Isochoric Heat Capacity Research Articles

The isochoric special heat capacity for 3,3,3-trifluoroprop-1-ene (R1243zf) at temperatures from (299 to 351) K and pressures up to 11 MPa

In this paper, isochoric specific heat capacity (cv) of 3,3,3-trifluoroprop-1-ene (R1243zf) in compressed liquid states were measured using an adiabatic batch calorimeter with intermittent heating. A total of 64 isochoric specific heat capacity data points over temperatures from (299 to 351) K and pressures up to 11 MPa was obtained for liquid R1243zf. The standard uncertainties were estimated to be 12 mK for temperature, 5 kPa for pressure, 0.20% for density and 0.87% for isochoric specific heat capacity. The experimental heat capacity data show good agreements with a Helmholtz equation of states (EOS) from Ref. [2], and the average absolute relative deviation (AARD) is 2.42%. A comparison of the present cv data with values calculated by the generalized equation of Zhong et al. (2019) [3] was carried out as well, and the results show good agreements and the deviations vary from −0.98% to 3.62% and the average absolute relative deviation (AARD) is 0.89%. Compared with the Helmholtz EOS, the generalized equation gives a better description for the data in this work.

Thermophysical Properties of 1-Butanol at High Pressures

1-Butanol can be considered as a good fuel additive, which can be used at high pressures. Therefore, the knowledge of high-pressure thermophysical properties is crucial for this application. In this paper, new experimental data on the speed of sound in 1-butanol in the temperature range from 293 to 318 K and at pressures up to 101 MPa are reported. The speed of sound at a frequency of 2 MHz was measured at atmospheric and high pressures using two measuring sets operating on the principle of the pulse–echo–overlap method. The measurement uncertainties were estimated to be better than ±0.5 m·s−1 and ± 1 m·s−1 at atmospheric and high pressures, respectively. Additionally, the density was measured under atmospheric pressure in the temperature range from 293 to 318 K using a vibrating tube densimeter Anton Paar DMA 5000. Using the experimental results, the density and isobaric and isochoric heat capacities, isentropic and isothermal compressibilities, isobaric thermal expansion, and internal pressure were calculated at temperatures from 293 to 318 K and at pressures up to 100 MPa.

High-pressure and high-temperature vibrational properties and anharmonicity of carbonate minerals up to 6 GPa and 500 °C by Raman spectroscopy

AbstractCarbonate minerals play a dominant role in the deep carbon cycle. Determining the high-pressure and high-temperature vibrational properties of carbonates is essential to understand their anharmonicity and their thermodynamic properties under crustal and upper mantle conditions. Building on our previous study on aragonite, calcite (both CaCO3 polymorphs), dolomite [CaMg(CO3)2], magnesite (MgCO3), rhodochrosite (MnCO3), and siderite (FeCO3) (Farsang et al. 2018), we have measured the pressure- and temperature-induced frequency shifts of Raman-active vibrational modes up to 6 GPa and 500 °C for all naturally occurring aragonite- and calcite-group carbonate minerals, including cerussite (PbCO3), strontianite (SrCO3), witherite (BaCO3), gaspeite (NiCO3), otavite (CdCO3), smithsonite (ZnCO3), and spherocobaltite (CoCO3). Our Raman and XRD measurements show that cerussite decomposes to a mixture of Pb2O3 and tetragonal PbO between 225 and 250 °C, smithsonite breaks down to hexagonal ZnO between 325 and 400 °C, and gaspeite to NiO between 375 and 400 °C. Spherocobaltite breaks down between 425 and 450 °C and otavite between 375 and 400 °C. Due to their thermal stability, carbonates may serve as potential reservoirs for several metals (e.g., Co, Ni, Zn, Cd) in a range of crustal and upper mantle environments (e.g., subduction zones). We have determined the isobaric and isothermal equivalents of the mode Grüneisen parameter and the anharmonic parameter for each Raman mode and compare trends in vibrational properties as a function of pressure, temperature, and chemical composition with concomitant changes in structural properties. Finally, we use the anharmonic parameter to calculate the thermal contribution to the internal energy and entropy, as well as the isochoric and isobaric heat capacity of certain carbonates.

