Uncertainty Of Density Measurements Research Articles

Unusual temperature-dependent volume properties of water as a solute in tertiary butylamine at ambient pressure

Densities of water solutions in tert-butylamine (t-BuNH2) with the solute molality from ca. (0.015 to 0.35) mol∙(kg solvent)−1 were measured at six temperatures, from T = (278.15 to 303.15) K, and p ∼ 0.1 MPa. The uncertainty in density measurements did not exceed 0.03 kg m−3. The standard (apparent at infinite dilution) molar volumes and expansibilities of water as a solute in t-BuNH2 were calculated. The origins for the phenomenon of the temperature-induced relative partial molar isobaric compaction of a solute (PMICS) in the system under study were discussed based on Ben-Naim’s concept of the “relative affinity parameter”.

Volume properties of bioactive glycoluril-derivatives of gamma-aminobutyric acid in aqueous solutions between 278.15 and 318.15 K

The densities of aqueous solutions of 4-(3,7-dioxo-2,4,6,8-tetraazabicyclo[3.3.0]oct-2-yl)butanoic acid or glycoluril-butyric acid (GUBA) and its N,N-dimethyl-substituted analogue (DMGUBA), with molality ranged from m = (0.004–0.06) mol·kg−1, were measured at T = (278.15, 288.15, 298.15, 308.15, and 318.15) K and p ≈ 0.1 MPa. The uncertainty in density measurements was estimated to be 3 × 10−5 g cm−3. The apparent and standard (at infinite dilution) molar volumes, V∅,2 and V2°, as we as the standard molar expansibilities, Ep,2°, of GUBA and DMGUBA were calculated. The volume-hydration effects, ΔtrV2°, induced by the conversion of glycoluril (GU) and N,N-dimethylglycoluril (DMGU) into the derivatives of γ-aminobutyric acid (GUBA and DMGUBA) point to squeezing of the structure of the non-methylated “hydration complex” and its loosening at N-methylation of one of glycolurilic rings of the solute under the influence of increasing temperature. It is inferred that the decisive role in the process of hydration of both GUBA and DMGUBA belongs to hydrophilic effects associated with the interactions of proton-donor/acceptor moieties of solution components as well as protons and carboxyl ions formed during the solute partial dissociation under the influence of an aqueous medium (electrostriction effect).

The phenomenon of “partial isobaric compression” of urea as a solute in tertiary butanol: Comparison with a similar effect in the (methanol + urea) system

The densities of urea (U) solutions in tert-butanol (t-BuOH) with the solute molality from (0.01 to 0.33) mol∙(kg solvent)-1 were measured at T = (299.15, 303.15, 308.15, 313.15, 318.15, 323.15, and 328.15) K and p = 0.1 MPa. The uncertainty in density measurements was estimated to be 0.03 kg m−3. The standard (at infinite dilution) molar volumes and expansibilities of U were calculated. Similar to the solution of water in t-BuOH, the phenomenon of negative partial expansibility or partial isobaric compression of a solute (PICS) was discovered for U solvated in the alkanol in question. The local structural aggregates or solvation complexes formed by U in t-BuOH becomes increasingly compact with increasing temperature due to that the solute – solvent affinity prevails over the affinity of the solvent molecules to each other.

Gaseous PVT Property Measurements of cis-1,3,3,3-Tetrafluoropropene

PVT properties in the vapor phase of cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) were measured by a multiple expansion method in the temperature range from 353 to 413 K and at pressures up to 2.7 MPa. Thirty data along four isotherms are obtained in the temperatures between 353 and 413 K. The vapor pressures at the temperatures were also measured by adding a sample of R1234ze(Z) to a sample cell at the vapor–liquid equilibrium conditions. The uncertainties in temperature and pressure measurements are estimated to be within 6 mK and 0.3 kPa, respectively. The expanded uncertainty in density measurement is estimated within no greater than 0.12% (k = 2). The obtained PVT properties and vapor pressures are compared with the existing equation of state.

