Two-phase Isochoric Heat Capacities Research Articles

Isochoric heat capacity, phase transition and derived key thermodynamic properties of methyl decanoate

In the present work single – and two–phase isochoric heat capacity (CV) and liquids-gas phase transition temperature (TS) and density (ρS) of methyl decanoate as component of biodiesel derived from coconut oil or babassu oil have been studied. The 15 liquid and vapor isochores between (152 and 834) kg·m−3 at temperatures from (300 to 463) K and at pressures up to 16 MPa were determined using high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. For each experimental isochores the measurements were conducted in the two-phase region in the immediate vicinity of the phase-transition temperatures (TS) to precisely determine the phase boundary density, one-phase and two-phase isochoric heat capacities (ρS,CV1, and CV2) using isochoric heat -capacity discontinuity behavior technique. For ten liquid isochores, the TSwas experimentally determined usingCVdiscontinuity method (irregular behaviour of CV). For vapor (152.09 and 204.55) kg·m−3 and near-critical (235.13 and 300.83) kg·m−3 isochores we have never reached isochoric heat-capacity discontinuity temperatures TSdue to thermal decomposition of the methyl decanoate at high temperatures (above 473 K). The measured CV2 as a function of specific volume (V) along the various isotherms (below 473 K) were used to accurately estimate the values of the second temperature derivatives of chemical potential and vapour-pressure using theoretically based Yang-Yang relation. The contributions of the vapour-pressure and the chemical potential to the measured total two-phase CV2 of methyl decanoate were estimated. The measured CV2ρS, and TS were used for determination many key thermodynamic properties of methyl decanoate along the saturation curve as well as the critical property data (TC=669.5 ± 5 K andρC = 287 ± 5 kg·m−3).

Thermodynamic and Transport Properties of Supercritical Fluids: Review of Thermodynamic Properties (Part 1)

This review presents the results of a detailed analysis of the role of isochoric heat capacity as a key thermodynamic property of matter in the investigation of critical and supercritical phenomena. A brief historical background is given on the role and contribution of Russian scientific schools to the experimental investigation of the isochoric heat capacity in the critical region in the development of the nonclassical (scaling) theory of critical phenomena, which drastically changed the understanding of the physical nature of critical and supercritical phenomena. The experimental behavior of the isochoric heat capacity and other thermodynamic properties of fluids in the critical and supercritical regions related to it is investigated in detail. The role of new experimental studies of two-phase isochoric heat capacity near the critical point in the development of a “complete” scaling theory is discussed. This theory allows us to understand the physical nature of the asymmetry of the liquid–gas coexistence curve near the critical point and to estimate the contribution of the chemical potential to the divergence of the two-phase isochoric heat capacity at the critical point. The review also focuses on supercritical phase transitions and the role of isochoric heat capacity in determining the Widom line, which separates the liquid-like and gas-like regions in supercritical states; i.e., it defines the boundaries of the coexistence of liquid-like and gas-like phases in supercritical fluids.

Isochoric heat capacity of near- and supercritical benzene and derived thermodynamic properties

As part of a continuing study of the critical and supercritical phenomena in fluids and fluid mixtures, one- (CV1) and two-phase (CV2) isochoric heat capacities, densities (ρS) and phase-transition temperatures (TS) of benzene were measured in the critical and supercritical regions. Measurements were made in the immediate vicinity of the liquid-gas phase transition and the critical points in order to accurately determine of the phase transition properties (TS,ρS,CV1, and CV2). The measurements cover the temperature range from (347 to 616) K for 10 liquid and vapor isochores between (265 and 653) kg·m−3 at pressure up to 7.5 MPa. The measurements were performed using a high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter. The standard uncertainties of the density, temperature, and isochoric heat capacity, CV, measurements are estimated to be 0.1%, 0.02 K, and 1.5%, respectively. The measured one- (CV1) and two-phase (CV2) isochoric heat capacities along the critical isochore and the saturated liquid (ρS') and vapor (ρS") densities near the critical point were used to accurately estimate the theoretically meaningful asymptotic critical amplitudes (A0±and B0) and related amplitudes for other properties (Γ0+, D0, ξ0), and their universal relations, A0+/A0−, A0+Γ0+B02, αA0+Γ0+B0−2, D0Γ0+B0δ−1, ξ0αA0+vC1/3. Saturated liquid and vapor densities (ρS′,ρS″) together with measured two-phase CV2 data were used to estimate the values of asymmetric parameters a3 (complete scaling parameter) and b2 of the coexistence curve singular diameter. Experimentally determined asymptotical critical amplitudes (A0±and B0 fluid-specific parameters) were used to check and confirm the predictive capability of the universal correlation in terms of their dependence on the acentric factor ω based on the generalized corresponding states principle. The measured values of two-phase CV2 as a function of the specific volume V along various isotherms were used to calculate second temperature derivatives of vapor pressure d2PSdT2 and chemical potential d2μdT2 and to estimate the value of Yang-Yang anomaly strength parameter Rμ = − 0.683 for benzene. The contributions of the vapor pressure, CVP=VCTd2PSdT2, and the chemical potential, CVμ=−Td2μdT2, to the measured total two-phase CV2 were derived from the measurements.

