Measurements of the Speed of Sound in the Refrigerants HFC227ea

Article pubs.acs.org/jced

Measurements of the Speed of Sound in the Refrigerants HFC227ea and HFC365mfc in the Liquid Region K. Meier*,† and S. Kabelac‡ Institut für Thermodynamik, Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg, Holstenhofweg 85, D-22043 Hamburg, Germany ABSTRACT: Accurate measurements of the speed of sound in the two refrigerants HFC227ea and HFC365mfc have been carried out by a doublepath-length pulse-echo technique. The measured data for HFC227ea cover parts of the liquid and supercritical regions in the temperature range from (280 to 420) K with pressures up to 50 MPa, while those for HFC365mfc extend in the liquid region from (250 to 420) K with pressures to 100 MPa. The measurement uncertainties amount to 3 mK for temperature, 0.01 % for pressures below 10 MPa, 0.005 % for pressures between (10 and 100) MPa, 0.03 % for speed of sound in HFC227ea, and 0.04 % for speed of sound in HFC365mfc. Comparisons with literature data demonstrate the high accuracy of the measurements.

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INTRODUCTION Both HFC227ea (1,1,1,2,3,3,3-heptafluoropropane) and HFC365mfc (1,1,1,3,3-pentafluorobutane) are hydrofluorocarbons with zero ozone depletion potential. HFC227ea is nonflammable, whereas HFC365mfc is flammable. HFC227ea is mainly used as a pure substance as a propellant in aerosol sprays in medical technology. Furthermore, HFC227ea can be used as a low vapor pressure refrigerant in refrigeration and airconditioning applications with high condensation temperatures. HFC365mfc is predominantly used as the main component in binary mixtures with 7 % or 13 % by weight HFC227ea, which are used as blowing agents in the production of polyurethane foams for insulation purposes. Mixtures of HFC365mfc and HFC227ea are also considered as possible working fluids in high temperature heat pump systems. With the addition of HFC227ea, the flammability of HFC365mfc is reduced. For designing and optimizing equipment for these applications, accurate fundamental equations of state, from which all thermodynamic properties can be calculated, are desirable. As part of the experimental data basis for the optimization process of fundamental equations of state, accurate speed of sound data are required. Five data sets for the speed of sound in HFC227ea are available in the literature. The data of Benedetto et al.1 and Zhang et al.2 cover a large part of the gas region at subcritical temperatures. Gruzdev et al.3 measured the speed of sound in the gas and liquid region. The liquid data cover the temperature range between (273 and 383) K but are restricted to moderate pressures below 3.5 MPa. Fröba et al.4 measured the speed of sound in the saturated vapor and liquid, while the data of Pires et al.5 cover the liquid region in the temperature range between (248 and 333) K with pressures up to 65 MPa. At present, there are no speed of sound data in the liquid region at high pressures above 333 K, and © 2013 American Chemical Society

also the speed of sound at supercritical temperatures has not yet been measured. Only a very limited number of data for the thermophysical properties of HFC365mfc is available in the literature. In particular, only one data set has been published for the speed of sound by Fröba et al.6 In that work, the dynamic surface light scattering technique was employed to measure the speed of sound in the saturated gas and liquid. Scott7 measured the speed of sound in the gas phase between (315 and 345) K. These data have not yet been published. The speed of sound in the single phase liquid region has not yet been measured. Our measurements in HFC227ea and HFC365mfc were carried out to provide accurate speed of sound data in the liquid regions of both fluids. They form part of a larger program in our laboratory to measure the speed of sound in several pure fluids.8,9 In parallel with this work, new fundamental equations of state for HFC227ea and HFC365mfc were developed by McLinden and Lemmon.10 In the optimization process of these equations of state, our speed of sound data were used as part of the experimental data sets, to which the equations of state were fitted.