Density, viscosity and specific heat capacity of diesel blends with rapeseed and soybean oil methyl ester

By 2020, the EU aims to have 10% of the transport fuel of every EU countries come from renewable sources such as biofuels. Fuel suppliers are also required to reduce the greenhouse gas intensity of the EU fuel mix by 6% in comparison to 2010. The thermophysical properties of biofuels are, therefore, required for the efficient design of every step in their production, distribution, and utilization. Despite of these needs, high pressure thermodynamical characterization of biofuels is not still exhaustive. Next generation injection systems work with pressure up to 300 MPa, but available measurements are limited to 200 MPa. Measurements extrapolation generally are not recommended at these pressure because it can hide freezing phenomena here documented at temperature of (20 and 30) °C. In this work, density and viscosity of pure and blended FAME (SME and RME) biofuels have been measured up to 300 MPa. Since the scope of the work is both to investigate cold start conditions found in engines and the thermal behaviour of fuels in tanks of cars, petrol station and dispenser, the temperature interval is limited to (0–60) °C. In particular, it has been observed a partial freezing even for temperature up to 30 °C. Density and viscosity values were obtained by direct experimental measurements, while heat capacities have been calculated using density and speed of sound results previously obtained. At ambient pressure conditions, the uncertainty in density measurements was between 0.005% and 0.01% (k=2) and for viscosity measurements the uncertainty was between 0.2% and 1.3% (k=2). At elevated pressures the uncertainty in density measurements was 0.08% (k=2), while for viscosity and heat capacity it was 2% (k=2).

Influence of polyimide precursor synthesis route and ortho-position functional group on thermally rearranged (TR) polymer properties: Conversion and free volume

Thermal rearrangement of polyimides with ortho-position groups to polybenzoxazoles and related structures has been of recent interest for producing gas separation membranes. This study explores the influence of synthesis route and ortho-position functional group on the thermal rearrangement process and the fractional free volume of thermally rearranged (TR) polymers produced from polyimides derived from 3,3′-dihydroxy-4,4′-diamino-biphenyl and 2,2′-bis-(3,4-dicarboxyphenyl) hexafluoropropane dianhydride (HAB–6FDA). Acetate, propanoate, and pivalate ortho-position functional groups were considered. Thermogravimetric analysis (TGA) was used to study thermal rearrangement at temperatures between 350 and 450 °C, and evolved gases from TGA were analyzed via mass spectrometry to characterize the byproducts of thermal rearrangement and thermal degradation. CO2 was the major byproduct of thermal rearrangement for all samples, and its evolution began well before the onset of thermal degradation. When non-hydroxyl ortho-position groups were present in the polymers, several byproducts other than CO2 were also observed due to the loss of these ortho-position groups before thermal rearrangement. Free volume generally increased with increasing extent of thermal rearrangement, but precise values of free volume could not be accurately determined for polymers with propanoate and pivalate ortho-position functional groups due to uncertainties in the chemical structure of partially converted materials. For polymers with acetate and hydroxyl ortho-position groups, free volume could be determined within the uncertainty of density measurements. Thermal rearrangement behavior and free volume results for acetate containing polymers synthesized via different routes were very similar. Based on these results, the chemical structure of the ortho-position functional group has a larger impact on TR polymer properties than the polyimide precursor synthesis route.

( $${p, \rho , T, x}$$ ) Properties of $$\text{ CO}_{2}$$ /Propane Binary Mixtures at 280 K to 440 K and 3 MPa to 200 MPa

The (p, $$\rho $$ , T, x) properties of binary mixtures of CO $$_{2}$$ (volume fraction purity 0.99999) and propane (mole fraction purity 0.9999) ( $$x_{1}$$ CO $$_{2}+x_{2}$$ propane; $$x_{1} = 0.1744$$ , 0.3863, 0.5837, and 0.7732) were measured in the compressed liquid phase using a metal-bellows variable volumometer. Measurements were conducted from 280 K to 440 K and 3 MPa to 200 MPa. The expanded uncertainties ( $$k = 2$$ ) were estimated to be temperature, $$<$$ 3 mK; pressure, 1.5 kPa ( $$p\le 7$$ MPa), 0.06 % (7 MPa $$< p\le 50$$ MPa), 0.1 % (50 MPa $$< p\le 150$$ MPa), 0.2 % ( $$p> 150$$ MPa); density, 0.10 %; and composition, $$4.4\times 10^{-4}$$ . At $$p >100$$ MPa and 280 K or 440 K, the uncertainties in density measurements increase to 0.14 % and 0.22 %, respectively. The data were compared with available equations of state. The excess molar volumes, $$v_\mathrm{m}^\mathrm{E}$$ , of the mixtures were calculated and plotted as a function of temperature and pressure.

