Ideal Gas Heat Capacity Research Articles

Speed of sound predictive modeling in a three-parameter corresponding states format: Application to pure and mixed haloalkanes

A three-parameter corresponding states model is proposed for the prediction of speed of sound surfaces of pure fluids and mixtures belonging to a homogeneous family of fluids as the halogenated alkanes. A preliminary conformality study is developed confirming the high potentiality of the corresponding states methods when applied within a property-dependent framework. A procedure that separately models the ideal-gas part and the residual contribution of the speed of sound surface is assumed. The ideal term is obtained for each target fluid from an individual equation for the ideal-gas isobaric heat capacity, whereas the residual term is represented with a three-parameter corresponding states technique introducing a fluid- and property-specific scaling parameter. A high effectiveness in the modeling of the whole speed of sound surface is obtained. The predictive character of the proposed model is evidenced by the few required inputs for a target fluid, i.e., a single speed of sound value at saturated liquid conditions for the assigned reduced temperature and its ideal-gas heat capacity function. The model format is directly extended to mixture simply by introducing enhanced mixing rules. The model has been successfully validated at both vapor and liquid conditions for 1978 experimental points of eight haloalkane fluids, obtaining the overall average absolute deviation (AAD) of 1.10%, and for mixtures in predictive mode for 927 experimental points, with the AAD of 0.62%. The correlative mode for mixtures has been applied to 600 points in the liquid region with an AAD of 0.67%, which is slightly better than the performance of the corresponding dedicated equations of state. The satisfactory results obtained assure the effectiveness of the proposed procedure.

The low-temperature heat capacity and ideal gas thermodynamic properties of isobutyl tert-butyl ether

The heat capacities of isobutyl tert-butyl ether in crystalline, liquid, supercooled liquid, and glassy states were measured by vacuum adiabatic calorimetry over the temperature range from (7.68 to 353.42) K. The purity of the substance, the glass-transition temperature, the triple point and fusion temperatures, and the enthalpy and entropy of fusion were determined. Based on the experimental data, the thermodynamic functions (absolute entropy and changes of the enthalpy and Gibbs free energy) were calculated for the solid and liquid states over the temperature range studied and for the ideal gas state at T = 298.15 K. The ideal gas heat capacity and other thermodynamic functions in wide temperature range were calculated by statistical thermodynamics method using molecular parameters determined from density-functional theory. Empirical correction for coupling of rotating groups was used to calculate the internal rotational contributions to thermodynamic functions. This correction was found by fitting to the calorimetric entropy values.

Comparison of ab initio and group additive ideal gas heat capacities

AbstractThree case studies comparing molecular ideal gas heat capacity estimations using empirical group additive methods and statistical mechanical methods using ab initio vibrational frequencies are reported. In the first study, results from several ab initio levels of theory are compared with the experimental heat capacities of piperidine and the heat capacities calculated from the observed vibrational frequencies. In the second study, heat capacities for a benchmark group of 27 organic molecules were calculated using vibrational frequencies from AM1, HF/3‐21G(d), and B3LYP/6‐31G(d) theory level, and the results were compared to three recently updated additivity schemes. In the third study, semiempirical corrections to the heat capacities of n‐alkanes were investigated. The strength of additivity schemes is that they are easy to use and understand, and often give reasonable results, but predict the same thermodynamic properties for isomers containing the same functional groups, and are of limited accuracy when the near‐neighbor interactions are strong or if the input data set is not appropriate. Ab initio vibrational frequencies can rapidly provide accurate heat capacities using the harmonic oscillator model, especially if one conformer dominates. The results can be comparable to additivity, and better for rigid molecules containing heteroatoms. Furthermore, ab initio results do not require a calibration data set. © 2004 American Institute of Chemical Engineers AIChE J, 51: 292–297, 2005