Тhermodynamic properties of isobutane/mineral compressor oil and isobutane/mineral compressor oil/fullerenes C60 solutions

In present study a new experimental data for the saturated liquid density and saturated vapor pressure along the boiling line for the solutions of the ”natural” refrigerant isobutane (R600a) with mineral compressor oil and solutions of R600a/compressor oil/fullerenes C60 is presented. Moreover, a new experimental data on the specific isobaric heat capacity, enthalpy and entropy along the boiling line for the R600a/compressor oil solutions is reported. Experimental data of the two-phase isochoric heat capacity was obtained for different compressor oil fraction in the refrigerant in the temperature range from 260 to 330 K. Obtained information was used to calculate the caloric properties of the R600a/compressor oil solutions. In addition, an influence of fullerene C60 on the specific isobaric heat capacity of mineral oil was examined. The measurements of the heat capacity for the R600a/compressor oil solutions, pure compressor oil and compressor oil containing fullerenes C60 were performed using an experimental setup that implements a direct heating method in adiabatic calorimeter. In addition, the heat capacity of oil and oil containing fullerenes C60 have been measured using differential scanning calorimetry. Finally, the heat capacity increase for the compressor oil with the additives of 0.0020 kg kg−1 of fullerenes C60 was observed.

One- and two-phase isochoric heat capacities and saturated densities of 2-propanol in the critical and supercritical regions

One- (CV1) and two-phase (CV2) liquid + vapor equilibrium isochoric heat capacities, densities (ρS), and phase-transition temperatures (TS) of 2-propanol were measured in the critical region. Measurements were made in the immediate vicinity of the liquid–gas phase transition and critical point in order to accurately determine the locus of phase-transition properties (TS, ρS, CV1, and CV2). Additional measurements were made over an extended temperature range from (317 to 525) K for 9 liquid and 3 vapor isochores between (234 and 697) kg⋅m−3 at pressure up to 6.5 MPa. The measurements were performed using a high-temperature, high-pressure, nearly constant-volume adiabatic piezo-calorimeter. The standard uncertainty of the density, temperature, and isochoric heat capacity (CV) measurements is estimated to be 0.1%, 0.02 K, and 1.5%, respectively. The measured one- (CV1) and two-phase (CV2) isochoric heat capacities along the critical isochore and the saturated liquid (ρS') and vapor (ρS'') densities near the critical point were used to derive theoretically meaningful asymptotic critical amplitudes (A0± and B0) and related amplitudes for other properties (Γ0+,D0,ξ0) and their universal relations, A0+/A0-, A0+Γ0+B02, αA0+Γ0+B0-2, D0Γ0+B0δ-1, ξ0αA0+vC1/3 and the asymmetric parameters a3 and b2 of the coexistence curve singular diameter. Experimental two-phase heat capacities CV2 as a function of specific volume V , along various isotherms, were used to calculate second temperature derivatives of vapor pressure d2PSdT2 and chemical potential d2μdT2 and to estimate the value of the Yang-Yang anomaly strength parameter Rμ for 2-propanol. The relative contributions of the vapor pressure, CVP=VCTd2PSdT2, and the chemical potential, CVμ=-Td2μdT2, to the measured total two-phase CV2 were estimated.

Thermodynamic Properties at Saturation Derived from Experimental Two-Phase Isochoric Heat Capacity of 1-Hexyl-3-methylimidazolium Bis[(trifluoromethyl)sulfonyl]imide.