Analytical Determination of the Nucleation-Prone, Low-Density Fraction of Subcooled Water.

Subcooled water is the primordial matrix for ice embryo formation by homogeneous and heterogeneous nucleation. The knowledge of the specific Gibbs free energy and other thermodynamic quantities of subcooled water is one of the basic prerequisites of the theoretical analysis of ice crystallization in terms of classical nucleation theory. The most advanced equation of state of subcooled water is the IAPWS G12-15 formulation. The determination of the thermodynamic quantities of subcooled water on the basis of this equation of state requires the iterative determination of the fraction of low-density water in the two-state mixture of low-density and high-density subcooled water from a transcendental equation. For applications such as microscopic nucleation simulation models requiring highly frequent calls of the IAPWS G12-15 calculus, a new two-step predictor-corrector method for the approximative determination of the low-density water fraction has been developed. The new solution method allows a sufficiently accurate determination of the specific Gibbs energy and of all other thermodynamic quantities of subcooled water at given pressure and temperature, such as specific volume and mass density, specific entropy, isothermal compressibility, thermal expansion coefficient, specific isobaric and isochoric heat capacities, and speed of sound. The misfit of this new approximate analytical solution against the exact numerical solution was demonstrated to be smaller than or equal to the misprediction of the original IAPWS G12-15 formulation with respect to experimental values.

The mechanical and thermodynamic properties of α-Na3(U0.84(2),Na0.16(2))O4: A combined first-principles calculations and quasi-harmonic Debye model study

The mechanical properties of α-Na3(U0.84(2),Na0.16(2))O4 have been researched using the first-principles calculations combined with the quasi-harmonic Debye model. The obtained lattice parameters agree well with the published experimental data. The results of elastic constants indicate that α-Na3(U0.84(2),Na0.16(2))O4 is mechanically stable. The polycrystalline moduli are predicted. The results show that the α-Na3(U0.84(2),Na0.16(2))O4 exhibits brittleness and possesses obvious elastic anisotropy. The hardness shows that it can be considered a “soft material”. Furthermore, the Debye temperature θD and the minimum thermal conductivity kmin are also discussed, respectively. Finally, the thermal expansion coefficient α, isobaric heat capacity CP and isochoric heat capacity CV are evaluated through the quasi-harmonic Debye model.

Accurate quantum-corrected cubic equations of state for helium, neon, hydrogen, deuterium and their mixtures

Cubic equations of state have thus far yielded poor predictions of the thermodynamic properties of quantum fluids such as hydrogen, helium and deuterium at low temperatures. Furthermore, the shape of the optimal α functions of helium and hydrogen have been shown to not decay monotonically as for other fluids. In this work, we derive temperature-dependent quantum corrections for the covolume parameter of cubic equations of state by mapping them onto the excluded volumes predicted by quantum-corrected Mie potentials. Subsequent regression of the Twu α function recovers a near classical behavior with a monotonic decay for most of the temperature range. The quantum corrections result in a significantly better accuracy, especially for caloric properties. While the average deviation of the isochoric heat capacity of liquid hydrogen at saturation exceeds 80% with the present state-of-the-art, the average deviation is 4% with quantum corrections. Average deviations for the saturation pressure are well below 1% for all four fluids. Using Péneloux volume shifts gives average errors in saturation densities that are below 2% for helium and about 1% for hydrogen, deuterium and neon. Parameters are presented for two cubic equations of state: Peng–Robinson and Soave–Redlich–Kwong. The quantum-corrected cubic equations of state are also able to reproduce the vapor-liquid equilibrium of binary mixtures of quantum fluids, and they are the first cubic equations of state that are able to accurately model the vapor-liquid equilibrium of the helium–neon mixture. Similar to the quantum-corrected Mie potentials that were used to develop the covolume corrections, an interaction parameter for the covolume is needed to represent the helium–hydrogen mixture to a high accuracy. The quantum-corrected cubic equation of state paves the way for technological applications of quantum fluids that require models with both high accuracy and computational speed.