Optical Density Measurements and Analysis for Single-Mode Initial-Condition Buoyancy-Driven Mixing

The Texas A&amp;M water channel experiment is modified to examine the effect of single-mode initial conditions on the development of buoyancy-driven mixing (Rayleigh-Taylor) with small density differences (low-Atwood number). Two separated stratified streams of ~5°C difference are convected and unified at the end of a splitter plate outfitted with a servo-controlled flapper. The top (cold) stream is dyed with Nigrosine and density is measured optically through the Beer-Lambert law. Quantification of the subtle differences between different initial conditions required the optical measurement uncertainties to be significantly reduced. Modifications include a near-uniform backlighting provided through quality, repeatable, professional studio flashes impinging on a white-diffusive surface. Also, a black, absorptive shroud isolates the experiment and the optical path from reflections. Furthermore, only the red channel is used in the Nikon D90 CCD camera where Nigrosine optical scatterring is lower. This new optical setup results in less than 1% uncertainty in density measurements, and 2.5% uncertainty in convective velocity. With the Atwood uncertainty reduced to 4% using a densitometer, the overall mixing height and time uncertainty was reduced to 5% and 3.5%, respectively. Initial single-mode wavelengths of 2, 3, 4, 6, and 8 cm were examined as well as the baseline case where no perturbations were imposed. All non-baseline cases commence with a constant velocity that then slows, eventually approaching the baseline case. Larger wavelengths grow faster, as well as homogenize the flow at a faster rate. The mixing width growth rates were shown to be dependent on initial conditions, slightly outside of experimental uncertainty.

The (p, ρ, T, x) properties for (propane + n-butane + isobutane) ternary mixtures over the temperature range from (280 to 440) K at pressures from (1 to 200) MPa

The (p,ρ,T,x) properties for (propane+n-butane+isobutane) ternary mixtures in the compressed liquid phase were measured by means of a metal-bellows variable volumometer over the temperature range from (280 to 440)K at pressures from (1 to 200)MPa. The mole fraction purities of the propane, n-butane, and isobutane used in the measurements were 0.9999, 0.9997, and 0.9999, respectively. The expanded uncertainties (k=2) in temperature, pressure, density, and composition measurements have been estimated to be less than ±3mK; 1.4kPa (p⩽7MPa), 0.06% (7MPa<p⩽50MPa), 0.1% (50MPa<p⩽150MPa), and 0.2% (p>150MPa); 0.09%; and 4.4·10−4, respectively. In the region above 100MPa at T=(280 and 440)K, the uncertainty in density measurements increases from 0.09% to 0.13% and 0.22%, respectively. Comparisons of the available equation of state with the present measurements are reported. On the basis of the present results, the excess molar volume vmE of the mixtures was calculated and illustrated as a function of temperature and pressure.

The (p, ρ, T, x) properties for (x1n-butane + x2 isobutane) with x1 = (0.2625, 0.4913, and 0.7508) in the temperature range from (280 to 440) K at pressures from (1 to 200) MPa

The (p,ρ,T,x) properties for (x1n-butane+x2 isobutane) with x1=(0.2625, 0.4913, and 0.7508) in the compressed liquid phase were measured by means of a metal-bellows variable volumometer over the temperature range from (280 to 440)K at pressures from (1 to 200)MPa. The mole fraction purities of the n-butane and isobutane used in the measurements were 0.9997 and 0.9999, respectively. The expanded uncertainties (k=2) in temperature, pressure, density, and composition measurements have been estimated to be less than ±3mK; 1.4kPa (p⩽7MPa), 0.06% (7MPa<p⩽50MPa), 0.1% (50MPa<p⩽150MPa), and 0.2% (p>150MPa); 0.09%; and 4.4·10−4, respectively. In the region above 100MPa at T=(280 and 440)K, the uncertainty in density measurements increase from 0.09% to 0.13% and 0.22%, respectively. Comparisons of the available equation of state with the present measurements are reported. On the basis of the present results, the excess molar volume vmE of the mixtures was calculated and illustrated as a function of temperature and pressure.

