Ideal Gas Heat Capacity Derived from Speed of Sound Measurementsin the Gaseous Phase for trans-1,3,3,3-TetrafluoropropeneYuya 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 airconditioning applications because of its low global warming potential. For the purpose of evaluation of thermophysical propertiesof HFO-1234ze(E), the speed of sound was measured in the dilute gas region in order to derive heat capacities in the ideal gasstate. The speed of sound was obtained from measurements of acoustic resonance frequencies of radial modes in a sphericalresonator filled with sample gas. Taking some perturbation effects into account, the speed of sound was determined with arelative uncertainty of 0.01 %. The speed of sound data were fitted to the acoustic virial equation. By extrapolating the speed ofsound data on each isotherm to zero pressure, the ideal gas heat capacities at constant pressure were determined with a relativeuncertainty of 0.1 %. The isobaric ideal gas heat capacities were represented by a third-order polynomial function in temperature.

1. INTRODUCTION

trans-1,3,3,3-Tetrafluoropropene (HFO-1234ze(E)) is expectedto be used as an alternative refrigerant in automobile airconditioning applications. Because the global warming potential(GWP) of HFO-1234ze(E) is estimated at 6,1 its environ-mental impact is much lower than that of existing hydro-fluorocarbons. A coefficient of performance in an air-conditioning system can be evaluated by using the thermody-namic equation of state for refrigerants. However, the ideal gasheat capacity, which is required to develop equations of state,has not yet been experimentally determined for HFO-1234ze(E). The ideal gas heat capacity can be accuratelyderived from the speed of sound in the dilute gas region. In thiswork, therefore, the speed of sound in HFO-1234ze(E) wasmeasured in the dilute gas region by means of an acousticresonance method using a spherical resonator. By extrapolatingthe speed of sound data on each isotherm to zero pressure, theideal gas heat capacity at constant pressure was determined.

2. MEASUREMENT SYSTEM

In this work, we used a spherical acoustic resonator to measurespeeds of sound in the gas phase. Details of the measurementapparatus and procedure have been reported elsewhere.2,3 Thespherical resonator, whose inner diameter is about 100 mm, ismounted in a pressure vessel so that inside and outsidepressures of the resonator should be approximately equal. Thismanner was applied to minimize a deformation of the resonatordue to pressure. Both the resonator and the pressure vessel aremade of stainless steel. Two commercially available capacitivemicrophones, 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 1kHz to 20 kHz into the resonator filled with sample gas, thenthe receiver microphone detects the sound signal travelingthrough the gas.

Received: April 23, 2013Accepted: September 20, 2013Published: October 9, 2013

Article

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© 2013 American Chemical Society 2966 dx.doi.org/10.1021/je4004564 | J. Chem. Eng. Data 2013, 58, 2966−2969

A schematic diagram of the experimental apparatus is shownin Figure 1. The pressure vessel is immersed in a liquid

thermostatic bath to control the temperature of the resonatorwithin ±1 mK. Water is used as a heat transfer medium, and itstemperature is controlled by a PID controller. The temperaturein the thermostatic bath is continuously measured by using astandard platinum resistance thermometer (SPRT) and athermometer bridge. Another thinner SPRT is put into thepressure vessel to monitor the sample gas temperature. On thebasis of the ITS-90,4 both of the SPRTs were calibrated beforethe measurements. A digital quartz pressure gauge, which isplaced outside the thermostatic bath, measures the samplepressure.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 transmitterwas scanned with a frequency synthesizer, then amplitude andphase-shift of the acoustic signal detected by the receiver weremeasured with a lock-in-amplifier. These frequency responsedata were nonlinearly fitted to the modified Lorentz resonancecurve to determine the resonance frequency and its half-width.5

The relation between w and f 0,n is given by,6

π= + Δ =f

wZ

rf n

2( 1, 2, ...)n

n0,

0,AC (1)

where r, Z0,n, and ΔfAC denote the inner radius of the sphericalcavity which was calibrated previously with argon as a referencesample, the nth root of the equation dj0(z)/dz = 0 where j0(z)is the spherical Bessel function of zeroth order, and frequencycorrections caused by some nonideal boundary conditions,respectively. On the basis of the acoustic perturbation theory

developed earlier,6 effects of the thermal boundary layer7 anddeformation of the spherical resonator8 were taken into accountto calculate the frequency corrections. The magnitude order ofthe frequency corrections caused by the thermal boundarylayer, 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.