Uncertainty estimation of the mean specific heat capacity for the major gases contained in biogas

The paper is focused on the uncertainty estimation of the mean isobaric and isochoric specific heat capacity calculation. The differences in the data among the individual sources for the technical calculation are presented in the first part of the paper. These differences are discussed in this paper. Research of scientific work with listed values of measurement uncertainties has been carried out in the second part of the paper. Furthermore, mathematical models were calculated which describe the dependence of the specific heat capacities and temperature. The maximal error models were carried out. Two approaches were used for the calculation of the mean specific heat capacity. The first approach is the calculation with help of integration of the function which describes the dependence of the specific heat capacity and temperature. The second approach is the calculation of a simple arithmetic mean of the specific heat capacity related to the maximal and minimal value of the temperature interval. The conclusion of the work shows that the time-effective second way is applicable in the case of a narrow temperature range. A value of 5.5% (Δ<sub>t</sub> = 200 K) was reached for the relative uncertainty. This is a similar value to that in the case of using the first way.

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.

Method for constructing fundamental equation of state based on the relationships of similarity theory and scaling hypothesis

On the basis of the new phenomenological theory of the critical point, the method for constructing fundamental equation of state (FEoS) of liquid and gas has been developed. Within the framework of the method proposed, a number of requirements are met: a) in the region of low densities, the transition of FEoS to the virial equation; b) in a wide vicinity of the critical point, the transition of FEoS to the Berestov equation; c) taking into account asymmetry in the behavior of the isochoric heat capacity, isothermal compressibility coefficient and other thermodynamic functions relative to the critical isochore. To calculate the singular component of FEoS, the Pokrovsky transformations and the similarity relation connecting the parameters of a lattice gas and a real liquid are used. It has been shown that such an approach requires only knowledge of the density data on the saturation line and the values of the critical indices to calculate the singular component of FEoS. This allows us to exclude data on the isochoric heat capacity from the calculation scheme and recommend this method for constructing FEoS of substances little studied in the vicinity of the critical point. The method has been tested on the example of constructing carbon dioxide FEoS. The workspace of FEoS has been set: by temperature 216.592 ≤ T ≤ 1100 K and by pressure up to 200 MPa. The results obtained are discussed.

Calculation Technique of Some Thermodynamic Functions using the Results of Joint Thermal and Acoustic Measurements

An original method of calculating isochoric and isobaric heat capacity based on the fundamental relationships of thermodynamics is presented. The theoretical development of the methodology for calculating isochoric and isobaric heat capacity can be used to obtain high metrological data on the thermophysical properties of new low-boiling working substances of power plants operating on the Rankine organic cycle and to replenish existing databases. The technique allows the use of heterogeneous experimental results of acoustic and thermal measurements to calculate the basic thermodynamic functions without information about the values of ideal gas functions, and also to evaluate the consistency of experimental data. Formulas are derived for calculating isobaric and isochoric heat capacities, which are based on reliable equations describing experimental data on the speed of sound and density depending on state parameters. The method was tested using both the characteristics of the reference substances (H2O and CO2), and own new experimental data on the thermal and acoustic properties of octafluorocyclobutane (c-C4F8) in the liquid phase for temperatures of 320 and 340 K and pressures from 4 to 10 MPa. The isochoric heat capacity was calculated from measurements of the density of octafluorocyclobutane and the speed of sound in it. According to the latest series of density measurements in a limited region of the states of the liquid phase of octafluorocyclobutane obtained by the constant volume piezometer method, the isochoric heat capacity was calculated using the equation proposed in this work. The uncertainty of the experimental data used for the test calculation of the density did not exceed 0.25%, and the speed of sound did not exceed 0.05%. The standard deviation in the description of the dependence of thermal quantities was 0.23%, and acoustic—0.15%.