New measurements are reported for the isochoric heat capacity of the ionic liquid substance 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([C6mim][NTf2]). These measurements extend the ranges of our earlier study [N.G. Polikhronidi et al., Phys. Chem. Liq. 52, 657 (2014)] by 5 % of the compressed liquid density and by 75 kelvins. An adiabatic calorimeter was used to measure one-phase (CV1) liquid and two-phase (CV2) liquid + vapor isochoric heat capacities, densities (ρS ), and phase-transition temperatures (TS ) of the ionic liquid (IL) substance. The combined expanded uncertainty of the density ρ and isochoric heat capacity CV measurements at the 95 % confidence level with a coverage factor of k = 2 is estimated to be 0.15 % and 3 %, respectively. Measurements are concentrated in the immediate vicinity of the liquid + vapor phase transition curve, in order to closely observe phase transitions. The present measurements and those of our earlier study are analyzed together, and are presented in terms of thermodynamic properties (TS, ρS, CV1 and CV2) evaluated at saturation and in terms of key derived thermodynamic properties Cp, CS, [Formula: see text], and [Formula: see text] on the liquid + vapor phase transition curve. A thermodynamic relation by Yang and Yang is used to confirm the internal consistency of measured two-phase heat capacities CV2, which are observed to fall perfectly on a line as a function of specific volume at a constant temperature. The observed linear behavior is exploited to evaluate contributions to the quantity CV2 = f(V,T) from chemical potential [Formula: see text] and from vapor pressure [Formula: see text]. The physical nature and specific details of the temperature and specific volume dependence of the two-phase isochoric heat capacity and some features of the other derived thermodynamic properties of IL at liquid saturation curve are considered in detail.

Internal pressure of liquids from the calorimetric measurements near the critical point

A new relation between the internal pressure and isochoric heat capacity jump of liquids along the coexistence curve near the critical point was found. Our previously reported one- and two-phase isochoric heat capacities and specific volumes at saturation were used to calculate internal pressure of molecular liquids (water, carbon dioxide, alcohols, n-alkanes, DEE, etc.).The internal pressure derived from the calorimetric measurements was compared with the values calculated from the reference (NIST, REFPROP) and crossover equations of state. Locus of the isothermal and isochoric internal pressure maxima and minima was studied using calorimetric data and the reference and crossover equations of state near the critical point. The maximum of the internal pressure of light and heavy water around the temperature of 460K along the liquid saturation curve was found. We also found very simple relation between the internal pressure, ΔPintsat, and isochoric heat capacity, ΔCV, jumps near the critical point.

Yang–Yang critical anomaly strength parameter from the direct two-phase isochoric heat capacity measurements near the critical point

New technique of the Yang–Yang critical anomaly strength function, Rμ(T), determination from direct two-phase liquid (CV2′) and vapor (CV2″) isochoric heat capacity and liquid (V′) and vapor (V″) specific volumes measurements at the saturation have been developed. Our measured two-phase (liquid and vapor) isochoric heat capacities (CV2″,CV2′) and liquid and vapor specific volumes (V″,V′) data at saturation near the critical point have been used to accurately determine the Yang–Yang anomaly strength parameter, Rμ(T = Tc) = Rμ0, for various molecular liquids. The derived values of the Yang–Yang critical anomaly strength function show trend to negative infinity near the critical point as predicted by the theory (Cerdeiriña et al., 2015) based on compressible cell gas (CCG) model that obey complete scaling with pressure mixing. The physical nature and details of the temperature and the specific volume dependences of the CV2 and correct estimations of the contributions of various terms (chemical potential CVμ and vapor-pressure CVP) to the measured total two-phase heat capacity were discussed in terms of the Yang–Yang anomaly parameter.

Experimental study of the isochoric heat capacity and liquid–gas coexistence-curve properties of sec-butanol in the near- and supercritical regions