3. MEASUREMENT RESULTS FOR SPEED OF SOUNDThe HFO-1234ze(E) sample was provided by Central GlassCo., Ltd. As shown in Table 1, the supplier claimed a purity of

99.96 area % for HFO-1234ze(E) by a gas chromatographyanalysis. The sample was degassed several times and then usedfor measurement. The speed of sound in HFO-1234ze(E) wasmeasured in the temperature range from (278.15 to 353.15) Kand the pressure range from (25 to 400) kPa. A measurementdatum for the speed of sound was derived from an average ofmeasured resonance frequencies of the (0, 2) to (0, 6) modes.The speed of sounds obtained from these five modes agreedwith a standard deviation of 0.002 %. The combined expandeduncertainties 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 HFO-

1234ze(E) are reported in Table 2. Relative deviations of thespeed of sound data from the equation of state of McLinden etal.9 and that of Akasaka10 are shown in Figures 2 and 3,respectively. All speed of sound data agree with both theequations of state within their uncertainties, which are 0.1 % forMcLinden et al. and 0.05 % for Akasaka. The root-mean-squaredeviations of the speed of sound data from the equations ofstate are 0.041 % for McLinden et al. and 0.014 % for Akasaka,both of which are larger than the measurement uncertainty inthis work. Therefore, our speed of sound data could be used toimprove the equations of state for HFO-1234ze(E).

3.1. Ideal Gas Heat Capacity. Using the speed of sounddata, the following acoustic virial equation was formulated foreach measured isotherm:

γ= + +wM

RT B p C p( )o

2a a

2(2)

In eq 2,M, γo, R, Ba, and Ca represent molar mass, ideal gas heatcapacity ratio, molar gas constant, second acoustic virialcoefficient, and third acoustic virial coefficient, respectively.The value of γo, which means the ideal gas heat capacity atconstant pressure, cp

o, divided by that at constant volume, cvo,

was determined by extrapolating eq 2 to zero pressure on eachisotherm. Consequently, the value of cp

o was obtained by usingthe thermodynamic relation of (cp

o − 1/γo) = R. Thedetermined values of cp

o are tabulated in Table 3. Theuncertainty of cp

o is estimated to be 0.1 % with 95 % confidencerange.Some estimated values of cp

o for HFO-1234ze(E) are shownin Figure 4, which are calculated from several groupcontribution methods reported by Joback and Reid,11 Rihani

Figure 1. Schematic diagram of the experimental apparatus:3 A,spherical resonator; B, pressure vessel; C, transmitter capacitivemicrophone; D, detector capacitive microphone; E, transmitteradapter; F, preamplifier; G, microphone power supply; H, poweramplifier; I, frequency synthesizer; J, lock in amplifier; K, quartzpressure 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, programmablepower supply; S, manual voltage controller; T, cooler; U, circular typethermostat; V1−5, valves; W1−2, heating coils; X, internal thermostat;Y, external prethermostat.

Table 1. HFO-1234ze(E) Sample Information

chemical name source purityanalysismethod

trans-1,3,3,3-tetrafluoropropene

Central Glass Co.,Ltd.

99.96 area % GCa

aGas chromatography.

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and Doraiswamy,12 and Yoneda.13 Additionally, the values of cpo

of this work are plotted in Figure 4 for comparison. The relativedifferences between the determined cp

o values and theestimated ones are 9.0 % for Joback and Reid, 9.7 % forRihani and Doraiswamy, and 1.4 % for Yoneda at 278.15 K,whereas 4.1 % for Joback and Reid, 6.1 % for Rihani andDoraiswamy, and 1.2 % for Yoneda at 353.15 K. Thedetermined cp

o values were correlated by a temperaturedependent polynomial function,

∑==

⎛⎝⎜

⎞⎠⎟c

TT

cpo

ii

c

i

0

3

(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 thecoefficient values of ci determined by linearly fitting eq 3 to the

cpo data shown in Table 3. Equation 3 with the coefficients of

Table 4 reproduces our ideal gas heat capacities with a standarddeviation of 0.09 %.

4. CONCLUSIONSThe speed of sound in the dilute gas region of HFO-1234ze(E)was measured by means of a spherical acoustic resonator on sixisotherms from (278.15 to 353.15) K with a combinedexpanded uncertainty of 0.01 %. Compared to the existingequations of state for HFO-1234ze(E), all of the speed ofsound data agreed with the equations within their uncertainties.Ideal gas heat capacities at constant pressure were derived fromthe speed of sound data with an expanded uncertainty of 0.1 %.