The (p, ρ, T, x) properties of (x1 propane + x2n-butane) with x1 = (0.0000, 0.2729, 0.5021, and 0.7308) over the temperature range from (280 to 440) K at pressures from (1 to 200) MPa

The (p,ρ,T,x) properties for (x1 propane+x2n-butane) with x1=(0.0000, 0.2729, 0.5021, and 0.7308) in the compressed liquid phase were measured by means of a metal-bellows variable volumometer over the temperature range from (280 to 440)K at pressures from (1 to 200)MPa. The mole fraction purities of the propane and n-butane used in the measurements were 0.9999 and 0.9997, respectively. The expanded uncertainties (k=2) in temperature, pressure, density, and composition measurements have been estimated to be less than ±3mK; 1.4kPa (p⩽7MPa), 0.06% (7MPa<p⩽50MPa), 0.1% (50MPa<p⩽150MPa), and 0.2% (p>150MPa); 0.09%; and 4.4·10−4, respectively. In the region above 100MPa at T=(280 and 440)K, the uncertainty in density measurements increases from 0.09% to 0.13% and 0.22%, respectively. Comparisons of the available equation of state with the present measurements are reported. On the basis of the present results, the excess molar volume vmE of the mixtures was calculated and illustrated as a function of temperature and pressure.

Force Transmission Errors in Magnetic Suspension Densimeters

Techniques to determine and compensate for the force transmission error (FTE), including the magnetic effects of the fluid being measured, in magnetic suspension densimeters are presented. For a two-sinker densimeter, the forces on the balance are expressed for each of the weighings comprising a density determination (i.e., the two sinkers plus balance calibration and tare weights). This yields a system of four equations, which are solved for the fluid density, a balance calibration factor, a coupling factor (related to the FTE), and a quantity related to the balance tare. For a single-sinker densimeter, an in situ weighing of the sinker in vacuum compensates for the FTE of the apparatus itself. A determination of the fluid-specific effect requires measurements with two different sinkers—analogous to the two-sinker analysis, but with the measurements spread out over time. The apparatus part of the FTE is generally less than ±20 ppm. Measurements on propane, helium, neon, nitrogen, argon, toluene, and air are analyzed for the fluid-specific effect; this effect is correlated with the magnetic susceptibility of the fluid together with an apparatus constant. With this analysis, the force transmission “error” becomes an effect that can be accounted for rather than a significant source of uncertainty in density measurements carried out with magnetic suspension densimeters.

The ( p, ρ, T, x) properties for { x propane + (1 − x) isobutane} with x = (1.0000, 0.2765, 0.5052, and 0.7468) in the temperature range from (280 to 440) K at pressures from (1 to 200) MPa

The ( p, ρ, T, x) properties for { x propane + (1 − x) isobutane} with x = (1.0000, 0.2765, 0.5052, and 0.7468) in the compressed liquid phase were measured by means of a metal-bellows variable volumometer in the temperature range from (280 to 440) K at pressures from (1 to 200) MPa. The mole fraction purities of the propane and isobutane used in the measurements were 0.9999 and 0.9999, respectively. The expanded uncertainties ( k = 2) in temperature, pressure, density, and composition measurements have been estimated to be less than ±3 mK; 1.4 kPa ( p ⩽ 7 MPa), 0.06% (7 MPa < p ⩽ 50 MPa), 0.1% (50 MPa < p ⩽ 150 MPa), and 0.2% ( p > 150 MPa); 0.09%; and 1.3 · 10 −4, respectively. In the region above 100 MPa at T (280 and 440) K, the uncertainty in density measurements increases from 0.09% to 0.13% and 0.22%, respectively. Comparisons of the available equation of state with the present measurements are reported. On the basis of the present results, the excess molar volume V m E of the mixtures was calculated and illustrated as a function of temperature and pressure.