Speed of Sound and Derivative Properties of Ethyl Laurate from Rayleigh–Brillouin Light-Scattering Spectroscopy

The experimental speeds of sound combined with Brillouin frequency shifts of ethyl laurate at temperatures from 294.97 to 572.89 K along six isobaric lines from 0.1 to 10.0 MPa were measured by Rayleigh–Brillouin light-scattering spectroscopy. The expanded relative uncertainty in the reported speeds of sound in ethyl laurate is estimated to be 1.3% (coverage factor k = 2 with a confidence level of 0.95). Within the temperature limits of 303.15–383.15 K and at pressures up to 10.0 MPa, the derived thermoacoustic properties of ethyl laurate including density, specific isobaric heat capacity, isentropic compressibility, isobaric thermal expansivity, isothermal compressibility, the difference in isobaric and isochoric heat capacity, internal pressure, and intermolecular free length were studied. Because of the heavily updated data of density and the speed of sound in the literature, a modified Jacobson’s model for biodiesels was proposed over the temperature range from 293.15 to 343.15 K, which is able to calculate the intermolecular free length of ethyl laurate with higher accuracy compared with Jacobson’s model.

Raman spectra of sillimanite, andalusite, and kyanite at various temperatures

High-temperature Raman spectra of natural sillimanite, andalusite and kyanite were measured in the temperature range of 296–1273 K at ambient pressure. No phase transition was observed over the temperature range in this study. Raman modes for the three samples vary with temperature linearly. The temperature and pressure dependence of the force constants for Si–O stretching vibrations in Al2SiO5 polymorphs were determined. The isobaric mode Gruneisen parameters of sillimanite, andalusite, and kyanite were determined from the temperature dependent of present high-temperature Raman spectra and previous results of thermal expansion coefficients. The intrinsic anharmonic mode parameters were estimated and nonzero, indicating the existence of intrinsic anharmonicity for sillimanite, andalusite and kyanite. Based on Kieffer model, the thermodynamic parameters, including isochoric heat capacity and entropy, were calculated.

High-pressure speed of sound and related thermodynamic properties of N-alkylpyridinium bis(trifluoromethylsulfonyl)imides

The speed of sound was measured in three N-alkylpyridinium bis(trifluoro-methylsulfonyl)imides containing cations with ethyl, butyl and hexyl chains at pressures up to 101 MPa over a temperature range from 293.15 to 323.15 K. This paper is the first reported direct measurement of the speed of sound in N-hexylpyridinium bis(trifluoro-methylsulfonyl)imide as a function of pressure and temperature at two frequencies (1.95 and 6.25 MHz), demonstrating the absence of ultrasonic velocity dispersion under experimental conditions. An acoustic method was used to determine the high-pressure density, isentropic compressibility, isothermal compressibility, isobaric thermal expansion, isobaric and isochoric heat capacities, and internal pressure. For the studied homologous series, the dependence of the speed of sound on the alkyl chain length of the pyridinium cation exhibits a minimum at both atmospheric and high pressures. With increasing pressure, the minimum becomes shallower and is shifted towards homologues with shorter carbon chains in the cation.

Supercritical Fluid Gaseous and Liquid States: A Review of Experimental Results.

