Saturated Liquid Heat Capacity Research Articles

Updated versions of the generalized Soave α-function suitable for the Redlich-Kwong and Peng-Robinson equations of state

More than 40 years after their publication, updated versions of the generalized Soave α-function (α(Tr,ω)=[1+m(ω)(1−Tr0.5)]2) suitable for the Redlich-Kwong (RK) and Peng-Robinson (PR) equations of state (EoS) are proposed in this work. The new mathematical expressions of mRK(ω) and mPR(ω) have been determined by correlating the optimal m values, fitted on vapor pressures (Psat) and/or enthalpies of vaporization (ΔvapH) and/or saturated-liquid heat capacities (cP,liqsat) against the acentric factor ω. The correlations determined in this study can be considered as broad-based and sound since they were established for 1721 pure compounds belonging to many different chemical families (hydrocarbons, halogenated, oxygenated, sulfur, nitrogen compounds …) for which experimental data were available. Significant improvements on the reproduction of vapor pressures were obtained for the PR EoS with respect to the original version. The updated SRK EoS achieved similar average deviations for the three properties of interest (Psat,ΔvapH and cP,liqsat), in comparison with the original SRK equation. A substantial improvement is however noticeable for heavy molecules with an acentric factor larger than 0.9.

Analysis of the Combinations of Property Data That Are Suitable for a Safe Estimation of Consistent Twu α-Function Parameters: Updated Parameter Values for the Translated-Consistent tc-PR and tc-RK Cubic Equations of State

The suitability of different combinations of property data among vapor-pressure (Psat), enthalpy of vaporization (ΔvapH) and saturated-liquid heat-capacity (cP,liqsat) data for fitting consistent Twu α-function parameters is evaluated. A given combination is declared to be suitable if the obtained fitted parameters produce acceptable predictions for the three considered properties for the 783 molecules included in the reference database. Calculations are carried out using the translated-consistent versions of the Peng–Robinson (tc-PR) and Redlich–Kwong (tc-RK) cubic equations of state (CEoS). It is demonstrated that reliable parameters are obtained on the condition that they are, at least, fitted to vapor-pressure data. It is strongly advised to not exclusively fit α-function parameters to enthalpy of vaporization and/or saturated-liquid heat capacity data. Finally, Twu α-function parameters (L, M, N) suitable for the tc-PR and tc-RK CEoS are determined for the 1721 molecules, for which at least accurate ...

An investigation of saturated vapor pressure regarding low-volatility organophosphorus extractants Di-(2-ethylhexyl) phosphoric acid and tributyl phosphate: Correlation and thermodynamics study

New saturated vapor pressure (psat) data of organophosphorus extractants, di-(2-ethylhexyl) phosphoric acid (D2EHPA) and tributyl phosphate (TBP), were investigated in T = (383.8–546.2) K and psat = (0.13–6.67) kPa using vacuum distillation method. The data was found to be a good fit with Antoine, August, Riedel and Wagner equation. Regression constants prove to be very useful in estimating psat at operating temperature. Intermolecular hydrogen bonding affected D2EHPA having lower psat in comparison with TBP. Thermodynamic properties of both molar enthalpy and molar entropy of vaporization were obtained using the Clausius-Clapeyron equation. As temperature increased, molar enthalpy and molar entropy of vaporization decreased showing a positive deviation from Trouton's rule. Using the relations of molar enthalpy and temperature, saturated liquid heat capacity was obtained. All data can be usefully employed for the design of a distillation column or evaporator for recycling of both extractants from organic wastewater.

Thermodynamic properties of pyrrole, 1-methylpyrrole, 2,4-dimethylpyrrole, and 2,5-dimethylpyrrole: Experimental and computational results

