Tsinghua Science and Technology Tsinghua University, China ISSN: 1007-0212 Vol. 6, Num. 5, 2001, pp. 479-483

Tsinghua Science and Technology, December 2001, 6(5), pp. 479-483

Speed of Sound and Ideal-Gas Heat Capacity at  Constant Pressure for HFC-125*

ZHANG Chang ,  DUAN Yuanyuan , WANG Xin , ZHU Mingshan

Department of Mechanical Engineering, Wuhan Institute of Science and Technology,  Wuhan 430073, China; Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

* Supported by the National Natural Science Foundation of China (No. 59906006)

Received: 2000-05-22; received: 2001-04-27

Code Number: ts01100

Abstract:

The gaseous speed of sound, the ideal-gas heat capacity at constant pressure, and the second Virial coefficient were determined for pentafluoroethane (HFC-125). A total of 49-data points of speed of sound for gaseous HFC-125 were measured for temperatures from 273 to  313 K  and pressures from 32 to 479 kPa with a cylindrical, variable-path acoustic interferometer. The ideal-gas heat capacity at constant pressure and the second acoustic Virial coefficient were determined over the temperature range from the speed of sound measurements and were correlated as functions of temperature. An analytical expression for the second Virial coefficient derived using the square-well intermolecular potential model was compared with the data.

Key words: pentafluoroethane  (HFC-125); speed of sound; ideal-gas heat capacity at constant pressure; second Virial coefficient

Introduction

According to the revisions of the Montreal Protocol, HCFCs are scheduled to be phased out before 2030. There is no single-component refrigerant to replace HCFC-22 at this moment, although some binary and ternary mixtures have been proposed, e.g., the HFC-32/125 binary system is considered to be a promising substitute to replace HCFC-22. HFC-125 is included in most of these mixture candidates, so its thermophysical properties should be accurately known.

Sound speed measurements are an important method for obtaining thermodynamic property data. The speed of sound is an important thermodynamic property, which can be used to calculate other thermodynamic properties, such as ideal-gas heat capacity, acoustic Virial coefficients, Virial coefficients, etc. In the present work, the speed of sound of gaseous HFC-125 was measured and the ideal-gas heat capacity at constant pressure was determined from the speed of sound data.

1 Working Equation

The relationship between the speed of sound, W, and the isoentropic compressibility is given by:

W² = (¶p/¶p) (1)

From thermodynamics, the acoustic Virial expansion is given by

The subscript, s, in Eq. (1) refers to an isoentropic process, M is the molar mass of the gas sample, p is the pressure gas, T is the gas temperature, R~i is the universal gas constant, g₀ is the zero-pressure limit of the heat capacity ratio, and b_a and g_a are the second and third acoustic Virial coefficients of the gas.

The speed of sound was measured 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:

W² = A₀ + A_1p +A₂p^{2 (3)}

where A₀, A₁, and A₂ are numerical constants for each isotherm. If both T and M are known, the heat capacity ratio, g₀, can be obtained. From Eqs. (2) and (3), the heat capacity ratio, g₀, can be determined from

g₀ = A₀M/RT (4)

The ideal-gas heat capacity at constant pressure, c⁰_p, can be determined from

c⁰_p = Rg₀/(g₀ -1) (5)

The second acoustic Virial coefficient of the gas, b_a, can be determined from

b_a = A₁M/g₀ (6)

2  Experimental System

The schematic of the entire measuring system is shown in Fig. 1[1]. A steel pressure vessel used to withstand the pressure was built of a cylinder with two pistons at opposite ends of the cylinder. One piston, equipped with an emitting transducer, was fixed; while the other, equipped with a reflector, could slide freely in the cylinder. The reflector also operated as a detector. The transducer was made of a piezoelectric crystal whose operating frequency was 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 gas sample pressures were measured with a deadweight tester and a differential pressure transducer with an uncertainty of ±500 Pa. During the experiment, 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 would interfere with each other when the distance between the two transducers was some integer multiple of half the wavelength. Once the changed distance, l, of the movable transducer and the number of the interference, n, were measured, the wavelength, l, could be determined according to the principle of ultrasonic interference. Then the speed of sound in the test gas sample could be determined from the wavelength, l, and the sound frequency, f. The frequency of the sound wave emitted from the piezoelectric crystal transducer was essentially constant, because the resonating frequency of the crystal was nearly independent of the environment[1]. Thus, the precision of the speed of sound determination depended 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 work. A discussion of the uncertainty for the apparatus was described in detail by Zhu et al.[1] The instrument was checked with argon and nitrogen before the HFC-125 sound speed measurements. The test results showed that the uncertainty of the measured speed of sound was less than ±0.05% and the uncertainty of the ideal-gas heat capacity at constant pressure determined from the speed of sound measurements was estimated to be less than ±0.5%.

3  Results and Analysis

The HFC-125 sample was obtained from ICI Co. and was used without further purification. The manufacturer stated that the mass purity of the sample was better than 99.98%.

