Article pubs.acs.org/jced
Ideal Gas Heat Capacity Derived from Speed of Sound Measurements in the Gaseous Phase for trans-1,3,3,3-Tetrafluoropropene Yuya Kano,* Yohei Kayukawa, and Kenichi Fujii National Institute of Advanced Industrial Science and Technology, Tsukuba Central 3, Umezono 1-1-1, Tsukuba 305-8563, Japan
Haruki Sato Department of System Design Engineering, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan
ABSTRACT: trans-1,3,3,3-Tetrafluoropropene (HFO-1234ze(E)) is considered as an alternative refrigerant in automobile air conditioning applications because of its low global warming potential. For the purpose of evaluation of thermophysical properties of HFO-1234ze(E), the speed of sound was measured in the dilute gas region in order to derive heat capacities in the ideal gas state. The speed of sound was obtained from measurements of acoustic resonance frequencies of radial modes in a spherical resonator filled with sample gas. Taking some perturbation effects into account, the speed of sound was determined with a relative uncertainty of 0.01 %. The speed of sound data were fitted to the acoustic virial equation. By extrapolating the speed of sound data on each isotherm to zero pressure, the ideal gas heat capacities at constant pressure were determined with a relative uncertainty of 0.1 %. The isobaric ideal gas heat capacities were represented by a third-order polynomial function in temperature.
1. INTRODUCTION
2. MEASUREMENT SYSTEM
trans-1,3,3,3-Tetrafluoropropene (HFO-1234ze(E)) is expected to be used as an alternative refrigerant in automobile air conditioning applications. Because the global warming potential (GWP) of HFO-1234ze(E) is estimated at 6,1 its environmental impact is much lower than that of existing hydrofluorocarbons. A coefficient of performance in an airconditioning system can be evaluated by using the thermodynamic equation of state for refrigerants. However, the ideal gas heat capacity, which is required to develop equations of state, has not yet been experimentally determined for HFO1234ze(E). The ideal gas heat capacity can be accurately derived from the speed of sound in the dilute gas region. In this work, therefore, the speed of sound in HFO-1234ze(E) was measured in the dilute gas region by means of an acoustic resonance method using a spherical resonator. By extrapolating the speed of sound data on each isotherm to zero pressure, the ideal gas heat capacity at constant pressure was determined.
In this work, we used a spherical acoustic resonator to measure speeds of sound in the gas phase. Details of the measurement apparatus and procedure have been reported elsewhere.2,3 The spherical resonator, whose inner diameter is about 100 mm, is mounted in a pressure vessel so that inside and outside pressures of the resonator should be approximately equal. This manner was applied to minimize a deformation of the resonator due to pressure. Both the resonator and the pressure vessel are made of stainless steel. Two commercially available capacitive microphones, one is a transmitter and the other is a receiver, are put onto the resonator to be flush with its inner surface wall. The transmitter microphone generates a sound wave from 1 kHz to 20 kHz into the resonator filled with sample gas, then the receiver microphone detects the sound signal traveling through the gas.
© 2013 American Chemical Society
Received: April 23, 2013 Accepted: September 20, 2013 Published: October 9, 2013 2966
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developed earlier,6 effects of the thermal boundary layer7 and deformation of the spherical resonator8 were taken into account to calculate the frequency corrections. The magnitude order of the frequency corrections caused by the thermal boundary layer, Δf t, and the shape deformation, Δfd, were Δf t/f 0,3 ≈ 0.0002 and Δfd/f 0,3 ≈ 0.00009 at 293.15 K and 100 kPa.
