data indicates that the behavior of the viscosity of steam near the critical point is similar to that observed for other fluids near the critical point. An interpolating equation for the viscosity of water and steam is presented that incorporates the critical viscosity enhancement.Nomenclature a critical region equation of state parameter - a _k coefficients in equation for ₀ - a _ij coefficients in equation for ¯ - b critical region equation of state parameter - c _p specific heat at constant pressure - c _v specific heat at constant volume - k critical region equation of state parameter - k _B Boltzmann constant - P pressure - P _r 22.115 MPa - P ^* P/P _r - P _c critical pressure - P _i coefficients in critical region equation of state - R~P (P-P _c )/P _c - q parameter in equation for critical viscosity enhancement - r parametric variable in critical region equation of state - T temperature in K (IPTS-48) - T _r 647.27 K - T ^* T/T _r - T _c critical temperature - T (T–T _c )/T _c - V volume - critical exponent of specific heat - critical exponent of coexistence curve - critical exponent of compressibility - critical exponent of chemical potential at T=T _c - dynamic viscosity - ₀ lim ₀ - ¯ normal viscosity - critical viscosity enhancement - ¯ thermal conductivity - normal thermal conductivity - critical thermal conductivity enhancement - parametric variable in critical region equation of state - correlation length - ₀ correlation length amplitude above T _c at = _c - critical exponent of correlation length - density - _r 317.763 kg/m³ - ^* / _r - _c critical density - (– _c )/ _c - _p estimated error of pressure - _T estimated error of temperature - estimated error of viscosity - exponent of critical viscosity enhancement - _t (/P) _T symmetrized compressibility - _T ^* _T P _r / _r ² - _{t t} P _c / _c ²     

Fast adiabatic heating and temperature relaxation in near-critical fluids under zero gravity

Heat transport in supercritical CO₂ is studied under microgravity conditions. A large temperature and density region around the critical point is explored (CO₂ cells were filled at critical density= _c and off-critical densities= _c±0.18 _c). Local heating is obtained by using a small thermistor located in the bulk fluid. Through interferometric observations, a new mechanism of thermalization has been evidenced. Thermal expansion of a warm diffusing boundary layer around the heating thermistor is responsible for rapid adiabatic heating of the bulk fluid through the emission of pressure waves at the border. The scaled thickness of the thermal boundary layer follows a power law. When the heat flow stops, the bulk adiabatic heating instantaneously vanishes and the temperature relaxation inside the thermal boundary layer follows locally a diffusive process.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Molar Heat Capacity Cv, Vapor Pressure, and (p, ρ, T) Measurements from 92 to 350 K at Pressures to 35 MPa and a New Equation of State for Chlorotrifluoromethane (R13)

Measurements of the molar heat capacity at constant volume C _v for chlorotrifluoromethane (R13) were conducted using an adiabatic method. Temperatures ranged from 95 to 338 K, and pressures were as high as 35 MPa. Measurements of vapor pressure were made using a static technique from 250 to 302 K. Measurements of (p, , T) properties were conducted using an isochoric method; comprehensive measurements were conducted at 15 densities which varied from dilute vapor to highly compressed liquid, at temperatures from 92 to 350 K. The R13 samples were obtained from the same sample bottle whose mole fraction purity was measured at 0.9995. A test equation of state including ancillary equations was derived using the new vapor pressures and (p, , T) data in addition to similar published data. The equation of state is a modified Benedict–Webb–Rubin type with 32 adjustable coefficients. Acceptable agreement of C _v predictions with measurements was found. Published C _v(, T) data suitable for direct comparison with this study do not exist. The uncertainty of the C _v values is estimated to be less than 2.0% for vapor and 0.5% for liquid. The uncertainty of the vapor pressures is 1 kPa, and that of the density measurements is 0.1%.     

A generalized scaled equation of state for n-alkanes (methane to n-nonane) in the critical region

A generalized scaled equation of state has been developed to calculate thermodynamic properties of n-alkanes from methane (CH₄) to n-nonane (C₉H₂₀) in the critical region. The equation is valid in the reduced density range 0.7 _c1.3 at T=T _c and up to 1.2T _c at = _c.     

Crossover equation of state of normal hexane in the critical region

The coefficients of the basic crossover equation of state of n-hexane are determined in the critical region from experimental P, , T and C_p, P, T data. In the reduced density and temperature ranges 0.35_c1.65 and 0.982T/T_c1.23 the root mean square errors of the calculated pressure, isobaric heat capacity, and isochoric heat capacity were 0.115%, 4.87%, and 3.04%, respectively.Academician M. D. Millionshchikov Petroleum Institute, Grozny, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 2, pp.185–191, August, 1993.