Table 2. Speed of Sound Data for HFO-1234ze(E)a

T/K p/kPa w/m·s−1

278.150 25.29 148.092278.150 50.54 147.189278.150 75.59 146.277278.150 101.07 145.329278.150 201.50 141.397278.150 248.53 139.419293.150 25.34 151.962293.150 50.41 151.199293.150 76.01 150.407293.150 100.83 149.618293.150 201.65 146.316293.150 301.97 142.793293.150 397.84 139.157308.150 25.32 155.712308.150 50.42 155.050308.150 75.99 154.370308.150 100.45 153.700308.150 199.82 150.941308.150 301.89 147.955308.150 399.59 144.929323.150 25.60 159.363323.150 50.42 158.779323.150 75.85 158.192323.150 100.84 157.599323.150 201.05 155.209323.150 301.37 152.716323.150 399.95 150.164338.150 25.35 162.917338.150 50.36 162.414338.150 75.28 161.911338.150 100.97 161.387338.150 199.59 159.336338.150 301.58 157.160338.150 400.19 154.984353.150 25.39 166.414353.148 50.57 165.964353.149 75.57 165.492353.151 100.60 165.045353.150 200.56 163.239353.149 301.71 161.367353.150 402.92 159.447

aThe expanded uncertainties are U(T) = 4 mK, U(p) = 0.1 kPa, andU(w) = 0.0001·w (level of confidence = 0.95).

Figure 2. Relative deviations of measured speed of sound from theequation 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 theequation of state of Akasaka.10 × , 278.15 K; ○, 293.15 K; △, 308.15K; □, 323.15 K; ◊, 338.15 K; and +, 353.15 K.

Table 3. Ideal Gas Heat Capacity of HFO-1234ze(E)a

T/K cpo/J·mol−1·K−1

278.150 96.46293.150 99.54308.150 102.46323.150 105.28338.150 108.14353.150 110.52

aThe expanded uncertainty is U(cpo) = 0.001·cp

o (level of confidence =0.95).

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The determined cpo values differ by up to 10 % from estimated

values by group contribution methods. On the basis of thedetermined ideal gas heat capacities, a temperature correlatingequation was formulated, which reproduces the determinedvalues with a standard deviation of 0.09 %. This cp

o equationcan contribute to the improvement of existing equations ofstate for HFO-1234ze(E).

■ AUTHOR INFORMATIONCorresponding Author*E-mail: yuya-kano@aist.go.jp.FundingThis work was supported by a joint research program withKyushu University, Saga University, Iwaki Meisei University,Kansai Electric Power Co., Inc., Hokkaido Electric Power Co.,Inc., Hitachi Appliances, Inc., Toshiba Carrier Corp., CentralGlass Co., Ltd., and Showa Tansan Co., Ltd.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors thank Central Glass Co., Ltd. for supplying thehigh purity HFO-1234ze(E) sample.

■ REFERENCES(1) Karber, K. M.; Abdelaziz, O.; Vineyard, E. A. In Experimentalperformance of R-1234yf and R-1234ze as drop-in replacements for R-134a in domestic refrigerators. Proceedings of International Refriger-ation and Air Conditioning Conference, Lafayette, IN, 2012; paper no.2241.(2) Hozumi, T.; Sato, H.; Watanabe, K. Speed-of-sound measure-ments in gaseous binary refrigerant mixtures of difluoromethane (R-32) + 1,1,1,2-tetrafluoroethane (R-134a). J. Chem. Eng. Data 1997, 42,541−547.

(3) Kano, Y.; Kayukawa, Y.; Fujii, K.; Sato, H. Ideal-gas heat capacityfor 2,3,3,3-tetrafluoropropene (HFO-1234yf) determined from speed-of-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 aspherical 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 sounddetermined 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 sphericalresonators. J. Acoust. Soc. Am. 1982, 71, 1109−1113.(9) McLinden, M. O.; Thol, M.; Lemmon, E. W. In Thermodynamicproperties of trans-1,3,3,3-tetrafluoropropene [R1234ze(E)]: measure-ments of density and vapor pressure and a comprehensive equation of state.Proceedings of International Refrigeration and Air ConditioningConference, Lafayette, IN, 2010; paper no. 1041.(10) Akasaka, R. New fundamental equations of state with a commonfunctional form for 2,3,3,3-tetrafluoropropene (R-1234yf) and trans-1,3,3,3-tetrafluoropropene (R-1234ze(E)). Int. J. Thermophys. 2011,32, 1125−1147.(11) Joback, K. G.; Reid, R. C. Estimation of pure-componentproperties from group-contributions. Chem. Eng. Commun. 1987, 57,233−243.(12) Rihani, D. N.; Doraiswamy, L. K. Estimation of heat capacity oforganic compounds from group contributions. Ind. Eng. Chem.Fundamen. 1965, 4, 17−21.(13) Yoneda, Y. An estimation of the thermodynamic properties oforganic compounds in the ideal gas state. I. Acyclic compounds andcyclic 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 andsaturated densities in the critical region for trans-1,3,3,3-tetrafluor-opropene (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; , correlationfunction (eq 3); −·−, Joback and Reid;11 −··, Rihani andDoraiswamy;12 ---, Yoneda.13

Table 4. Values of ci in Equation 3

i ci/J·mol−1·K−1

0 55.3891 10.7842 99.2503 −49.880

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