Vapour pressure of diethyl phthalate

Measurements of vapour pressure in the liquid phase and of enthalpy of vaporisation and results of calculation of ideal-gas properties for diethyl phthalate are reported. The method of comparative ebulliometry, the static method, and the Knudsen mass-loss effusion method were employed to determine the vapour pressure. A Calvet-type differential microcalorimeter was used to measure the enthalpy of vaporisation. Simultaneous correlation of vapour pressure, of enthalpy of vaporisation and of difference in heat capacities of ideal gas and liquid/solid phases was used to generate parameters of the Cox equation that cover both the (vapour + solid) equilibrium (approximate temperature range from 220 K to 270 K) and (vapour + liquid) equilibrium (from 270 K to 520 K). Vapour pressure and enthalpy of vaporisation derived from the fit are reported at the triple-point temperature T = 269.92 K ( p = 0.0029 Pa, Δ vap H m = 85.10 kJ · mol −1 ), at T = 298.15 K ( p = 0.099 Pa, Δ vap H m = 82.09 kJ · mol −1), and at the normal boiling temperature T = 570.50 K (Δ vap H m = 56.49 kJ · mol −1). Measured vapour pressures and measured and calculated enthalpies of vaporisation are compared with literature data.

Speed-of-Sound Measurements Using Spherical Resonator and Acoustic Virial Coefficients for Gaseous Pentafluoroethane (R125)

Speed-of-sound measurement with a spherical resonator is recognized as one of the most precise and reliable approaches to determine ideal-gas heat capacities and to reveal thermodynamic properties of rarefied gases. In this study, a spherical resonator was used to measure the speed of sound in gaseous pentafluoroethane, R125. Eighty speed-of-sound values were obtained along five isotherms from 277 K to 343 K and up to 600 kPa in pressure. In addition, cp° values and second acoustic virial coefficients were determined at each temperature. Sample purity was 99.9% of the gas-chromatograh area fraction analyzed by the manufacturer. The expanded uncertainties with k = 2 are estimated at 11 mK in temperature, 0.31 kPa in pressure, and 72 ppm in speed of sound. The cp° values reported here were compared with those from spectroscopic data. The agreement between them was within ±0.2%.

Towards an understanding of the heat capacity of liquids. A simple two-state model for molecular association.

A model for the temperature dependence of the isobaric heat capacity of associated pure liquids C(p,m)(o)(T) is proposed. Taking the ideal gas as a reference state, the residual heat capacity is divided into nonspecific C(p) (res,ns) and associational C(p) (res,ass) contributions. Statistical mechanics is used to obtain C(p)(res,ass) by means of a two-state model. All the experimentally observed C(p,m)(o)(T) types of curves in the literature are qualitatively described from the combination of the ideal gas heat capacity C(p)(id)(T) and C(p)(res,ass)(T). The existence of C(p,m)(o)(T) curves with a maximum is predicted and experimentally observed, for the first time, through the measurement of C(p,m)(o)(T) for highly sterically hindered alcohols. A detailed quantitative analysis of C(p,m)(o)(T) for several series of substances (n-alkanes, linear and branched alcohols, and thiols) is made. All the basic features of C(p,m)(o)(T) at atmospheric and high pressures are successfully described, the model parameters being physically meaningful. In particular, the molecular association energies and the C(p)(res,ns) values from the proposed model are found to be in agreement with those obtained through quantum mechanical ab initio calculations and the Flory model, respectively. It is concluded that C(p,m)(o)(T) is governed by the association energy between molecules, their self-association capability and molecular size.

A Fundamental Equation for Calculation of the Thermodynamic Properties of Ethanol

A formulation for the thermodynamic properties of ethanol (C2H5OH) in the liquid, vapor, and saturation states is presented. The formulation is valid for single-phase and saturation states from 250 to 650 K at pressures up to 280 MPa. The formulation includes a fundamental equation and ancillary functions for the estimation of saturation properties. The experimental data used to determine the fundamental equation include pressure-density-temperature, ideal gas heat capacity, speed of sound, and vapor pressure. Saturation values computed from the ancillary functions were used to ensure thermodynamic consistency at the vapor-liquid phase boundary. Comparisons between experimental data and values computed using the fundamental equation are given to verify the uncertainties in the calculated properties. The formulation presented may be used to compute densities to within ±0.2%, heat capacities to within ±3%, and speed of sound to within ±1%. Saturation values of the vapor pressure and saturation densities are represented to within ±0.5%, except near the critical point.

