Effects of measurement deviation in gaseous speed of sound on derived thermodynamic properties

doi:10.3969/j.issn.0438-1157.2014.04.002

Abstract

Abstract: Gaseous speed of sound is an important thermophysical property measured with high precision. The ideal gas heat capacity and the second virial coefficient can be derived from the speed of sound. The systematic errors in measurements of sound speed using fixed path interferometers are analyzed. Mathematic modes are proposed for the influences of fixed absolute error (δ_FAE) and fixed fractional error (δ_FFE) on thermodynamic properties derived from gaseous speed of sound. The influences from the errors in measurements are also simulated. The results show that the heat capacity ratio of ideal gas varies with 2δ_FAE by the effect of the fixed absolute error, but the influence on isobaric heat capacity of ideas gas may be higher than -100δ_FAE and increases with temperature for polyatomic gas. The second acoustic virial coefficient is affected by the fixed fractional error. Substances have the same absolute deviations in the second acoustic virial coefficients at the same temperature and fixed fractional error. The influences of fixed absolute error and fixed fractional error on the second virial coefficients are lower.

Key words: thermodynamic properties, simulation, measurement, gaseous speed of sound, virial coefficient, ideal gas heat capacity, fixed path interferometer

摘要： 气相声速是测量准确度最高的热物性之一，并可以导出理想气体比定压热容和第二维里系数等其他热力学性质。分析了定程干涉法中存在的系统偏差，建立了绝对系统偏差（δ_FAE）和相对系统偏差（δ_FFE）对导出热力性质影响的数学模型，并开展了模拟计算。研究结果表明，理想气体比热容比受绝对系统偏差的影响为2δ_FAE，但是绝对系统偏差对多原子气体的理想气体比定压热容的影响大，可高于-100δ_FAE，且温度越高，影响越大；相对系统偏差主要影响声速维里系数，在温度和相对系统偏差相同时，不同工质的第二声速维里系数的绝对变化量相同。绝对系统偏差和相对系统偏差在导出第二维里系数中的影响较小。

关键词: 热力学性质, 模拟, 测量, 气相声速, 维里系数, 理想气体比热容, 定程干涉法

CLC Number:

TK123

LIU Qiang, FENG Xiaojuan, DUAN Yuanyuan. Effects of measurement deviation in gaseous speed of sound on derived thermodynamic properties[J]. CIESC Journal, DOI: 10.3969/j.issn.0438-1157.2014.04.002.

刘强, 冯晓娟, 段远源. 气相声速测量偏差对导出热力学性质的影响[J]. 化工学报, DOI: 10.3969/j.issn.0438-1157.2014.04.002.