( p, ρ, T) Properties for n-butane in the temperature range from 280 K to 380 K at pressures up to 200 MPa

The ( p, ρ, T) properties for n-butane in the compressed liquid phase were measured by means of a metal-bellows variable volumometer in the temperature range from 280 K to 380 K at pressures up to 200 MPa. The mole fraction purity of the n-butane used in the measurements was 0.9997. The expanded uncertainties ( k = 2) in temperature, pressure, and density measurements have been estimated to be less than ±3 mK; 1.4 kPa ( p ⩽ 7 MPa), 0.06% (7 MPa < p ⩽ 50 MPa), 0.1% (50 MPa < p ⩽ 150 MPa), and 0.2% ( p > 150 MPa); and 0.09%, respectively. In the region above100 MPa at T = 280 K and T = 440 K, the uncertainty in density measurements increases from 0.09% to 0.13% and 0.22%, respectively. Eight ( p, ρ, T) measurements at the same temperatures and pressures as the literature values have been conducted for comparisons. In addition, comparisons of the available equations of state with the present measurements are reported.

Measurements of ( p, ρ, T) properties for isobutane in the temperature range from 280 K to 440 K at pressures up to 200 MPa

Measurements of ( p, ρ, T) properties for isobutane in the compressed liquid phase have been obtained by means of a metal-bellows variable volumometer in the temperature range from 280 K to 440 K at pressures up to 200 MPa. The volume-fraction purity of isobutane used was 0.9999. The expanded uncertainties ( k = 2) of temperature, pressure, and density measurements have been estimated to be less than 3 mK, 1.5 kPa ( p ⩽ 7 MPa), 0.06% (7 MPa < p ⩽ 50 MPa), 0.1% (50 MPa < p ⩽ 150 MPa), and 0.2% ( p > 150 MPa), and 0.11%, respectively. In region more than 100 MPa at 280 K and 440 K, the uncertainty in density measurements rise up to 0.15% and 0.23%, respectively. The differences of the present density values at the same temperature between two series of measurements, in which the sample fillings are different, are within the maximum deviation of 0.09% in density, which is enough lower than the expanded uncertainty in density. Eight ( p, ρ, T) measurements at the same temperatures and pressures as the literature values have been conducted for comparison. In addition, vapour pressures were measured at T = (280, 300) K. Moreover, the comparisons of the available equations of state with the present measurements are reported.

Thermodynamic properties of the butenes: Part I. Experimental densities, vapor pressures, and critical points

For the four aliphatic C4H8 isomers (1-butene, isobutene, cis-2-butene, and trans-2-butene), densities, vapor pressures, and critical constants were measured, thus filling several gaps in the thermodynamic data for these compounds. Densities of the four isomers were measured with a computer-controlled high temperature, high-pressure vibrating-tube densimeter system (DMA-HDT) in the subcritical and supercritical states. The densities were measured at temperatures from 273 to 523K and pressures up to 40MPa (1725 overall data points), for which densities between 83 and 677kg/m3 were covered. The uncertainty in density measurement was estimated to be better than 0.1% in the liquid and compressed supercritical states. Near the critical temperature and pressure, the uncertainty increases to a maximum of 1%. Using a variable volume apparatus with a sapphire tube, vapor pressures and critical data were determined. Vapor pressures were measured from about 280K up to near the critical point with an uncertainty of ±(0.1kPa+0.001PkPa and 0.07K). The critical points were determined visually with an uncertainty of 1% for the critical volume, 0.1K for the critical temperature, and 5kPa for the critical pressure. The new vapor pressures and compressed liquid densities were correlated with the TRIDEN model. The new data along with other literature measurements were used to develop fundamental Helmholtz equations of state and are reported by Lemmon and Ihmels [E.W. Lemmon, E.C. Ihmels, Fluid Phase Equilib. 228–229 (2005) 173–187] in part II of this project.