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EXPERIMENTAL PROCEDURE Our speed of sound instrument has been described in detail in ref 11. The measurement principle of our acoustic sensor is a double-path-length pulse-echo technique, which was introduced by Muringer et al.12 Our sensor employs a piezoelectric quartz crystal as a sound emitter and receiver, which is operated at its resonance frequency of 8 MHz. The acoustic path length in the sensor and the thermal expansion coefficient of the sensor Received: October 28, 2012 Accepted: December 28, 2012 Published: January 22, 2013 446

dx.doi.org/10.1021/je301164d | J. Chem. Eng. Data 2013, 58, 446−454

Journal of Chemical & Engineering Data

Article

material were determined by calibration measurements with liquid water at ambient pressure as described in detail in ref 11. In the analysis of the measurements, corrections for changes of the distances in the speed of sound sensor with temperature, for compression of the sensor with pressure, and for diffraction effects are applied. The uncertainty of the speed of sound measurement is u(c) = (7·10−5 + 2.5·10−7·p/MPa)·c, excluding contributions from sample impurities and from measurement uncertainties of temperature and pressure. In this equation, c is the speed of sound, p denotes pressure, and the second term accounts for the uncertainty of the sensor compression with pressure. The speed of sound sensor is mounted in a pressure vessel, which is thermostatted in a circulating liquid-bath thermostat. The temperature inside the pressure vessel is kept constant within 0.5 mK. The temperature was measured by a Pt25 sensor calibrated on the ITS-90, which was located in the wall of the pressure vessel with an estimated uncertainty of 3 mK. The pressure in the pressure vessel was measured with two nitrogenoperated gas pressure balances with the measurement range of

(5 to 100) MPa. The pressure balances were coupled to the sample liquid via a differential pressure null indicator (Ruska membrane type cell). The uncertainty of the pressure measurement is estimated to be 0.01 % below 10 MPa and 0.005 % between 10 and 100 MPa. These measurement uncertainties refer to a 95 % confidence level.

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MATERIALS The HFC227ea sample was provided by Solvay Fluor GmbH and had a volume purity better than 99.5 % according to the manufacturer’s specifications (see Table 1). The sample was degassed and examined by gas chromatography. Its volume purity was found to be better than 99.975 %. Besides the main HFC227ea peak, four peaks with 0.010 %, 0.008 %, 0.006 %, and 0.001 % in area fraction were detected. The peak with 0.008 % could be identified as water, and no nitrogen or oxygen was detected. The nature of the remaining impurities was not identified. It is assumed that they are other hydrofluorocarbons, which occur as byproducts in the production process. The contribution of the impurities to the uncertainty of the speed of sound data is estimated to be smaller than 0.01 %. The reproducibility of the speed of sound measurements at the same state point after pressure and temperature cycles was within 0.01 %. In our measurements with propane a much better reproducibility of 0.002 % was achieved.9 The lower reproducibility is probably due to a Viton O-ring seal in a hand pump, which is used to change the pressure in the pressure vessel. It is assumed that small amounts of the Viton elastomer material dissolve in HFC227ea or even react with it, which adds small impurities to the sample and, thus, causes small changes of the speed of sound. Including the sample impurities and the measurement reproducibility, the uncertainty of the speed of sound is estimated to be u(c) = (2.7·10−4 + 2.5·10−7·p/MPa)·c. The uncertainty contributions to the speed of sound due to the uncertainties of the temperature and pressure measurements are estimated by the fundamental equation of state of McLinden and Lemmon.10 They are lower than 0.003 % and 0.002 %, respectively. For the measurements at the lowest pressures on the supercritical isotherms, the contribution from the uncertainty of the pressure measurement is higher, amounting to 0.01 %. Taking these additional contributions into account, the combined uncertainty of the speed of sound becomes Uc(c) = (3.2·10−4 + 2.5·10−7·p/MPa)·c. At the lowest pressures on the highest subcritical isotherms and on supercritical isotherms, 3.2·10−4 has to be replaced by 4.0·10−4. The HFC365mc sample was also provided by Solvay Fluor GmbH (see Table 1). It had a stated volume purity better than 99.5 %. The sample was degassed in an ultrasonic bath before it was filled into the apparatus. After the degassing process, the purity of the sample was analyzed by gas chromatography, and two peaks with 0.001 % and 0.006 % in area fraction besides the

Table 1. Chemical Sample Descriptions initial volume purification chemical name source fraction purity method HFC227eaa HFC365mfcc

Solvay Solvay

0.995 0.995

final volume fraction analysis purity method

degassing degassing

GCb GC

0.99975 0.99993

a

1,1,1,2,3,3,3-Heptafluoropropane. bGas chromatography. c1,1,1,3,3Pentafluorobutane.

Figure 1. Distribution of our measurements and literature data for the speed of sound in HFC227ea in the p,T plane. The gray area denotes the region of our measurements. ×, this work; +, ref 1; ▽, ref 2; □, ref 3; △, ref 4; ○ ref 5; and , vapor pressure.

