Reference Values of the Dielectric Constant of Natural Gas Components Determined with a Cross Capacitor

A novel toroidal cross capacitor was used to measure accurately the dielectric polarizability(p) (i.e., the dielectric constant as a function of the pressure) of helium, argon, nitrogen, methane, and carbon dioxide atT=50°C. The data extend up to 7 MPa (5 MPa for CO₂) and may be useful for calibrating on-line, capacitance-based systems that are designed to measure the heating value of natural gas. The uncertainties ofandpare 4×10^–6and (3.0×10^–5 p+84 Pa), respectively. The properties of helium that had been calculatedab initiofrom quantum mechanics were used to verify that the cross capacitor deformed in a predictable manner under hydrostatic (gas) pressure. Thus, a common cause of systematic errors in measuring the dielectric constant of gases was avoided. For helium, the rms deviation of(p) from the calculations was only 2.7×10^–7. This suggests that the estimated uncertainty is very conservative.     

The Dielectric Permittivity of Saturated Liquid Carbon Dioxide and Propane Measured Using Cross Capacitors

Relative dielectric permittivities ε_r of saturated liquid carbon dioxide (CO₂) and propane (C₃H₈) were measured using well-characterized cross capacitors in the range 260 K < T < 300 K. The molar polarizability of CO₂ was calculated using the equation of state of Span and Wagner to convert our values of the saturation vapor pressure p_sat to values of the saturated liquid density ρ_sat. In the range 260 K < T < 300 K, cm³· mol⁻¹. The systematic difference between measurements made with two different capacitors was 0.001 cm³· mol⁻¹; this difference is equivalent to a shift of 12 mK in the liquid temperature. The uncertainty of from the equation of state of CO₂ is approximately 0.002 cm³· mol⁻¹. Our values of for CO₂ are consistent with the results of Moriyoshi et al. and of May et al.; however, our values are 0.5 % larger than the values determined by Haynes. For saturated liquid propane, our values of ε_r agree with the values of Haynes and Younglove within the combined uncertainty of 0.0003.     

The Viscosity of Seven Gases Measured with a Greenspan Viscometer

The viscosity of seven gases (Ar, CH₄, C₃H₈, N₂, SF₆, CF₄, C₂F₆) was determined by interpreting frequency-response data from a Greenspan acoustic viscometer with a detailed model developed by Gillis, Mehl, and Moldover. The model contains a parameter _r that characterizes the viscous dissipation at the ends of the viscometer's duct. It was difficult to determine _r accurately from dimensional measurements; therefore, _r was adjusted to fit the viscosity of helium on the 298 K isotherm (0.6 MPa<p<3.4 MPa). This calibration was tested by additional viscosity measurements using four, well-studied, polyatomic gases (CH₄, C₂H₆, N₂, and SF₆) near 300 K and by measurements using argon in the range 293 K<T<373 K. For these gases, all of the present results agree with reference values to within ±0.5% (±0.4% in the limit of zero density). The viscosities of CF₄ and C₂F₆ were measured between 210 and 375 K and up to 3.3 MPa with average uncertainties of 0.42 and 0.55%, respectively. At the highest density studied for CF₄ (2746 molm^–3), the uncertainty increased to 1.9%; of this 1.9%, 0.63% resulted from the uncertainty of the thermal conductivity of CF₄, which other researchers estimated to be 2% of its value at zero density. As an unexpected bonus, the present Greenspan viscometer yielded values of the speed of sound that agree, within ±0.04%, with reference values.     

Can a Pressure Standard be Based on Capacitance Measurements?

We consider the feasibility of basing a pressure standard on measurements of the dielectric constant ϵ and the thermodynamic temperature T of helium near 0 °C. The pressure p of the helium would be calculated from fundamental constants, quantum mechanics, and statistical mechanics. At present, the relative standard uncertainty of the pressure u_r(p) would exceed 20 × 10⁻⁶, the relative uncertainty of the value of the molar polarizability of helium A_ϵ calculated ab initio. If the relativistic corrections to A_ϵ were calculated as accurately as the classical value is now known, a capacitance-based pressure standard might attain u_r(p) < 6 × 10⁻⁶ for pressures near 1 MPa, a result of considerable interest for pressure metrology. One obtains p by eliminating the density from the virial expansions for p and ϵ − 1. If ϵ − 1 were measured with a very stable, 0.5 pF toroidal cross capacitor, the small capacitance and the small values of ϵ − 1 would require state-of-the-art capacitance measurements to achieve a useful pressure standard.     

On the extrapolation behavior of empirical equations of state

Generally, the extrapolation behavior of empirical equations of state is regarded as poor, but it can be shown that state-of-the-art equations of state yield reliable results well beyond the range where they were fitted to experimental data. During the past years a new generation of highly accurate equations of state which yield reasonable results even up to the limits of chemical stability of the considered substances has been developed. In this paper, the positive influence of recent methods for the development of equations of state on their extrapolation behavior is discussed. The influence of the mathematical structure on the extrapolation characteristics is analyzed and requirements for a reasonable behavior up to extreme temperatures and pressures are formulated. As possible ways for assessment of the extrapolation behavior of an equation of state, comparisons with experimental data at very high pressures and temperatures and with theoretically predicted features of the so-called “ideal curves” of a fluid are discussed. Finally, the current status of our knowledge of the extrapolation behavior of empirical equations of state is summarized and its shortcomings are pointed out.     

The correlation and prediction of thermal conductivity and other properties of gases at zero density

This paper presents a comparative study of the correlation of thermal conductivities in the limit of zero density for dilute gases including nitrogen, carbon monoxide, carbon dioxide, methane, and tetrafluoromethane. A theoretically based correlation scheme employing independent experimental information has been examined and found to be useful for the correlation of thermal conductivity data as well as for the evaluation of related quantities, e.g., effective collision cross sections. The latter provide the basis for further studies concerning the anisotropy of the intermolecular pair potential. The paper includes results regarding the simplified expression for the thermal conductivity proposed by Thijsse et al., which has been found to be especially useful for practical purposes.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Equations of State for Technical Applications. II. Results for Nonpolar Fluids

New functional forms have been developed for multiparameter equations of state for non- and weakly polar fluids and for polar fluids. The resulting functional forms, which were established with an optimization algorithm which considers data sets for different fluids simultaneously, are suitable as a basis for equations of state for a broad variety of fluids. The functional forms were designed to fulfill typical demands of advanced technical applications with regard to the achieved accuracy. They are numerically very stable and their substance-specific coefficients can easily be fitted to restricted data sets. In this way, a fast extension of the group of fluids for which accurate empirical equations of state are available becomes possible. This article deals with the results found for the non- and weakly polar fluids methane, ethane, propane, isobutane, n-butane, n-pentane, n-hexane, n-heptane, n-octane, argon, oxygen, nitrogen, ethylene, cyclohexane, and sulfur hexafluoride. The substance-specific parameters of the new equations of state are given as well as statistical and graphical comparisons with experimental data. General features of the new class of equations of state such as their extrapolation behavior and their numerical stability have been discussed in a preceding article. Results for typical polar fluids will be discussed in a subsequent article.