New measurements of critical temperature, saturated liquid heat capacity from temperature T≈315K to T≈550K, and saturated liquid density from T=323K to T≈475K are reported for pyrrole (Chemical Abstracts registry number [109-97-7]), 1-methylpyrrole [96-54-8], 2,4-dimethylpyrrole [625-82-1], and 2,5-dimethylpyrrole [625-84-3]. New measurements of vapor pressure are reported for 2,4-dimethylpyrrole {338<(T/K)<477} and 2,5-dimethylpyrrole {341<(T/K)<479}, as well as the enthalpy of combustion determined with oxygen-bomb calorimetry for 2,4-dimethylpyrrole. These new measurements are combined with literature values to calculate thermodynamic properties in the ideal-gas state for extended ranges of temperature for all compounds: pyrrole {298<(T/K)<550}, 1-methylpyrrole {298<(T/K)<530}, 2,4-dimethylpyrrole {298<(T/K)<600}, and 2,5-dimethylpyrrole {298<(T/K)<560}. Molar thermodynamic functions (enthalpies, entropies, and Gibbs energies) for the liquid and ideal-gas states were derived from the experimental studies at selected temperatures. Statistical calculations were performed with optimized geometries, scaled vibrational frequencies, and methyl rotational potentials performed using B3LYP hybrid density functional theory with the def2-TZVPPD basis set. Methyl torsional barriers were evaluated at the DLPNO-CCSD(T)/def2-QZVP level of theory using the B3LYP/def2-TZVPPD geometries. Computed ideal-gas properties are shown to be in excellent accord with ideal-gas entropies derived from thermophysical property measurements, as well as with reported experimental heat capacities for the ideal-gas state. All experimental results are compared with property values available in the literature.

Heat capacity of isobutane in liquid phase at temperatures from 303 K to 413 K and pressures up to 12 MPa

The measurements of isobaric heat capacity for isobutane were carried out using a flow calorimeter in both compressed liquid and supercritical phase. 250 data of heat capacity were obtained at the temperature range from 303K to 413K at pressures up to 12MPa. The relatively expanded uncertainty in the heat capacity measurement was estimated to be less than 1% with k=2 (95%). An empirical equation was correlated to represent the experimental values with an average absolute deviation of 0.7%. In addition, the saturated liquid heat capacities of isobutane were also derived by extrapolating the empirical equation to the corresponding saturated pressure.

Measurements of the isobaric heat capacity of pressurized liquid trans-1,3,3,3-tetrafluoropropene [R1234ze(E)] by scanning calorimetry

Isobaric heat capacity of pressurized liquid trans-1,3,3,3-tetrafluoropropene [R1234ze(E)] was measured by scanning calorimetry. The experimental system basically consists of a Calvet calorimeter (Setaram C80) and a pressure balance unit. A total of 95 data points were obtained at temperatures from 310.15 to 365.15 K and pressures up to 5.5 MPa. An empirical equation was used to correlate the experimental data with an average absolute percentage deviation of 0.18 %. Besides, a comparison was carried out between present data and literature data and three latest fundamental equations of state. Finally, saturated liquid heat capacity of R1234ze(E) was also investigated in this paper.

Measurements of the isobaric heat capacity of R1234yf in liquid phase at temperatures from 305 K to 355 K and pressures up to 5 MPa

2,3,3,3-Tetrafluoropropene (R1234yf) is an environmentally friendly promising alternative to 1,1,1,2-tetrafluoroethane (R134a) in air conditioning applications. The heat capacity of R1234yf in liquid phase was investigated in this study. The measurements were carried out with a modified heat conduction calorimeter. A total of 74 data points were obtained among 305–355K and 1.5–5MPa. The uncertainty of the heat capacity measurements was estimated to be less than 1.7%. An empirical equation was correlated to reproduce the experimental result with its terms chosen by a stepwise method. The maximum deviation between the correlating equation and the experimental data was 1.5%. Furthermore, saturated liquid heat capacity of R1234yf was obtained by extrapolating the correlation to saturated pressures. Finally, a comparison was done between the present data and literature experimental data and calculations from a fundamental equation of state.

Predictive correlations for liquid heat capacity – including the critical region

A predictive correlation relating isobaric liquid specific heat capacity to absolute temperature and elemental composition was recently reported. The Dadgostar–Shaw correlation, valid where CV≫T(∂V/∂T)P(∂P/∂T)V, is modified in the present work to accommodate the critical region and the consequent variation of liquid phase isobaric heat capacity among isomers at the same absolute temperature. The results obtained for a training data set and a test data set are presented and compared with results obtained with the Dadgostar–Shaw correlation, and two variants of the Rowlinson–Bondi correlation. The CP° contribution is calculated using either compound specific correlations or the predictive universal Laštovka–Shaw equation for ideal gases. For pure hydrocarbon liquids where compound specific CP° correlations, Tc and ω are available, the Rowlinson–Bondi based approach should be used to compute saturated liquid heat capacities. If only Tc and ω are available, the Rowlinson–Bondi based approach+the predictive Laštovka–Shaw equation for CP° values is preferred. If the liquid is a multicomponent or ill-defined hydrocarbon liquid, the modified Dadgostar–Shaw correlation is preferred over the Dadgostar correlation as long as Tc is available or can be estimated. The accuracy penalty for use of the modified Dadgostar–Shaw correlation appears small relative to either Rowlinson–Bondi based calculation approaches.