A schematic diagram of the experimental apparatus is shown in Figure 1. The pressure vessel is immersed in a liquid
3. MEASUREMENT RESULTS FOR SPEED OF SOUND The HFO-1234ze(E) sample was provided by Central Glass Co., Ltd. As shown in Table 1, the supplier claimed a purity of Table 1. HFO-1234ze(E) Sample Information chemical name trans-1,3,3,3tetrafluoropropene a
thermostatic bath to control the temperature of the resonator within ±1 mK. Water is used as a heat transfer medium, and its temperature is controlled by a PID controller. The temperature in the thermostatic bath is continuously measured by using a standard platinum resistance thermometer (SPRT) and a thermometer bridge. Another thinner SPRT is put into the pressure vessel to monitor the sample gas temperature. On the basis of the ITS-90,4 both of the SPRTs were calibrated before the measurements. A digital quartz pressure gauge, which is placed outside the thermostatic bath, measures the sample pressure. We measured the resonance frequencies of several radial modes, f 0,n, to obtain the speed of sound, w, in the sample gas. The frequency of the sound wave generated by the transmitter was scanned with a frequency synthesizer, then amplitude and phase-shift of the acoustic signal detected by the receiver were measured with a lock-in-amplifier. These frequency response data were nonlinearly fitted to the modified Lorentz resonance curve to determine the resonance frequency and its half-width.5 The relation between w and f 0,n is given by,6 wZ0, n 2πr
+ ΔfAC
(n = 1, 2, ...)
purity
analysis method
Central Glass Co., Ltd.
99.96 area %
GCa
Gas chromatography.
99.96 area % for HFO-1234ze(E) by a gas chromatography analysis. The sample was degassed several times and then used for measurement. The speed of sound in HFO-1234ze(E) was measured in the temperature range from (278.15 to 353.15) K and the pressure range from (25 to 400) kPa. A measurement datum for the speed of sound was derived from an average of measured resonance frequencies of the (0, 2) to (0, 6) modes. The speed of sounds obtained from these five modes agreed with a standard deviation of 0.002 %. The combined expanded uncertainties are estimated to be 0.01 % for the speed of sound, 4 mK for temperature, and 0.1 kPa for pressure, respectively, with 95 % confidence range. Measurement results for the speed of sound in HFO1234ze(E) are reported in Table 2. Relative deviations of the speed of sound data from the equation of state of McLinden et al.9 and that of Akasaka10 are shown in Figures 2 and 3, respectively. All speed of sound data agree with both the equations of state within their uncertainties, which are 0.1 % for McLinden et al. and 0.05 % for Akasaka. The root-mean-square deviations of the speed of sound data from the equations of state are 0.041 % for McLinden et al. and 0.014 % for Akasaka, both of which are larger than the measurement uncertainty in this work. Therefore, our speed of sound data could be used to improve the equations of state for HFO-1234ze(E). 3.1. Ideal Gas Heat Capacity. Using the speed of sound data, the following acoustic virial equation was formulated for each measured isotherm:
Figure 1. Schematic diagram of the experimental apparatus:3 A, spherical resonator; B, pressure vessel; C, transmitter capacitive microphone; D, detector capacitive microphone; E, transmitter adapter; F, preamplifier; G, microphone power supply; H, power amplifier; I, frequency synthesizer; J, lock in amplifier; K, quartz pressure transducer; L, digital pressure computer; M, sample bomb; N, vacuum pump; O1−2, standard platinum resistance thermometers; P1−2, thermometer bridges; Q, circulator pump; R, programmable power supply; S, manual voltage controller; T, cooler; U, circular type thermostat; V1−5, valves; W1−2, heating coils; X, internal thermostat; Y, external prethermostat.