Thermodynamic Properties of Gaseous Nitrous Oxide and Nitric Oxide from Speed-of-Sound Measurements

The speed of sound was measured in gaseous nitrous oxide (N2O) and nitric oxide (NO) using an acoustic resonance technique with a relative standard uncertainty of less than 0.01%. The measurements span the temperature range 200 to 460 K at pressures up to the lesser of 1.6 MPa or 80% of the vapor pressure. The data were analyzed to obtain the constant-pressure ideal-gas heat capacity p0 as a function of temperature with a relative standard uncertainty of 0.1%. For N2O, the values of p0 agree within 0.1% with those determined from spectroscopic data. For NO, the values of p0 differ from spectroscopic results by as much as 1.5%, which is slightly more than the combined uncertainties. The speed-of-sound data were fitted by virial equations of state to obtain temperature-dependent density virial coefficients. Two virial coefficient models were employed, one based on square-well intermolecular potentials, and the second based on a hard-core Lennard-Jones intermolecular potential. The resulting virial equations reproduced nearly all the sound-speed data to within ±0.01% and may be used to calculate vapor densities with relative standard uncertainties of 0.1% or less.

Determination of a vapour phase Helmholtz equation for 1,1,1-trifluoroethane (HFC-143a) from speed of sound measurements

The speed of sound in gaseous 1,1,1-trifluoroethane has been obtained at temperatures between (270 and 370) K from measurements of the resonance frequency of the radial modes of a spherical resonator. Ideal gas heat capacities and acoustic virial coefficients have been calculated from the results. The acoustic data have been used to determine density virial coefficients with a hard-core square-well intermolecular potential equation of state. A Helmholtz energy equation of state is proposed, whose parameters are directly fitted to the present speed of sound data and uses the acoustically determined temperature dependence of the perfect gas heat capacity. The Helmholtz equation so obtained compares favourably with other conventional methods and provides a high accuracy equation specific for the vapour phase of the fluid. The performance of the equation, in terms of the accuracy of the thermodynamic properties derived from it, has been determined by comparison of predicted densities with available experimental data. The equation of state shows very good extrapolation behaviour beyond the range of temperatures and pressures of the experimental data to which it was fitted.

Low-temperature heat capacity and thermodynamic properties of 1,1,1-trifluoro-2,2-dichloroethane

The heat capacity of Freon R-123, CF 3CHCl 2, was measured by adiabatic calorimetry over the temperature range 8.55–297.52 K. The temperature of the λ-anomaly, T trs=125.5±0.1 K, the triple point temperature, T tp=145.68±0.02 K, and the enthalpy and entropy of fusion, Δ fus H m=5.51±0.01 kJ mol −1 and Δ fus S m=37.83±0.05 J mol −1 K −1 were determined. The main thermodynamic functions of CF 3CHCl 2: S° m( T), ( H° m( T)− H° m(0)), and ( G° m( T)− H° m(0)) were calculated at T=298.15 K. The low-temperature differences between the heat capacities of ideal gas and liquid, Δ C p,m = C° p,m (g)− C p,m (l), were used for simultaneous treatment with the saturated vapor pressure data of R-123 [Int. J. Thermophys. 13 (1992) 999], which had been measured from 256.4 to 453.8 K, in order to extrapolate the saturation vapor pressure from T=256 K down to T tp.

Measurement of Speed of Sound with a Spherical Resonator: HCFC-22, HFC-152a, HFC-143a, and Propane

A spherical resonator and acoustic signal measurement apparatus have been designed and developed for measuring the speed of sound in the gaseous phase. The inner radius of the spherical resonator, being about 6.177 cm, was determined by measuring the speed of sound in gaseous argon at temperatures between 293 and 323 K and at pressures up to 200 kPa. Measurements of the speed of sound in four halogenated hydrocarbons are presented, the compounds are chlorodifluoromethane (CHClF2 or HCFC-22), 1,1-difluoroethane (CH3CHF2 or HFC-152a), 1,1,1-trifluoroethane (CH3CF3 or HFC-143a), and propane (CH3CH2CH3 or HC-290). Ideal-gas heat capacities and acoustic virial coefficients were directly deduced from the present data. The results were compared with those from other studies. In this work, the experimental uncertainties in temperature, pressure, and speed of sound are estimated to be less than ±14 mK, ±2.0 kPa, and ±0.0037%, respectively. In addition, equations for the ideal-gas isobaric specific heat capacity for HFC-152a, HFC-143a, and propane are proposed, which are applicable in temperature ranges 240 to 400 K for HFC-152a, 250 to 400 K for HFC-143a, 225 to 375 K for propane. The purities for each of the samples of HCFC-22, HFC-152a, HFC-143a, and propane are better than 99.95 mass%.