Saturated-liquid heat capacity calculation of alkanes

An empirical model for the calculation of the heat capacity of alkanes is recommended. This model was tested and compared to known models (Luria-Benson and R?zicka-Domalski) using 68 sets with 1155 literature experimental heat capacity data of 39 alkanes. The obtained results indicate that the new model is slightly better of the existing models, especially near the critical point.

Saturated-liquid heat capacity of organic compounds: New empirical correlation model

A new saturated-liquid heat capacity model is recommended. This model is tested and compared with the known polynomial and quasi-polynomial models on 39 sets with 1453 experimental heat capacity data. The obtained results indicate that the new model is better then the existing models, especially near the critical point.

Saturated-liquid heat capacity: New polynomial models and review of the literature experimental data

In this paper a review of selected literature experimental data for saturated-liquid heat capacities was presented. Two-, three- and four-parameter polynomial correlation models are tested on those data. Obtained results lead to the conclusion that correlation quality depends on the number of parameters, and slightly on the type of models. The best two three- and four-parameter models were proposed.

Measurement of Heat Capacities for 12 Organic Substances by Tian−Calvet Calorimetry

Heat capacities for 1,2-dimethoxybenzene, 2,5,8,11-triethylene glycol dimethyl ether, N-ethyl-2-pyrrolidone, isopentyl acetate, 2-ethylhexanal, toluene, 1-phenylethanol, propyl acetate, octyl acetate, dimethyl sulfoxide, diethyl phthalate, and diethyl carbonate were measured with the “three-step” method using a Tian−Calvet batch calorimeter. The measurements of saturated liquid heat capacity have an approximate uncertainty of ±0.5% and cover a temperature range between 310 K and 420 K. Furthermore, the experimental results were compared with three group contribution methods for liquid heat capacities.

Estimation of Thermophysical Properties of Heavy Hydrocarbons through a Group Contribution Based Equation of State

This paper presents an improved version of a purely predictive thermodynamic model proposed previously by Coniglio et al. (Fluid Phase Equilib. 1993, 87, 53−88). The main feature of this model is to be based on a Peng−Robinson type equation of state with parameters determined through homogeneous group contribution methods. The new model estimates vapor pressures, saturated liquid densities, heats of vaporization, saturated liquid heat capacities, and speed of sound in saturated liquids of a large number of hydrocarbons within the experimental accuracy, from the triple point to 2 bar. The required inputs for each compound are the molecular structure and the experimental normal boiling point or at least one vapor pressure measurement. The applicability of the new model was verified through prediction of vapor pressures of non-hydrocarbon organic compounds (acids, esters, alcohols, ...). The obtained results confirm the reliability of the new model when extrapolating to non-hydrocarbon organic compounds.

Measurement of Heat Capacities for Nine Organic Substances by Tian−Calvet Calorimetry

Heat capacities for n-heptane, 2-methyl-1-propanol, toluene, and 1-propanol were measured with the “step by step” method and those for 2-methyl-1-propanol, 1-propanol, methylcyclohexane, toluene, 2,4-pentanedione, 1-bromooctane, dibenzyl ether, and benzoic acid with the “three-step” method using a Tian−Calvet batch calorimeter. The measurements of saturated liquid heat capacity have an approximate uncertainty of ±0.5% and cover temperatures within the range 288 K to 363 K.

Isochoric heat capacity measurements for 2,2-dichloro-1,1,1-trifluoroethane (R123) at temperatures from 167 to 341 K and 1-chloro-1,2,2,2-tetrafluoroethane (R124) from 94 to 341 K at pressures to 35 MPa

Molar heat capacities at a constant volume (C v) of 2,2-dichloro-1,1,1-trifluoroethane (R123) and 1-chloro-1,2,2,2-tetrafluoroethane (R124) were measured with an adiabatic calorimeter. Temperatures ranged from 167 K for R123 and from 94 K for R124 to 341 K, and pressures were up to 33 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C (2) v), saturated liquid (C σ or C′ x ), and single-phase (C v) molar heat capacities. The C σ data were used to estimate vapor pressures for values less than 100 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. Due to the tendency of both R123 and R124 to subcool, the triple-point temperature (T tr) and the enthalpy of fusion (Δ fus H) could not be measured. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded uncertainty (at the 2σ level) for C v is estimated to be 0.7%, for C (2) v it is 0.5%, and for C σ it is 0.7%.