One- and two-phase isochoric heat capacities (CV) and saturated liquid and vapor properties (TS,ρ′S,ρ″S) of sec-butanol in the wide temperature and density ranges including near- and supercritical conditions have been measured with a high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. The measurements were made in the temperature range from 307K to 551K for 22 liquid and vapor isochores from 76.44kgm−3 to 794.06kgm−3. The isochoric heat capacity jump (quasi-static thermograms) technique have been used to accurately measure of the phase transition parameters (TS, ρS) near the critical point. The total experimental uncertainty of density (ρ), temperature (T), and isochoric heat capacity (CV) measurements at the 95% confidence level with a coverage factor of k=2 were estimated to be 0.06%, 15mK, and 2–3%, respectively. The critical temperature (TC=535.95±0.02K) and the critical density (ρC=276.40±2kgm−3) for sec-butanol were determined from the measured saturated properties (CVS,TS, ρS) near the critical point. The values of the asymptotical critical amplitude of the two-phase CV along the critical isochore A¯0−=37.95) and saturated density (B0=1.7441) near the critical point have been calculate using the measured isochoric heat capacity data. The measured two-phase liquid and vapor isochoric heat capacities at saturation and saturation liquid and vapor specific volumes (V′, V″) were used to calculate the values of second temperature derivatives of the vapor pressure and chemical potential near the critical point. The values of asymmetry parameters a3=−0.3664 and b2=−0.2527 of the coexistence curve diameter for sec-butanol were determined from the measured heat capacity and saturated density data near the critical point. A new technique of the Yang-Yang anomaly strength parameter (Rμ) determination from the direct simultaneously two-phase isochoric heat capacity (C″V2,C′V2) and specific volumes (V″, V′) measurements at saturation have been proposed. The value of Yang-Yang anomaly strength parameter (Rμ=−0.59) for sec-butanol has been determined using the new technique.

Experimental study of the isochoric heat capacity and coexistence-curve singular diameter of sec-butanol near the critical point and Yang-Yang anomaly strength

One- and two-phase isochoric heat capacities () and saturated liquid and vapour densities (, and ) of sec-butanol near the critical point have been measured with a high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. The measurements were made in the temperature range from 307 K to 551 K for 22 liquid and vapour isochores from 76.44 to 794.06 kg m−3. The isochoric heat capacity jump (quasi-static thermograms supplemented by the sensor of adiabatic control) technique have been used to accurately measure of the phase transition parameters () near the critical point. The total experimental uncertainty of density (), temperature () and isochoric heat capacity () measurements were estimated to be 0.06%, 15 mK and 2–3%, respectively. The critical temperature ( = 535.95 ± 0.02 K) and the critical density ( = 276.40 ± 2 kg m−3) for sec-butanol were determined from the measured saturated properties (, ) near the critical point. The measured and saturated density () data near the critical point have been analysed and interpreted in terms of extended scaling theory for the selected thermodynamic paths (critical isochore and coexistence curve) to accurately calculate the values of the asymptotical critical amplitudes of heat capacity () and coexistence curve (). The measured thermodynamic properties (, ) of sec-butanol near the critical point were also interpreted in terms of the ‘complete scaling’ theory of critical phenomena and the theory of logarithmic singularity of . In particular, the contributions of the ‘incomplete’ () and ‘complete’ () scaling terms on the coexistence-curve singular diameter were estimated. We determined the values of the asymmetry parameters and of the ‘complete’ scaling theory of coexistence curve singular diameter. The strength of the Yang-Yang anomaly R μ for sec-butanol was estimated using asymmetry parameters and the contribution of the second temperature derivative of vapour-pressure and chemical potential in the singularity of two-phase isochoric heat capacity, , at the critical point.

Experimental study of the PVT and CVVT properties of n-butanol in the critical region

The PVT and CVVT properties of n-butanol have been measured in the near- and supercritical regions. Measurements of PVT relation for n-butanol was made along 6 liquid and vapor near-critical isochores in the density range from (113.76 to 470.00)kgm−3 and at temperatures from (497 to 616)K and at pressures up to 10MPa. The measurements were performed with a constant-volume piezometer technique. Caloric (CVVT) properties of n-butanol were measured along the critical isochore and coexistence curve (liquid and vapor branches) in the one- and two-phase regions. The temperatures, densities, and pressures at the liquid-gas boundary curve (PS,TS,ρS) and the critical parameters (TC=563.05±0.2 K, PC=4.405±0.01 MPa, ρC=270.0±2 kg m−3) for n-butanol were obtained using the isochoric (P–T) break-point and quasi-static thermograms (CV jumps) techniques. The expanded uncertainty of the density, pressure, and temperature measurements at the 95% confidence level with a coverage factor of k=2 is estimated to be 0.10% (at high densities) to 0.12% (at low densities), 0.0005–0.005MPa, and 15mK, respectively. The total experimental uncertainty of isochoric heat capacity (CV) measurements were estimated to be 2–3%. The measured CV, PVT, saturated density (ρS,TS) and vapor-pressure (PS,TS) data near the critical point have been analyzed and interpreted in terms of extended scaling equations for the selected thermodynamic paths (critical isochore, critical isotherm, and coexistence curve) to accurately calculate the values of the asymptotic critical amplitudes (A0±, Γ0±, D0, B0) and to check their universal ratios. The measured saturated density data of n-butanol near the critical point were also interpreted in terms of the “complete scaling” theory of critical phenomena. In particularly, the contributions of the “incomplete”, B2t1−α, and “complete scaling”, B4t2β, terms on the coexistence-curve singular diameter were estimated. The values of the asymmetry parameters a3 and b2 of the coexistence curve singular diameter have been calculated. The strength of the Yang-Yang anomaly Rμ for n-butanol was estimated using asymmetry parameters a3 and the contributions of the second temperature derivatives of vapor-pressure, (d2PS/dT2), and chemical potential, (d2μ/dT2), in the singularity of two-phase isochoric heat capacity, CV2. The measured values of saturated one- (CV1′, CV1″) and two-phase (CV2′, CV2″) liquid and vapor isochoric heat capacities and saturated density data (ρS,TS) together with measured vapor-pressure (PS,TS) data were used to calculate other derived thermodynamic properties, such as KT, ΔHvap, CP, CS, W, (∂P/∂T)V′, (∂V/∂T)P′, (d2PS/dT2), and (d2μ/dT2) of n-butanol at saturation near the critical point. The results were compared with the direct measurements of these properties.