Ideal-Gas Heat Capacity Values and Equations for Hydrofluorocarbon (HFC) Refrigerants Based on Speed-of-Sound Measurements

Final values of ideal-gas heat capacity c0p derived from speed-of-sound measurements using an acoustic spherical resonator and equations of c0p as a simple function of temperature are provided from an overall assessment of speed-of-sound measurements for five hydrofluorocarbon (HFC) refrigerants, difluoromethane (R32), pentafluoroethane (R125), 1,1,1,2-tetrafluoroethane (R134a), 1,1,1-trifluoroethane (R143a), and 1,1-difluoroethane (R152a). Some of the experimental results had systematic errors in comparison with theoretical calculations based on spectroscopic data, which seem to result from the impurity of the sample fluids. The agreement of the experimentally determined and theoretically calculated c0p values was confirmed for HFC refrigerants. The uncertainty of c0p values calculated from the proposed equations is estimated to be 0.1 or 0.2% corresponding to an ISO uncertainty with a coverage factor of k=1. An erratum for Table I in a previous report by Yokozeki et al. in 1999 is provided as an appendix.

Thermophysical Properties of Nitrogen Trifluoride, Ethylene Oxide, and Trimethyl Gallium from Speed-of-Sound Measurements

The speed of sound was measured in gaseous nitrogen trifluoride, ethylene oxide, and trimethyl gallium using a highly precise acoustic resonance technique. The measurements span the temperature range 200 to 425 K and reach pressures up to the lesser of 1500 kPa or 80% of the sample vapor pressure. The speed-of-sound measurements have a relative standard uncertainty of less than 0.01%. The data were analyzed to obtain the constant-pressure ideal-gas heat capacity C0p as a function of temperature with a relative standard uncertainty of 0.1%. The values of C0p are in agreement with those determined from spectro- scopic data. The speed-of-sound data were fitted by virial equations of state to obtain temperature-dependent density virial coefficients. Two virial coefficient models were employed, one based on square-well intermolecular potentials, and the second based on a hard-core Lennard-Jones intermolecular potential. The resulting virial equations reproduced the sound-speed data to within ±0.02%, and may be used to calculate vapor densities with relative standard uncertainties of 0.1% or less.

Thermophysical Properties of Chlorine from Speed-of-Sound Measurements

The speed of sound was measured in gaseous chlorine using a highly precise acoustic resonance technique. The data span the temperature range 260 to 440 K and the pressure range 100 kPa to the lesser of 1500 kPa or 80% of the sample's vapor pressure. A small correction (0.003 to 0.06%) to the observed resonance frequencies was required to account for dispersion caused by the vibrational relaxation of chlorine. The speed-of-sound measurements have a relative standard uncertainty of 0.01%. The data were analyzed to obtain the ideal-gas heat capacity as a function of the temperature with a relative standard uncertainty of 0.1%. The reported values of C o p are in agreement with those determined from spectroscopic data. The speed-of-sound data were fitted by virial equations of state to obtain the temperature dependent density virial coefficients. Two virial coefficient models were employed, one based on square-well intermolecular potentials and the second based on a hard-core Lennard–Jones intermolecular potential. The resulting virial equations reproduced the sound speed data to within 0.01% and may be used to calculate vapor densities with relative standard uncertainties of 0.1% or less.

Equations of state for fluorinated ether refrigerants, pentafluoroethyl methyl ether and heptafluoropropyl methyl ether

Thermodynamic properties of two fluorinated ethers, that meet the criteria of the potential new-generation refrigerants with considerably low global warming potential (GWP) and the zero ozone depletion potential (ODP), are studied in the present paper. The recommended candidates are pentafluoroethyl methyl ether, CF 3CF 2OCH 3 (245cbEβγ), and heptafluoropropyl methyl ether, CF 3CF 2CF 2OCH 3 (347sEγδ), proposed as alternative refrigerants to replace 1,2-dichloro-1,1,2,2-tetrafluoroethane, CClF 2CClF 2 (R-114) and trichlorofluoromethane, CCl 3F (R-11), respectively. The present paper summarizes the current thermodynamic property studies of the above fluorinated ethers, and their thermodynamic property modeling will be presented. The formulations are developed exclusively on the basis of the PVT property data, both in the single phase and at the saturation states. Using estimated ideal gas heat capacity data, derived properties including heat capacities and speeds of sound are calculated in a wide range of temperature and pressure, and their behaviors show the typical and physically sound characteristics of pure fluid.