f0, n =
source
γo (RT + Ba p + Cap2 ) (2) M o In eq 2, M, γ , R, Ba, and Ca represent molar mass, ideal gas heat capacity ratio, molar gas constant, second acoustic virial coefficient, and third acoustic virial coefficient, respectively. The value of γo, which means the ideal gas heat capacity at constant pressure, cpo, divided by that at constant volume, cvo, was determined by extrapolating eq 2 to zero pressure on each isotherm. Consequently, the value of cpo was obtained by using the thermodynamic relation of (cpo − 1/γo) = R. The determined values of cpo are tabulated in Table 3. The uncertainty of cpo is estimated to be 0.1 % with 95 % confidence range. Some estimated values of cpo for HFO-1234ze(E) are shown in Figure 4, which are calculated from several group contribution methods reported by Joback and Reid,11 Rihani w2 =
(1)
where r, Z0,n, and ΔfAC denote the inner radius of the spherical cavity which was calibrated previously with argon as a reference sample, the nth root of the equation dj0(z)/dz = 0 where j0(z) is the spherical Bessel function of zeroth order, and frequency corrections caused by some nonideal boundary conditions, respectively. On the basis of the acoustic perturbation theory 2967
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Table 2. Speed of Sound Data for HFO-1234ze(E)a T/K
p/kPa
w/m·s−1
278.150 278.150 278.150 278.150 278.150 278.150 293.150 293.150 293.150 293.150 293.150 293.150 293.150 308.150 308.150 308.150 308.150 308.150 308.150 308.150 323.150 323.150 323.150 323.150 323.150 323.150 323.150 338.150 338.150 338.150 338.150 338.150 338.150 338.150 353.150 353.148 353.149 353.151 353.150 353.149 353.150
25.29 50.54 75.59 101.07 201.50 248.53 25.34 50.41 76.01 100.83 201.65 301.97 397.84 25.32 50.42 75.99 100.45 199.82 301.89 399.59 25.60 50.42 75.85 100.84 201.05 301.37 399.95 25.35 50.36 75.28 100.97 199.59 301.58 400.19 25.39 50.57 75.57 100.60 200.56 301.71 402.92
148.092 147.189 146.277 145.329 141.397 139.419 151.962 151.199 150.407 149.618 146.316 142.793 139.157 155.712 155.050 154.370 153.700 150.941 147.955 144.929 159.363 158.779 158.192 157.599 155.209 152.716 150.164 162.917 162.414 161.911 161.387 159.336 157.160 154.984 166.414 165.964 165.492 165.045 163.239 161.367 159.447
Figure 2. Relative deviations of measured speed of sound from the equation of state of McLinden et al.9 × , 278.15 K; ○, 293.15 K; △, 308.15 K; □, 323.15 K; ◊, 338.15 K; and +, 353.15 K.
Figure 3. Relative deviations of measured speed of sound from the equation of state of Akasaka.10 × , 278.15 K; ○, 293.15 K; △, 308.15 K; □, 323.15 K; ◊, 338.15 K; and +, 353.15 K.
Table 3. Ideal Gas Heat Capacity of HFO-1234ze(E)a
a
The expanded uncertainties are U(T) = 4 mK, U(p) = 0.1 kPa, and U(w) = 0.0001·w (level of confidence = 0.95).
⎛ T ⎞i c ∑ i⎜ ⎟ T i=0 ⎝ c ⎠
cpo/J·mol−1·K−1
278.150 293.150 308.150 323.150 338.150 353.150
96.46 99.54 102.46 105.28 108.14 110.52
a The expanded uncertainty is U(cpo) = 0.001·cpo (level of confidence = 0.95).
and Doraiswamy,12 and Yoneda.13 Additionally, the values of cpo of this work are plotted in Figure 4 for comparison. The relative differences between the determined cpo values and the estimated ones are 9.0 % for Joback and Reid, 9.7 % for Rihani and Doraiswamy, and 1.4 % for Yoneda at 278.15 K, whereas 4.1 % for Joback and Reid, 6.1 % for Rihani and Doraiswamy, and 1.2 % for Yoneda at 353.15 K. The determined cpo values were correlated by a temperature dependent polynomial function,
cpo data shown in Table 3. Equation 3 with the coefficients of Table 4 reproduces our ideal gas heat capacities with a standard deviation of 0.09 %.
4. CONCLUSIONS The speed of sound in the dilute gas region of HFO-1234ze(E) was measured by means of a spherical acoustic resonator on six isotherms from (278.15 to 353.15) K with a combined expanded uncertainty of 0.01 %. Compared to the existing equations of state for HFO-1234ze(E), all of the speed of sound data agreed with the equations within their uncertainties. Ideal gas heat capacities at constant pressure were derived from the speed of sound data with an expanded uncertainty of 0.1 %.