We review the experimental evidence, from both historic and modern literature of thermodynamic properties, for the non-existence of a critical-point singularity on Gibbs density surface, for the existence of a critical density hiatus line between 2-phase coexistence, for a supercritical mesophase with the colloidal characteristics of a one-component 2-state phase, and for the percolation loci that bound the existence of gaseous and liquid states. An absence of any critical-point singularity is supported by an overwhelming body of experimental evidence dating back to the original pressure-volume-temperature (p-V-T) equation-of-state measurements of CO2 by Andrews in 1863, and extending to the present NIST-2019 Thermo-physical Properties data bank of more than 200 fluids. Historic heat capacity measurements in the 1960s that gave rise to the concept of “universality” are revisited. The only experimental evidence cited by the original protagonists of the van der Waals hypothesis, and universality theorists, is a misinterpretation of the isochoric heat capacity Cv. We conclude that the body of extensive scientific experimental evidence has never supported the Andrews–van der Waals theory of continuity of liquid and gas, or the existence of a singular critical point with universal scaling properties. All available thermodynamic experimental data, including modern computer experiments, are compatible with a critical divide at Tc, defined by the intersection of two percolation loci at gaseous and liquid phase bounds, and the existence of a colloid-like supercritical mesophase comprising both gaseous and liquid states.

On the Empirical Determination of a Gas–Liquid Supercritical Mesophase and its Phenomenological Definition

We respond to recent articles (Int. J. Thermophysics 39 139 2018, ibid.40 21 2019) that seek to deny the veracity of the empirical discovery and thermodynamic description of a gas–liquid supercritical mesophase. These IJT articles are misleading because they are based upon a false premise that the mesophase is a hypothetical concept. There is no “mesophase hypothesis” as wrongly stated in the title of article IJT, 40 21, 2019. Unlike the critical point continuity hypothesis of van der Waals (1873), or the universal critical point scaling hypothesis advocated by Anisimov and Sengers, and others since 1965, the supercritical mesophase is an empirical entity. If a hypothetical van der Waals fluid with the properties of a critical-state point with divergent isochoric heat capacity, and with the scaling properties of “universality” theory, were to exist, it could be used to vitiate the second law of thermodynamics. By contrast, the supercritical mesophase, discovered originally from computer experiments, is an empirically established equilibrium fluid region, of two-state systems of gas plus liquid, within a single Gibbs phase; the properties of which are determined by the laws of thermodynamics. Here, we provide a phenomenological definition of the gas–liquid supercritical mesophase that accords with the body of compelling experimental results over a 150-year period since van der Waals including modern computer experiments.

Low-temperature thermophysical and crystallographic properties of BaZrO3 perovskite

The temperature dependence of the crystallographic and thermoelastic properties of BaZrO3 perovskite in the temperature range 4.2 K and 450 K has been investigated using high-resolution time-of-flight neutron powder diffraction and literature values of the isobaric heat capacity. At all measured temperatures, BaZrO3 is cubic, space group Pmoverline{3} m, with no clear evidence for diffuse scattering at critical points of the primitive cubic Brillouin zone. Simultaneous fitting of the temperature dependences of the isochoric heat capacity and unit cell volume showed the thermophysical properties of BaZrO3 were consistent with a two-term Debye model in which the cations and anions behave independently of one another with Debye temperatures of 220(2) K and 730(5) K, respectively. This model is further consistent with the temperature variations of the atomic displacement parameters fitted to a modified Debye model in which the vibrational Debye temperatures of the anion are significantly larger than those associated with the cations. The evolution of the crystallographic parameters of BaZrO3 is compared to those of BaCeO3, for barium in the cavity site, and SrZrO3, for zirconium in the octahedral site.

Measurements of pρTx and specific heat capacity c for (R290 + R1243zf) binary mixtures at temperatures from (292 to 350) K and pressures up to 11 MPa

Abstract In this paper, isochoric pρTx and specific heat capacity (cv) for (R290 + R1243zf) binary mixtures were measured using an adiabatic batch calorimeter with intermittent heating. A total of 57 pρTx data points over temperatures from (292 to 350) K and 82 isochoric specific heat capacity data points over temperatures from (299 to 350) K were obtained for liquid with mole fractions of R290 at (0.788, 0.606, 0.435 and 0.170). The standard uncertainties were estimated to be 12 mK for temperature, 5 kPa for pressure, 0.30% for density and 0.96% for isochoric specific heat capacity. The experimental density and heat capacity data agree well with the Helmholtz equation of state (EOS) developed by Bell and Lemmon (2016), and the average absolute relative deviation (AARD) are 0.27% and 1.01%, respectively. Comparisons of the present cv data with values calculated by the generalized equation developed by Zhong et al. (2019a) was carried out as well, and the results show good agreements with deviations varying from −3.00% to 3.16% and the average absolute relative deviation (AARD) of 0.91%.

