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Speed of Sound, Ideal-Gas Heat Capacity at Constant Pressure, And http://www.paper.edu.cn Fluid Phase Equilibria 178 (2001) 73–85 Speed of sound, ideal-gas heat capacity at constant pressure, and second virial coefficients of HFC-227ea Chang Zhang1, Yuan-Yuan Duan∗, Lin Shi, Ming-Shan Zhu, Li-Zhong Han Department of Thermal Engineering, Tsinghua University, Beijing 100084, PR China Received 5 April 2000; accepted 3 October 2000 Abstract The speed of sound of the gaseous 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) was measured for tempera- tures 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. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Ideal state function; Data; Speed of sound; Second virial coefficients; Heat capacity; 1,1,1,2,3,3,3-Heptafluoropropane; HFC-227ea 1. Introduction 1,1,1,2,3,3,3-Heptafluoropropane (HFC-227ea) is a recently introduced, commercially available hydrofluorocarbon (HFC) and is useful in fire suppression, refrigeration, sterilization and propellant applications. It can be used as an alternative to halon, and blends containing HFC-227ea are potential alternatives to HCFC-22 and R502. Effective use of HFC-227ea requires that the thermodynamic and transport properties be accurately measured, but there are few data available, especially no available speed of sound data. Wirbser et al. [1] measured the specific heat capacity and Joule–Thomson coefficient of HFC-227ea; Salvi-Narkhede et al. [2] measured the vapor pressure, liquid molar volumes and critical properties; Park [3] measured the gaseous PVT properties with a Burnett apparatus at five temperatures; Klomfar et al. [4] measured the liquid PVT properties; Robin [5] listed the thermophysical properties of ∗ Corresponding author. Tel.: +86-10-62788608; fax: +86-10-62770209. E-mail address: [email protected] (Y.-Y. Duan). 1 Visiting Scholar from Wuhan Institute of Science and Technology, Wuhan 430073, PR China. 0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S0378-3812(00)00477-5 转载 中国科技论文在线 http://www.paper.edu.cn 74 C. Zhang et al. / Fluid Phase Equilibria 178 (2001) 73–85 HFC-227ea including estimated transport properties; Defibaugh and Moldover [6] measured the liquid PVT behavior and the saturated liquid density; Weber [7] measured the vapor pressure of HFC-227ea; Laesecke and Hafer [8] measured the viscosity of HFC-227ea with a coiled capillary viscometer at low temperature and a straight capillary viscometer at high temperature; Pátek et al. [9] measured PVT properties of HFC-227ea with a Burnett apparatus at temperatures of 393 and 423 K; Shi et al. [10] mea- sured the vapor pressure; Liu et al. [11,12] measured the saturated liquid viscosity and gaseous thermal conductivity; Shi et al. [13] measured PVT properties of HFC-227ea. This paper reports the experimental results of the speed of sound of the gaseous HFC-227ea mea- sured for temperatures from 273.15 to 333.215 K and pressures from 26 to 315 kPa, with a cylindrical, variable-path acoustic interferometer operating at 156.252 kHz. 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 present ideal-gas heat capacity data at constant pressure were compared with the available data [1]. Second virial coefficients calculated from the present speed of sound measurements were compared with results from the literature determined from PVT measurements [3,9,13]. The sample of HFC-227ea was obtained from Shanghai Huiyou Chemical Corp., China and was used without further purification. The manufacturer stated that the water content was less than 20 ppm. From the gas chromatographic analysis, the purity of the sample was better than 99.9 mol%. 2. Working equation The relationship between the speed of sound W and the isoentropic compressibility is given by ∂p W 2 = (1) ∂ρ s From thermodynamics, the acoustic virial expansion is given by γ RT β γ W 2 = 0 1 + a p + a p2 +··· (2) M RT RT The subscript s in Eq. (1) refers to an isoentropic process, M is the molar mass of the sample gas, p the gas pressure, T the gas temperature, R the universal gas constant, γ 0 the zero-pressure limit of the heat capacity ratio and βa and γ a the second and third acoustic virial coefficients of the gas. The speed of sound was measured as a function of pressure at constant temperatures and at low pressures. The measured speed of sound results along each isotherm were correlated as a function of pressure with the following function 2 2 W = A0 + A1p + A2p (3) where A0, A1 and A2 are numerical constants