3
cpo =
T/K
(3)
where Tc denotes the critical temperature of HFO-1234ze(E) reported by Higashi et al. to be 382.51 K.14 Table 4 reports the coefficient values of ci determined by linearly fitting eq 3 to the 2968
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(3) Kano, Y.; Kayukawa, Y.; Fujii, K.; Sato, H. Ideal-gas heat capacity for 2,3,3,3-tetrafluoropropene (HFO-1234yf) determined from speedof-sound measurements. Int. J. Thermophys. 2010, 31, 2051−2058. (4) Preston-Thomas, H. The international temperature scale of 1990 (ITS-90). Metrologia 1990, 27, 3−10. (5) Mehl, J. B. Analysis of resonance standing-wave measurements. J. Acoust. Soc. Am. 1978, 64, 1523−1525. (6) Moldover, M. R.; Trusler, J. P. M.; Edwards, T. J.; Mehl, J. B.; Davis, R. S. Measurement of the universal gas constant R using a spherical acoustic resonator. J. Res. Natl. Bur. Stand 1988, 93, 85−144. (7) Ewing, M. B.; Goodwin, A. R. H.; McGlashman, M. L.; Trusler, J. P. M. Thermophysical properties of alkanes from speeds of sound determined using a spherical resonator. I. Apparatus, acoustic model, and results for dimethylpropane. J. Chem. Thermodyn. 1987, 19, 721− 739. (8) Mehl, J. B. Acoustic resonance frequencies of deformed spherical resonators. J. Acoust. Soc. Am. 1982, 71, 1109−1113. (9) McLinden, M. O.; Thol, M.; Lemmon, E. W. In Thermodynamic properties of trans-1,3,3,3-tetrafluoropropene [R1234ze(E)]: measurements of density and vapor pressure and a comprehensive equation of state. Proceedings of International Refrigeration and Air Conditioning Conference, Lafayette, IN, 2010; paper no. 1041. (10) Akasaka, R. New fundamental equations of state with a common functional form for 2,3,3,3-tetrafluoropropene (R-1234yf) and trans1,3,3,3-tetrafluoropropene (R-1234ze(E)). Int. J. Thermophys. 2011, 32, 1125−1147. (11) Joback, K. G.; Reid, R. C. Estimation of pure-component properties from group-contributions. Chem. Eng. Commun. 1987, 57, 233−243. (12) Rihani, D. N.; Doraiswamy, L. K. Estimation of heat capacity of organic compounds from group contributions. Ind. Eng. Chem. Fundamen. 1965, 4, 17−21. (13) Yoneda, Y. An estimation of the thermodynamic properties of organic compounds in the ideal gas state. I. Acyclic compounds and cyclic compounds with a ring of cyclopentane, cyclohexane, benzene, or naphthalene. Bull. Chem. Soc. Jpn. 1979, 52, 1297−1314. (14) Higashi, Y.; Tanaka, K.; Ichikawa, T. Critical parameters and saturated densities in the critical region for trans-1,3,3,3-tetrafluoropropene (HFO-1234ze(E). J. Chem. Eng. Data 2010, 55, 1594−1597.
Figure 4. Comparison of the determined cpo values with estimated values from group contribution methods: ○, this work; , correlation function (eq 3); −·−, Joback and Reid;11 −··, Rihani and Doraiswamy;12 ---, Yoneda.13
Table 4. Values of ci in Equation 3 i
ci/J·mol−1·K−1
0 1 2 3
55.389 10.784 99.250 −49.880
The determined cpo values differ by up to 10 % from estimated values by group contribution methods. On the basis of the determined ideal gas heat capacities, a temperature correlating equation was formulated, which reproduces the determined values with a standard deviation of 0.09 %. This cpo equation can contribute to the improvement of existing equations of state for HFO-1234ze(E).
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Funding
This work was supported by a joint research program with Kyushu University, Saga University, Iwaki Meisei University, Kansai Electric Power Co., Inc., Hokkaido Electric Power Co., Inc., Hitachi Appliances, Inc., Toshiba Carrier Corp., Central Glass Co., Ltd., and Showa Tansan Co., Ltd. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank Central Glass Co., Ltd. for supplying the high purity HFO-1234ze(E) sample. REFERENCES
(1) Karber, K. M.; Abdelaziz, O.; Vineyard, E. A. In Experimental performance of R-1234yf and R-1234ze as drop-in replacements for R134a in domestic refrigerators. Proceedings of International Refrigeration and Air Conditioning Conference, Lafayette, IN, 2012; paper no. 2241. (2) Hozumi, T.; Sato, H.; Watanabe, K. Speed-of-sound measurements in gaseous binary refrigerant mixtures of difluoromethane (R32) + 1,1,1,2-tetrafluoroethane (R-134a). J. Chem. Eng. Data 1997, 42, 541−547. 2969
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