Table 2. Literature Data for the Speed of Sound in HFC227ea

a

author

year

method

data

T/K

p/MPa

purity

uncertainty

Benedetto et al.1 Fröba et al.4 Gruzdev et al.3 Pires et al.5 Zhang et al.2

2001 2006 2002 2000 2001

SRa LSc IF f PEg IF

78 33 180 259 72

270−370 293−374 273−393 248−333 273−333

0.5 sat. linesd 4.07 65 0.32

> 0.9999b > 0.999e > 0.9999b > 0.9998h > 0.999b

< 0.01 % < 0.5 % < 0.2 % < 0.8 % < 0.05 %

Spherical resonator. bMole fraction. cDynamic light scattering. dSaturated gas and liquid. eVolume fraction. fCylindrical interferometer. gPulse-echo. Mass fraction.

h

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Table 3. Results for the Speed of Sound in Liquid and Supercritical HFC227eaa T/K

p/MPa

c/m·s−1

280.0035 280.0038 280.0035 280.0037 280.0043 280.0044 280.0042 280.0038 280.0042 280.0043 280.0047

0.603721 1.10441 1.60474 2.10500 3.10575 4.10623 5.10705 6.10793 7.10930 8.11003 9.11073

494.100 498.919 503.638 508.265 517.265 525.950 534.351 542.491 550.398 558.074 565.550

T/K

p/MPa

c/m·s−1

280.0040 280.0048 280.0043 280.0040 280.0044 280.0056 280.0053 280.0046 280.0047 280.0048 280.0048

10.1114 12.6131 15.1148 17.6165 20.1182 25.1217 30.1253 35.1289 40.1324 45.1359 50.1394

572.834 590.292 606.803 622.498 637.478 665.604 691.693 716.105 739.098 760.882 781.612

299.9986 299.9989 299.9992 299.9996 299.9990 299.9991 299.9991 299.9993 299.9994 299.9992

12.6125 15.1141 17.6158 20.1175 25.1221 30.1255 35.1289 40.1323 45.1357 50.1391

526.497 545.087 562.568 579.107 609.848 638.038 664.188 688.658 711.710 733.553

320.0043 320.0046 320.0044 320.0044 320.0044 320.0041 320.0041 320.0040 320.0047 320.0051

12.6116 15.1133 17.6150 20.1168 25.1203 30.1241 35.1276 40.1313 45.1349 50.1384

466.658 487.610 507.059 525.273 558.715 589.028 616.897 642.796 667.061 689.948

339.9974 339.9972 339.9978 339.9980 339.9980 339.9980 339.9980 339.9982 339.9979 339.9980

12.6115 15.1133 17.6148 20.1166 25.1201 30.1236 35.1270 40.1304 45.1342 50.1377

410.840 434.431 455.998 475.960 512.152 544.541 574.057 601.301 626.696 650.546

360.0068 360.0068 360.0070 360.0071 360.0076 360.0076 360.0079 360.0080 360.0079

15.1143 17.6161 20.1181 25.1218 30.1252 31.1286 40.1320 45.1353 50.1388

385.622 409.395 431.124 470.004 504.362 535.406 563.882 590.291 615.002

380.0009 380.0010 380.0007 380.0013

17.6150 20.1167 22.6185 25.1198

367.500 390.902 412.360 432.252

T = 280 K

T = 300 K 299.9941 299.9946 299.9941 299.9971 299.9974 299.9974 299.9973 299.9976 299.9978 299.9985 299.9988

1.10305 1.60341 2.10383 3.10645 4.10719 5.10793 6.10865 7.10936 8.11009 9.11015 10.1108

417.610 423.610 429.454 440.664 451.301 461.451 471.174 480.509 489.502 498.181 506.582

320.0031 320.0033 320.0025 320.0030 320.0039 320.0039 320.0041 320.0043 320.0046 320.0042

1.10417 2.10489 3.10546 4.10565 5.10634 6.10704 7.10773 8.10837 9.10899 10.1098

332.956 349.109 363.819 377.386 390.039 401.935 413.178 423.866 434.063 443.834

339.9964 339.9966 339.9974 339.9975 339.9977 339.9974 339.9976 339.9975 339.9972 339.9974