Experimental study of the isochoric heat capacity of isobutanol in the critical and supercritical regions

The one- and two-phase isochoric heat capacities (CV) of isobutanol in the critical and supercritical regions have been measured with a high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. The measurements were made in the temperature range from 324K to 575K for 23 isochores (16 liquid and 7 vapor) from 73.2kgm−3 to 772.2kgm−3. The isochoric heat capacity jump (quasi-static thermograms supplemented by the sensor of adiabatic control) technique have been used to accurately measure of the phase transition parameters (TS, ρS). The total experimental uncertainty of density (ρ), temperature (T), and isochoric heat capacity (CV) were estimated to be 0.06%, 15mK, and 2–3%, respectively. The critical temperature (TC=547.65±0.2K) and the critical density (ρC=272.95±2kgm−3) for isobutanol were determined from the measured saturated properties (CVS, TS, ρS) near the critical point. The measured CV and saturated density (TS, ρS) data near the critical point have been analyzed and interpreted in terms of extended scaling type equations for the selected thermodynamic paths (critical isochore and coexistence curve) to accurately calculate the values of the asymptotical critical amplitudes of heat capacity (A0±) and coexistence curve (B0). The experimentally derived value of the critical amplitude ratio A0+/A0−=0.522 is in good agreement with the value predicted by various scaling theories. The measured thermodynamic properties (CV, TS, ρS) of isobutanol near the critical point were also interpreted in the terms of “complete scaling” theory of critical phenomena. In particularly, the contributions of the “complete” and “incomplete” scaling terms on the coexistence-curve singular diameter were estimated. We determined the values of the asymmetry parameters a3 and b2 of the coexistence curve singular diameter. The strength of the Yang–Yang anomaly Rμ for isobutanol was estimated using asymmetry parameters a3 and the contribution of the second temperature derivative of vapor-pressure and chemical potential in the singularity of two-phase CV2. The measured values of saturated one- and two-phase liquid and vapor isochoric heat capacities (C′V1,C″V1,C′V2,C″V2) and saturated thermal (ρS, TS) properties together with vapor-pressure (PS, TS) data were used to calculate other derived thermodynamic properties such as (KT, ΔHvap, CP, CS, W, (∂P/∂T)′V, (∂V/∂T)′P, (d2PS/dT2), and (d2μ/dT2) of isobutanol at saturation near the critical point.

Experimental study of the isochoric heat capacity of tert-butanol in the critical and supercritical regions