for each isotherm. If both T and M are known, the heat capacity ratio γ 0 can be obtained. From Eqs. (2) and (3), the heat capacity ratio γ 0 can be determined from γ0 = A0M/RT (4) 中国科技论文在线 http://www.paper.edu.cn C. Zhang et al. / Fluid Phase Equilibria 178 (2001) 73–85 75 0 The ideal-gas heat capacity at constant pressure Cp can be determined from Rγ 0 0 Cp = (5) γ0 − 1 The second acoustic virial coefficients of the gas βa can be determined from A1M βa = (6) γ0 3. Experimental instrument The experimental instrument, which was described previously [14–16], will be introduced again briefly here. The schematic of the entire measuring system is shown in Fig. 1. A steel pressure vessel was used in the instrument to withstand the pressure. The vessel consisted of a cylinder with two pistons at opposite ends of the cylinder. One piston equipped with an emitting transducer was fixed, while the other one Fig. 1. Schematic of the speed of sound measuring system: (1) main body; (2) thermostat; (3 and 4) displacement measuring system; (5) generator; (6) amplifier; (7) frequency meter; (8) wave indicator; (9) phase detector; (10) temperature acquisition unit; (11) three-way valve; (12) gas sample bottle; (13) temperature controller; (14) vacuum pump; (15) vacuum meter; (16) differential pressure detector; (17) digital pressure detector; (18) dead weight tester. 中国科技论文在线 http://www.paper.edu.cn 76 C. Zhang et al. / Fluid Phase Equilibria 178 (2001) 73–85 equipped with a reflector, could slide freely in the cylinder. The reflector also operated as a detector. The operating frequency of the emitting transducer was determined by a frequency generator made of piezoelectric crystal, which is placed outside of the thermostat, so the frequency is a constant and does not change with the experimental temperature, pressure and fluid property. The operating frequency is 156.252 kHz with an uncertainty of 1 Hz. The vessel was suspended in a stirred fluid bath during the course of the experiment. The temperature uncertainty was less than 10 mK. The pressures of the gas sample were measured with a dead weight tester, a digital pressure gauge and a differential pressure transducer with an uncertainty of 200 Pa. During the experiments, the movable transducer was slid relative to the fixed transducer. The wave emitted by the fixed transducer and the wave reflected by the free transducer will interfere with each other, when the distance between the two transducers is same integer multiple of half the wavelength. Once the changed distance l of the movable transducer and the number of the interference N are measured, the wavelength λ can be determined according to the principle of ultrasonic interference. Then the speed of sound in the test gas sample can be determined with the wavelength λ and the sound frequency f. The frequency of the sound wave emitted from the piezoelectric crystal transducer is essentially constant, because the resonating frequency of the crystal is nearly independent of the environment [14]. Thus, the precision of the determination of the speed of sound depends mainly on the precision of the wavelength measurement. The precision of the wavelength measurements was improved by moving the piston more than 30 wavelengths in this study. A discussion of the uncertainty in the experiment has been described in detail in the previous publication [14]. The instrument was checked with argon and nitrogen before HFC-227ea speed of sound measurements; the measured results showed that the uncertainty of the speed of sound measured with this instrument is less than 0.05% and the uncertainty of the ideal-gas heat capacity at constant pressure determined with the measured speed of sound is estimated less than 0.5%. 4. Results and analysis Wavelength measurements for HFC-227ea were made along 10 isotherms between 273.15 and 333.215 K. The maximum pressure along the isotherms was about 315 kPa. The speed of sound of HFC-227ea was obtained from the corrected wavelengths together with the fixed frequency. The measurement values were corrected for diffraction and guided mode dispersion [17] using the empirical equation " # λ 4 λ 6 1λ = λ α + α dg 2 D 3 D (7) where λ is the wavelength, D the diameter of the resonance tube (75.04 mm in this study), α2 = 0.3806 and α3 = 79.74 [14]. The measured speed of sound was corrected for absorption dispersion using the Kirchhoff Helmholtz (boundary layer) absorption coefficient αKH and the classical absorption coefficient αCL.
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