Molar Heat Capacity at Constant Volume of 1,1-Difluoroethane (R152a) and 1,1,1-Trifluoroethane (R143a) from the Triple-Point Temperature to 345 K at Pressures to 35 Mpa

Molar heat capacities at constant volume (C v) of 1,1-difluoroethane (R152a) and 1,1,1-trifluoroethane (R143a) have been measured with an adiabatic calorimeter. Temperatures ranged from their triple points to 345 K, and pressures up to 35 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase ((C v (2) ), saturated-liquid (C σ or C x ' ), and single-phase (C v) molar heat capacities. The C σ data were used to estimate vapor pressures for values less than 105 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. The triple-point temperature and the enthalpy of fusion were also measured for each substance. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded relative uncertainty (with a coverage factor k=2 and thus a two-standard deviation estimate) for C v is estimated to be 0.7%, for C v (2) it is 0.5%, and for C σ it is 0.7%.

An equation of state for the thermodynamic properties of R143a (1,1,1-trifluoroethane)

Thermodynamic properties of 1,1,1-trifluoroethane (R143a) are expresed in terms of a 32-term modified Benedict-Webb-Rubin (MBWR) equation of state. Coefficients are reported for the MBWR equation and for ancillary equations used to lit the ideal-gas heat capacity, and the coexisting densities and pressure along the saturation boundary. The MBWR coefficients were determined from a multiproperty fit that used the following types of experimental data:PVT: isochoric, isobaric, and saturated-liquid heat capacities: second virial coefficients: speed of sound and properties at coexistence. The equation of state was optimized to the experimental data from 162 to 346 K and pressures to 35 MPa with the exception of the critical region. Upon extrapolation to 500 K and 60 MPa, the equation gives thermodynamically reasonable results. Comparisons between calculated and experimental values are presented.

Molar heat capacity at constant volume of difluoromethane (R32) and pentafluoroethane (R125) from the triple-point temperature to 345 K at pressures to 35 MPa

Molar heat capacities at constant volume (C v) of dill uoromethane (R32) and pentalluoroethane (R125) were measured with an adiabatic calorimeter. Temperatures ranged from their triple points to 345 K, and pressures up to 35 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C v (2) ), saturated liquid (C σ orC′ x ), and singlephase (C v) molar heat capacities. TheC σ data were used to estimate vapor pressures for values less than 0.3 MPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. The triple-point temperature (T tr) and the enthalpy of fusion (Δfus H) were also measured for each substance. The principal sources of uncertainty are the temperature rise measurement and the change-ofvolume work adjustment. The expanded uncertainty (at the two-sigma level) forC v is estimated to be 0.7%, forC v (2) it is 0.5%, and forC σ it is 0.7%.

On the dependence of liquid heat capacity on temperature and molecular structure

On the basis of the similarity of the shapes of the liquid heat capacity and vapour pressure curves, and the concept that a property such as heat capacity (energy storage capacity) should directly depend on the constitution and structure of the molecules, a corresponding state-type relation has been formulated and tested: C σL = R M(5.4571 − 0.3098 T R − 1 ) where C σL (J mol −1 K −1) is the saturated liquid heat capacity, R M (cm 3 mol −1) is the molar refraction and T R is the reduced temperature. The extension of the method, which predicts liquid heat capacities of pure non-polar liquids with an average absolute deviation of 5.5%, to polar liquids and several binary mixtures is also discussed.

Representation and prediction of thermophysical properties of heavy hydrocarbons

Thermophysical properties (vapor pressures, saturated liquid densities, heats of vaporization and saturated liquid heat capacities) of a wide variety of hydrocarbons present in petroleum fluids are calculated with a Peng-Robinson type equation of state. The form of the temperature dependent parameter found by Carrier et al. (1988) is slightly modified. Each component is characterized by three parameters: the normal boiling absolute temperature, the pseudocovolume and the shape parameter, both calculated by a Bondi-like group contribution method. A consistent correction which improves volumetric estimations is also developed using a group contribution model. The proposed approach yields good representation of pure component saturated properties.