An equation of state and compressed liquid and supercritical densities for sulfur dioxide

Densities of sulfur dioxide (SO 2) have been measured with a computer-controlled high-temperature, high-pressure vibrating-tube densimeter system (DMA-HDT) in the sub- and supercritical states. The densities were measured at temperatures from 273 to 523 K and pressures up to 35 MPa (363 overall data points), for which a density range between 194 and 1485 kg/m 3 was covered. The uncertainty in density measurement was estimated to be better than 0.1% in the liquid and compressed supercritical states. Near the critical temperature and pressure, the uncertainty increases to a maximum of 1%. Using the measured densities and additional thermodynamic data from the literature, a 12-parameter equation explicit in Helmholtz energy was developed for SO 2. The equation of state (EoS) is valid from 197.7 to 523 K and for pressures up to 35 MPa. The uncertainty in density of the EoS ranges from 0.1% at low temperatures in the liquid and vapor to 0.5% at the highest temperatures. The uncertainty in heat capacities is 2%, and the uncertainty in vapor pressure is 0.4% at temperatures above 270 K. In the critical region, the uncertainties are higher for all properties except vapor pressure.

Liquid Densities of γ-Butyrolactone and N-Methyl-2-pyrrolidone from 273 to 473 K and at Pressures up to 40 MPa

Densities of γ-butyrolactone and N-methyl-2-pyrrolidone (NMP) have been measured with a com-puter-controlled high-temperature, high-pressure vibrating tube densimeter system (DMA-HDT) in the liquid state. The uncertainty in density measurement was estimated to be less than ±0.2 kg·m-3. The densities were measured for temperatures from 273 K to 473 K and pressures from 0.3 MPa up to 40 MPa, whereby a density range between (947 and 1168) kg·m-3 for γ-butyrolactone (353 data points) and between (865 and 1068) kg·m-3 for NMP (370 data points) was covered. The experimental data were correlated with the three-dimensional density correlation system (TRIDEN) and compared with published data.

Densities of Sulfur Hexafluoride and Dinitrogen Monoxide over a Wide Temperature and Pressure Range in the Sub- and Supercritical States

Densities of sulfur hexafluoride (SF6) and dinitrogen monoxide (N2O) have been measured with a fully computer-controlled high-temperature high-pressure vibrating tube densimeter system in the sub- and supercritical states. The uncertainty in density measurement was estimated to be between ±0.2 and ±0.3 kg·m−3 depending on the temperature. With respect to accuracy, reliability, suitability, and time consumption, this system has significant advantages for measuring PρT properties in the compressed liquid and supercritical states. The densities were measured for temperatures from 273 to 623 K and at pressures up to 30 MPa for SF6 (442 data points) and from 273 to 473 K and up to 40 MPa for N2O (251 data points), which encompassed density ranges between 142.9 and 1778.5 kg·m−3 for SF6 and between 124.4 and 1051.1 kg·m−3 for N2O. Furthermore, the liquid densities of SF6 and N2O were correlated with a new three-dimensional density correlation system (TRIDEN) and the complete set of PρT data in the sub- and supercritical states were correlated with a virial-type equation of state. For checking the accuracy and suitability of the vibrating tube densimeter system, the experimental densities of SF6 were compared with published data and with the results of a reference equation of state.

Advance in density measurements by means of an automatic hydrostatic weighing system of 100 g capacity

An analytical balance (capacity, 100 g; sensitivity, 100 div/mg) has been converted into a fully automated hydrostatic balance at the Istituto di Metrologia ‘Gustavo Colonnetti’ (IMGC). The project was developed in steps as follows: transformation of the commercial balance into a hydrostatic balance and improvement of its performance through small mechanical changes; servo-control of the beam and construction of two parallel devices for automatic loading and unloading of the pan and of the immersed syspension, providing for exchange of different loads both in air and in liquid; control of the whole weighing process by means of a desk computer, and development of appropriate software. The performance of the balance has greatly improved; hydrostatic weighing results are particularly satisfying considering the difficulty of weighing small specimens. Standard deviations are about 10 μg both for air and hydrostatic weighing. The uncertainty of density measurements is limited to within 10 ppm.