Speed-of-Sound Measurements Using Spherical Resonator and Acoustic Virial Coefficients for Gaseous 1,1,1-Trifluoroethane (R143a)

Speed-of-sound measurement with a spherical resonator is recognized as one of the most precise and reliable approachs to determine ideal-gas heat capacities and to reveal thermodynamic properties of rarefied gases. In this study, we applied a spherical resonator to measure the speed of sound in gaseous 1,1,1-trifluoroethane, R143a. Seventy speed-of-sound values were obtained along five isotherms from 303 K to 343 K and up to 500 kPa in pressure. In addition, cp° values and acoustic second virial coefficients were determined at each temperature of isotherm. Sample purity was 99.95% of the gas chromatograph area fraction analyzed by the manufacturer. The expanded uncertainties with k = 2 are estimated to be 8 mK in temperature, 0.2 kPa in pressure, and 72 ppm in speed of sound. We compared the cp° values determined from the measurements with those from theoretical calculation and confirmed the agreement between them within ±0.1%.

Speed of sound, ideal-gas heat capacity at constant pressure, and second virial coefficients of HFC-227ea

The speed of sound of the gaseous 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) was measured for temperatures from 273 to 333 K and pressures from 26 to 315 kPa with a cylindrical, variable-path acoustic interferometer operating at 156.252 kHz. The uncertainty of the speed of sound was less than ±0.05%. The ideal-gas heat capacity at constant pressure and the second acoustic virial coefficients were determined over the temperature range from the speed of sound measurements. The uncertainty of the ideal-gas heat capacity at constant pressure was estimated to be less than ±0.5%. The ideal-gas heat capacity at constant pressure results and second virial coefficients calculated from the present speed of sound measurements were compared with the available data.

Determination of the Fundamental Frequencies of Fluorochloro-Derivatives of Ethane and Its Application to Calculate Ideal Gas Heat Capacities

Quantum mechanical calculations for all fluorochloro-derivatives of ethane were performed. It was shown that the B3LYP/cc-pVDZ density functional method and single-point MP2/cc-pVTZ calculations lead to an accuracy of the molecular data that is sufficient for prediction of ideal gas heat capacities. Finally, reliable experimental heat capacity data reveal that an uncertainty of the heat capacity calculations of ±1.5% or less is achieved.

Vapor-phase Helmholtz equation for HFC-227ea from speed-of-sound measurements

This work presents measurements of the speed-of-sound in the vapor phase of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea). The measurements were obtained in a stainless-steel spherical resonator with a volume of ∼900 cm3 at temperatures between 260 and 380 K and at pressures up to 500 kPa. Ideal-gas heat capacities and acoustic virial coefficients are directly produced from the data. A Helmholtz equation of state of high accuracy is proposed, whose parameters are directly obtained from speed-of-sound data fitting. The ideal-gas heat capacity data are fit by a functions and used when fitting the Helmholtz equation for the vapor phase. From this equation of state other thermodynamic state function are derived. Due to the high accuracy of the equation, only very precise experimental data are suitable for the model validation and only density measurements have these requirements. A very high accuracy is reached in density prediction, showing the obtained Helmholtz equation to be very reliable. The deduced vapor densities are furthermore compared with those obtained from acoustic virial coefficients with the temperature dependences calculated from hard-core square-well potentials.

Thermodynamic Properties of 1,1,1,2,3,3,3-Heptafluoropropane

A vapor pressure equation has been developed for 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) based on previous measurements from 202 to 375K, from which the boiling point of HFC-227ea was determined. Based on the previous pressure–volume–temperature (PVT) measurements in the gaseous phase for HFC-227ea, virial coefficients, saturated vapor densities, and the enthalpy of vaporization for HFC-227ea were also determined. The vapor pressure equation and the virial equation of state for HFC-227ea were compared with the available data. Based on the previous measurements of speed of sound in the gaseous phase for HFC-227ea, the ideal-gas heat capacity at constant pressure and the second acoustic virial coefficient of HFC-227ea were calculated. A correlation of the second virial coefficient for HFC-227ea was obtained by a semiempirical method using the square-well potential for the intermolecular force and was compared with results based on PVT measurements. A van der Waals-type surface tension correlation for HFC-227ea was proposed, based on our previous experimental data by the differential capillary rise method from 243 to 340K.