A total of 49 speed of sound data points for gaseous HFC-125 were measured at temperatures from 273 to 313 K and pressures from 32 to 479 kPa, Table 1. Figure 2 shows the speed of sound variation with pressure along each isotherm. The ideal-gas heat capacity data at constant pressure, c⁰_p and the corresponding second acoustic Virial coefficient, b_a, are listed in Table 2.

The ideal-gas heat capacity at constant pressure and the second acoustic Virial coefficient were derived by regression analysis of the speed of sound data. The c⁰_p data was correlated by the following equation:

where R is the universal gas constant. Figure 3 shows the data versus temperature. Figure 4 shows the deviations of the present ideal-gas heat capacity at constant pressure and the literature data from Eq. (7).

The b_a data was correlated with

b_a/(cm³ · mol^-1) = -4385.121 68 + 20.343 23 (T/K) - 0.025 91(T/K)² (8)

Figure 5  shows the b_a data versus temperature. Figure 6 shows the deviations of the experimental b_a data from  Eq.(8) . The RMS deviation of the present b_a data from Eq. (8) was 0.441%.

The maximum deviations of the available c⁰_p data from  Eq.(7) , d_c , and the maximum deviations of the b_a data from Eq. (8), d_b, are listed in Table 3.

The thermodynamic relation between b_a and second Virial coefficient,

B, is given by

where g₀ is the ideal-gas heat capacity ratio. We adopted a semi-empirical method to solve this second order differential equation. This procedure is similar to that described in detail by Ewing  et al [5 - 7].

For the second Virial coefficient, the square-well model leads to the simple equation[8]:

Equations (9) - (11) include three parameters to be fit to the data: the co-volume b_o, the scaled well depth e/k, and the ratio of the well radius to the hard core radius r. From  Eq.(9) , the corresponding expression for b_a is

The numerical constants in this equation were determined by trial-and-error analysis using the present b_a values and the equation for c⁰_p. The regression analysis led to the parameters: b₀= 224.325 cm³·mol^-1  , e/k =250 K, and r= 1.455 679 . The second Virial coefficient, B, was correlated as

The second Virial coefficient, B, calculated from  Eq.(13)  is compared with that from a standard equation of state[9], as shown in  Fig.7 . The differences between  Eq.(13)  and literature data are less than  5.29%  for the temperature range from 230 to  435 K.

4  Conclusions

The speed of sound for gaseous HFC-125 was measured with an accuracy of approximately  ±0.05%  at the temperatures from 273 to 313 K and the pressures from 32 to 479 kPa. 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 and compared with available data. The second Virial coefficient calculated from the present speed of sound measurements compared well with the calculated results from a standard equation of state, with deviations within 5.29% for the temperature range from 230 to  435 K.

References

1. Zhu M S, Han L Z, Zhang K Z, et al. Sound velocity and ideal-gas specific heat of 1,1,1,2-tetrafluoroethane. Int J Thermophys, 1993, 14: 1039 – 1050
2. Gillis K A. Thermodynamic properties of seven gaseous halogenated hydro-carbons from acoustic measurements: CHClFCF₃ , CHF₂CF₃ , CF₃CH₃ , CHF₂CH₃ , CF₃CHFCHF₂, CF₃CH₂CF₃ , and CHF₂- CF₂CH₂F. Int J Thermophy, 1997, 18(1): 73-135.
3. Hozumi T, Sato H, Watanabe K. Ideal-gas specific heat and second Virial coefficient of HFC-125 based on sound-velocity measurements. Int J Thermophy, 1996, 17(3): 587-595.
4. Ichikawa T, Ogawa K, Sato H, et al. Speed of sound measurements for gaseous pentafluoroethane and binary mixture of pentafluoroethane +1,1,1-trifluoroethane. In: Kim M S, Ro S T, eds. Proc 5th Asian Thermophysical Properties Conference. Seoul, 1998: 535-538.
5. Ewing M B, Goodwin A R H, McGlashan M L, et al. Thermophysical properties of alkanes from speeds of sound determined using a spherical resonator, 1 Apparatus, acoustic model, and results for dimethylpropane. J Chem Thermodyn, 1987, 19: 721-739.
6. Ewing M B, Goodwin A R H, McGlashan M L, et al. Thermophysical properties of alkanes from speeds of sound determined using a spherical resonator, 2 n-butane. J Chem Thermodyn, 1988, 20: 243-256.
7. Ewing M B, Goodwin A R H, Trusler J P M. Thermophysical properties of alkanes from speeds of sound determined using a apherical resonator, 3 n-pentane. J Chem Thermodyn, 1989, 21: 867-877.
8. Hirschfelder J O, Curtiss C F, Bird R B. Molecular Theory of Gases and Liquids. New York: Wiley, 1954.
9. Piao C C, Noguchi M. An international standard equation of state for the thermodynamic properties of HFC-125 (pentafluoroethane). J Phys Chem Ref Data, 1998, 27(4): 775-806.

Copyright 2001 - Tsinghua Science and Technology

The following images related to this document are available:

Photo images