The one- and two-phase isochoric heat capacities ( C V ) of tert-butanol in the critical and supercritical regions have been measured with a high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. The measurements were made in the temperature range from 296 K to 524 K for 21 liquid and 7 vapor isochores from 70.56 kg m −3 to 763.98 kg m −3. The isochoric heat capacity jump (quasi-static thermograms supplemented by the sensor of adiabatic control) technique was used to accurately measure of the phase transition parameters ( ρ S , T S ) in the critical region. The total experimental uncertainty of density ( ρ S ), temperature ( T S ), and isochoric heat capacity ( C V ) measurements were estimated to be 0.02%, 15 mK, and 2–3%, respectively. The critical temperature ( T C = 506.35 ± 0.2 K) and the critical density ( ρ C = 268.1 ± 2 kg m −3) for tret-butanol were extracted from the measured saturated properties ( C VS , T S , ρ S ) near the critical point. The measured C V and saturated density ( ρ S , T S ) data near the critical point 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 amplitude ( A 0 ± and B 0). The experimentally derived value of the critical amplitude ratio A 0 + / A 0 − = 0.525 is in good agreement with the value predicted by various scaling theories. The measured thermodynamic properties of tert-butanol near the critical point were also interpreted in terms of the “complete scaling” theory of critical phenomena. In particularly, the contributions of the “complete” and “incomplete scaling” terms on the coexistence-curve singular diameter were estimated. The Yang–Yang anomaly of strength parameter R μ = −0.036 for tert-butanol was estimated using derived second temperature derivatives of pressure and chemical potential. The measured values of saturated one- ( C ′ V 1 and C ″ V 1 ) and two-phase ( C ′ V 2 and C ″ V 2 ) liquid and vapor isochoric heat capacities and saturated thermal properties ( ρ S , T S ) together with reported vapor–pressure ( P S , T S ) data were used to calculate other derived thermodynamic properties such as K T , Δ H vap, C P , C S , W, ( ∂ P / ∂ T ) ′ V , ( ∂ V / ∂ T ) ′ P , ( d 2 P S / dT 2), and ( d 2 μ/ dT 2) of tert-butanol at saturation near the critical point.

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 (ρc = 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 V VT 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 0.98Tc≤ T ≤ 1.5Tc and in the density range 0.35ρc ≤ ρ leq 1.65 ρc, CREOS97-04 represents all available experimental thermodynamic data for pure methanol to within their experimental uncertainties.

Isochoric heat capacity measurements for a CO 2 + n-decane mixture in the near-critical and supercritical regions

The isochoric heat capacity of a (0.7367 mole fraction) CO 2 + (0.2633 mole fraction) n-decane mixture was measured in a range of temperatures from 362 to 577 K, at nine near-critical liquid and vapor densities between 298 and 521 kg m −3 by using a high-temperature, high-pressure, nearly constant volume adiabatic calorimeter. The measurements were performed in both one- and two-phase regions including the vapor + liquid coexistence curve. Uncertainties of the heat capacity measurements are estimated to be 2% (in this work we use a coverage factor k = 2). The uncertainty in temperature is 10 mK and that for density measurements is 0.15%. The liquid and vapor one- ( C ′ V 1 , C ″ V 1 ) and two-phase ( C ′ V 2 , C ″ V 2 ) isochoric heat capacities, temperatures ( T S) and densities ( ρ S) at saturation were extracted from the experimental data for each filling density. The critical temperature ( T C = 509.71 ± 0.2 K), the critical density ( ρ C = 344.7 ± 5 kg m −3), and the critical pressure ( P C = 15.37 ± 0.5 MPa) for the (0.7367 mole fraction) CO 2 + (0.2633 mole fraction) n-decane mixture were extracted from isochoric heat capacity measurements using the well-established method of quasi-static thermograms. The observed isochoric heat capacity along the critical isochore of the CO 2 + n-decane mixture exhibits a renormalization of the critical behavior of C V unlike that of the pure components. 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 isochoric heat capacity. The Krichevskii parameter for this mixture was calculated by using the critical loci for the mixture and vapor pressure data for the pure solvent (CO 2), and the results are compared with published values.