References

[1] Moldover M R, Trusler J P M, Edwards T J, et al. Measurement of the universal gas constant R using a spherical acoustic resonator [J]. J. Res. Nat. Bur. Stand., 1988, 93(2): 85-144
[2] Jones N. The new & improved Kelvin [J]. Nature, 2009, 459(7249): 902-904
[3] Pitre L, Sparasci F, Truong D, et al. Measurement of the Boltzmann constant k_B using a quasi-spherical acoustic resonator[J]. Int. J. Thermophys., 2011, 32(9): 1825-1886
[4] Gavioso R M, Benedetto G , Albo P A G , et al. A determination of the Boltzmann constant from speed of sound measurements in helium at a single thermodynamic state [J]. Metrologia, 2010, 47: 387-409
[5] Lin H, Feng X J, Gillis K A, et al. Improved determination of the Boltzmann constant using a single, fixed-length cylindrical cavity [J]. Metrologia, 2013, 50(4): 417-432
[6] Span R. Multiparameter Equations of State —An Accurate Source of Thermodynamic Property Data [M]. Berlin: Springer, 2000
[7] Span R, Wagner W. Equations of state for technical applications(Ⅰ): Simultaneously optimized functional forms for nonpolar and polar fluids [J]. Int. J. Thermophys. , 2003, 24(1): 1-39
[8] Zhou Yong (周永), Wu Jiangtao (吴江涛). Equation of state for methyl tert-butyl ether [J]. CIESC Journal (化工学报), 2012, 63(2): 356-363
[9] Tegeler Ch, Span R, Wagner W. A new equation of state for argon covering the fluid region for temperatures from the melting line to 700 K at pressures up to 1000 MPa [J]. J. Phys. Chem. Ref. Data, 1999, 28(3):779-850
[10] Span R, Lemmon E W, Jacobsen R T, et al. A reference quality thermodynamic property formulation for nitrogen [J]. J. Phys. Chem. Ref. Data, 2000, 29(6):1361-1433
[11] Span R, Wagner W. A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa [J]. J. Phys. Chem. Ref. Data, 1996, 25(6):1509-1596
[12] Lemmon E W, McLinden M O, Wagner W. Thermodynamic properties of propane(Ⅲ): A reference equation of state for temperatures from the melting line to 650 K and pressures up to 1000 MPa [J]. J. Chem. Eng. Data, 2009, 54(12): 3141-3180
[13] Lemmon E W, Jacobsen R T. An international standard formulation for the thermodynamic properties of 1,1,1-trifluoroethane (HFC-143a) for temperatures from 161 to 450 K and pressures to 50 MPa [J]. J. Phys. Chem. Ref. Data, 2000, 29(4):521-552
[14] Esper G, Lemming W, Beckermann W, et al. Acoustic determination of ideal gas heat capacity and second virial coefficient of small hydrocarbons [J]. Fluid Phase Equilib. , 1995, 105(2): 173-192
[15] Beckermann W, Kohler F. Acoustic determination of ideal-gas heat capacity and 2nd virial coefficients of some refrigerants between 250 and 420 K [J]. Int. J. Thermophys. , 1995, 16(2):455-464
[16] Trusler J P M, Wakeham W A, Zarari M P. Second and third interaction virial coefficients of the (methane plus propane) system determined from the speed of sound [J]. Int. J. Thermophys. , 1996, 17(1):35-42
[17] Hozumi T, Sato H, Watanabe K. Ideal-gas specific heat and second virial coefficient of HFC-125 based on sound-velocity measurements [J]. Int. J. Thermophys. , 1996, 17(3):587-595
[18] Gillis K A, Moldover M R. Practical determination of gas densities from the speed of sound using square-well potentials [J]. Int. J. Thermophys. , 1996, 17(6):1305-1324
[19] Wu Jiangtao (吴江涛), Liu Zhigang (刘志刚). Determination of the second virialcoeff icent and intermolecular potential parameters of HFC125 from sound speed [J]. Journal of Xi’an Jiaotong University (西安交通大学学报), 2000, 34(11): 5-8
[20] He Maogang (何茂刚), Liu Zhigang (刘志刚), Zhao Xiaoming (赵小明), et al. Speed- of-sound measurements and idea-l gas heat capacity for 1, 1, 1-trifluoroethane [J]. Journal of Xi’an Jiaotong University (西安交通大学学报), 2001, 35(11): 1101-1104
[21] He Maogang (何茂刚), Liu Zhigang (刘志刚). Speed-of-sound, ideal-gas heat capacity, and second acoustic virial coefficient for mixing refrigerant difluoroethane (HFC152a)+difluoromethane (HCFC22) [J]. J. Therm. Sci. Tech. (热科学与技术), 2002, 1(1): 87-91
[22] Liu Qiang (刘强), Feng Xiaojuan (冯晓娟), Duan Yuanyuan (段远源). Determination of the second virial coefficient for working fluid using a cylindrical resonator [J]. CIESC Journal (化工学报), 2013, 64(8): 2711-2717
[23] Liu Qiang (刘强), Duan Yuanyuan (段远源), Feng Xiaojuan (冯晓娟), et al. Influence of impurity on acoustic measurements [J]. J. Therm. Sci. Tech. (热科学与技术), 2013, 12(1): 57-61
[24] Eubank P T, Van Peursem D, Chao Y P, et al. Random and system errors in thermophysical property measurements [J]. AIChE J., 1994, 40(9): 1580-1593
[25] Dymond J H, Marsh K N, Wilhoit R C, et al. Virial Coefficients of Pure Gases and Mixtures—Subvolume A [M]. Berlin: Springer, 2002
[26] Gillis K A. Thermodynamic properties of 2 gaseous halogenated ethers from speed-of-sound measurements- difluoromethoxy- difluoromethane and 2-difluoromethoxy-1,1,1-trifluoroethane [J]. Int. J. Thermophys., 1994, 15(5): 821-847
[27] Feng Xiaojuan (冯晓娟), Liu Qiang (刘强), Zhou Mengxia (周孟夏), et al. Experimental study on the speed of sound measurement system using a cylindrical resonator [J]. J. Eng. Thermophys. (工程热物理学报), 2012, 33(1): 7-10