Nonlinear Effects in the Phonon System of Diamond Crystal

Thermodynamic properties of diamond are theoretically investigated on the ground of self-consistent description of a phonon gas in lattice, which generalizes the Debye model with taking into account the phonon-phonon interaction. In many cases properties of crystals of certain symmetry can be well approximated by a model of an isotropic continuous medium, if its elastic moduli are chosen optimally. They should be found for a crystal of each symmetry from the condition of their proximity to the exact elastic moduli, which are measured experimentally and are given in the corresponding tables. At high temperatures, the nonlinear phonon interaction takes into account both three- and four-phonon interactions. In this reason we take into account not only the second-order elastic moduli tensor in the reduced isotropic crystal model, but also the third- and fourth-order elastic moduli tensors, which are all together characterized by nine independent components. Account of the phonon-phonon interaction leads to the redefinition of the phonon’s speed and of the Debye energy. Their dependence on the temperature occurs. In the absence of interaction and neglecting the nonlinear effects, the phonons are the same as that of the Debye model. They are called "bare" or "Debye". Phonons whose speed is renormalized due to the interaction are called the “self-consistent” ones. It is shown that, at high temperatures, the theory predicts the linear in the temperature deviation of the isochoric heat capacity from the Dulong-Petit law. Unlike for the most crystals, where the decrease in the isochoric heat capacity is observed, our calculations for diamond and crystals with diamond structure predict the linear increase of the isochoric heat capacity with the temperature, viewed experimentally. The isobaric heat capacity of diamond, similar to other substances, linearly increases with the temperature.

Thermophysical and volumetric properties of mixtures {carvacrol + ethanol} at several temperatures and atmospheric pressure

Experimental molar heat capacities at atmospheric pressure have been determined for the mixture {carvacrol + ethanol} every 10 K in the temperature interval (298.15–328.15) K and over the entire composition range with a Calvet type calorimeter. Densities, necessary for determining isobaric heat capacities, and ultrasonic speed of sound have been also measured at the same conditions. From these properties isobaric thermal expansivities, isentropic compressibilities, isothermal compressibilities, internal pressures and isochoric molar heat capacities have been calculated. Furthermore, in order to complete our thermophysical study the corresponding excess properties have been calculated and discussed in terms of molecular interactions. Finally, excess molar isobaric heat capacities have been calculated with COSMO-RS and compared to the experimental values.

Speed of sound for three binary (CH4 + H2) mixtures from p = (0.5 up to 20) MPa at T = (273.16 to 375) K

Speed of sound is one of the thermodynamic properties that can be measured with least uncertainty and is of great interest in developing equations of state. Moreover, accurate models are needed by the H2 industry to design the transport and storage stages of hydrogen blends in the natural gas network. This research aims to provide accurate data for (CH4 + H2) mixtures of nominal (5, 10, and 50) mol-% of hydrogen, in the p = (0.5 up to 20) MPa pressure range and with temperatures T = (273.16, 300, 325, 350, and 375) K. Using an acoustic spherical resonator, speed of sound was determined with an overall relative expanded (k = 2) uncertainty of 220 parts in 106 (0.022%). Data were compared to reference equations of state for natural gas-like mixtures, such as AGA8-DC92 and GERG-2008. Average absolute deviations below 0.095% and percentage deviations between 0.029% and up to 0.30%, respectively, were obtained. Additionally, results were fitted to the acoustic virial equation of state and adiabatic coefficients, molar isochoric heat capacities and molar isobaric heat capacities as perfect-gas, together with second and third acoustic virial coefficients were estimated. Density second virial coefficients were also obtained.