Resolving the Yang-Yang Dilemma in3He Near the Critical Point

A challenging problem is to experimentally resolve the Yang-Yang dilemma for fluids-whether the critical singularity of the isochoric heat capacity is shared between the second temperature derivatives of pressure and chemical potentials. In the lattice-gas model, which serves as a well-established guidance to study fluid criticality, the divergence of the second derivative of pressure is solely responsible for the heat capacity anomaly. If it is proven that the heat capacity singularity is shared between the pressure and chemical potential derivatives, a revision of the conventional scaling theory for fluids based on the analogy between fluids and lattice-gas model will be required. Thus far, experiments on real fluids have been inconclusive, in particular, because of possible impurity effects and the intrinsic vapor-liquid asymmetry. A study of the 3He isotope gives a unique opportunity to resolve the Yang-Yang dilemma. In 3He all other impurities except 4He are frozen out. The almost perfect purity of the available 3He samples (typically less than 1 ppm of 4He in 3He) enables the elimination or quantitative study of impurity effects. Also the well-known symmetry of the 3He coexistence curve implies an absence of confluent singularities caused by liquid-gas asymmetry. In this paper we reanalyze early experimental data of near-critical 3He and show that they are internally not completely consistent. While the second derivative of chemical potential obtained from the density dependence of the two-phase isochoric heat capacity does not show a noticeable anomaly, the analysis of the same property obtained by combining the PVT and heat capacity implies the existence of the Yang-Yang anomaly. An unambiguous test of the Yang-Yang dilemma will require more accurate heat-capacity measurements closer to the critical point. To thoroughly distinguish between these alternatives one may ultimately require a microgravity experiment that will allow measurements very close to the critical point.

Vapor-pressure for the pure fluids from calorimetric measurements near the critical point

We report the values of second temperature derivatives of the vapor-pressure curve (d 2 P S/d T 2) and chemical potential (d 2 μ/d T 2) for pure fluids derived from precise two-phase isochoric heat capacity measurements over a wide temperature range including the critical region. The values of (d 2 P S/d T 2) derived from C V 2 measurements were compared with the values calculated from direct differentiation of the vapor-pressure equation from the literature. The derived (d 2 P S/d T 2) data has been used to develop a scaling-type vapor-pressure equation in the critical region. A description of the vapor-pressure calculation procedure from C V 2 measurements is given. The values of the critical pressure P C and slope of the vapor-pressure curve (d P S/d T) C at the critical point were calculated by using calorimetric measurements. The asymptotic behavior of the second temperature derivatives of the vapor-pressure curve (d 2 P S/d T 2) and chemical potential (d 2 μ/d T 2) near the critical point are discussed. The strength of the Yang–Yang anomaly, R μ , defined by Fisher as R μ = A μ /( A μ + A P ), where A μ and A P are the amplitudes of the singularity of − T(d 2 μ/d T 2)≈ A μ t − α and TV C(d 2 P S/d T 2)≈ A P t − α was estimated from derived results.

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 kg⋅m−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 kg⋅m−3) in both the one- and two-phase regions. The result for the phase-transition temperature (the critical temperature, TC, this work=647.104±0.003 K) agreed, within experimental uncertainty, with the critical temperature (TC, IAPWS=647.096 K) adopted by IAPWS.

Impurity effects on the two-phase isochoric heat capacity of fluids near the critical point

It has been generally assumed that the asymptotic critical behavior of real fluids can be characterized in terms of the same physical variables as that of the lattice gas. This assumption implies that, below Tc, the second derivative of the pressure with respect to temperature should asymptotically diverge like the isochoric heat capacity CV, while the second derivative of the chemical potential with respect to the temperature should remain finite at the critical point. The validity of this assumption has recently been questioned on the basis of an analysis of experimental two-phase CV data in terms of the so-called Yang–Yang relation. In this paper we show how such an analysis may be affected by the presence of a small amount of impurity as well as by other nonasymptotic deviations from lattice-gas symmetry. When corrections for a small amount of impurity are applied and allowance is made for the leading asymmetric Wegner correction, the experimental CV data are not inconsistent with previous treatments in which the second derivative of the chemical potential exhibits a cusplike singularity with a finite limiting value at the critical temperature.

Isochoric Heat Capacity Measurements for Heavy Water Near the Critical Point

Isochoric heat capacity measurements of D2O are presented as a function of temperature at fixed densities of 319.60, 398.90, 431.09, and 506.95 kg·m−3. The measurements cover a range of temperatures from 551 to 671 K and pressures up to 32 MPa. The coverage includes one- and two-phase states and the coexistence curve near the critical point of D2O. 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 to 3%. Temperatures at saturation TS(ρ) were measured isochorically using a quasi-static thermogram method. The uncertainty of the phase transition temperature measurements is about ±0.02 K. The measured CV data for D2O were compared with values predicted from a parametric crossover equation of state and six-term Landau expansion crossover model. The critical behavior of second temperature derivatives of the vapor pressure and chemical potential were studied using measured two-phase isochoric heat capacities. From measured isochoric heat capacities and saturated densities for heavy water, the values of asymptotic critical amplitudes were estimated. It is shown that the critical parameters (critical temperature and critical density) adopted by IAPWS are consistent with the TS–ρS measurements for D2O near the critical point.