1.60311 2.10344 3.10407 4.10477 5.10541 6.10599 7.10668 8.10810 9.10893 10.1097

249.976 262.383 283.962 302.590 319.168 334.231 348.103 361.031 373.151 384.599

360.0035 360.0038 360.0041 360.0043 360.0041 360.0063 360.0063 360.0063 360.0066

3.60430 4.10476 5.10564 6.10651 7.10735 8.10916 9.10996 10.1107 12.6125

209.764 223.691 247.372 267.427 285.071 300.979 315.530 329.013 359.172

379.9993 379.9991 380.0000 380.0000

7.10725 8.10808 9.10887 10.1096

224.902 244.614 262.077 277.876

T = 320 K

T = 340 K

T = 360 K

T = 380 K

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Article

Table 3. continued T/K

p/MPa

c/m·s−1

T/K

p/MPa

c/m·s−1

380.0012 380.0015 380.0017 380.0019 380.0021

30.1232 35.1266 40.1300 45.1335 50.1371

468.391 500.790 530.341 557.638 583.091

400.0032 400.0029 400.0030 400.0031 400.0031 400.0029 400.0032 400.0038 400.0037

20.1156 22.6175 25.1193 27.6210 30.1227 35.1263 40.1299 45.1334 50.1370

355.433 378.038 398.877 418.285 436.495 470.021 500.463 528.484 554.550

420.0042 420.0043 420.0042 420.0041 420.0044 420.0043 420.0044 420.0045 420.0048 420.0048 420.0047

27.6203 30.1221 35.1253 40.1289 45.1326 50.1361 55.1396 60.1432 70.1504 80.1575 90.1653

389.816 408.537 442.895 474.011 502.591 529.122 553.961 577.360 620.636 660.116 696.591

T = 380 K 380.0000 380.0006 380.0002 380.0006 380.0001

11.1103 12.1110 13.1118 14.1125 15.1132

292.378 305.841 318.447 330.324 341.583

400.0023 400.0022 400.0027 400.0027 400.0027 400.0027 400.0028 400.0032 400.0030 400.0030

10.1078 11.1086 12.1093 13.1100 14.1107 15.1114 16.1122 17.1130 18.1139 19.1148

232.805 249.036 263.931 277.747 290.668 302.834 314.355 325.312 335.776 345.801

420.0040 420.0039 420.0042 420.0039 420.0040 420.0040 420.0041 420.0038 420.0039 420.0042 420.0039

13.1092 14.1099 15.1106 16.1114 17.1121 18.1129 19.1137 12.1084 20.1147 22.6166 25.1184

243.754 257.314 270.060 282.108 293.546 304.449 314.877 229.233 324.882 348.298 369.823

T = 400 K

T = 420 K

Uncertainty of temperature: u(T) = 3 mK. Relative uncertainty of pressure: ur(p) = 1·10−4 for p < 10 MPa, ur(p) = 5·10−5 for p > 10 MPa. Combined uncertainty of the speed of sound: Uc(c) = (3.2·10−4 + 2.5·10−7·p/MPa)·c (all uncertainties refer to a level of confidence = 0.95). a

Figure 3. Distribution of our measurements and literature data from ref 6 and ref 7 for the speed of sound in HFC365mfc in the p,T plane. The gray area denotes the region of our measurements. ×, this work; △, ref 6; +, ref 7, and , vapor pressure.

Figure 2. Speed of sound in HFC227ea as a function of pressure. ○, 280 K; ▲, 300 K; □, 320 K; ▼, 340 K; ◊, 360 K; ●, 380 K; △, 400 K; ⧫, 420 K; , speed of sound obtained from the equation of state of McLinden and Lemmon; and ---, saturated liquid speed of sound obtained from the equation of state of McLinden and Lemmon.

The contribution of the impurities to the uncertainty of the speed of sound data is estimated to be smaller than 0.004 %. To assess the reproducibility of the speed of sound measurement, measurements on the isotherm 300 K at different pressures were repeated several times with new samples filled into the apparatus. The speed of sound in the sample decreased by up to 0.018 % over seven days, indicating that it changed in the

main HFC365mfc peak were detected. The nature of these peaks could not be identified. As with HFC227ea, it is assumed that they are other hydrofluorocarbons, which are remains from the production process. No water, nitrogen, or oxygen was detected. The volume purity of the sample is assumed to be 99.993 %. 449



Article

Table 4. Literature Data for the Speed of Sound in HFC365mfc author

year

method

data

T/K

p/MPa

purity

uncertainty

Fröba et al.6 Scott7

2004 2000

LSa SRd

29 29

298−459 315−345

sat. linesb 0.19

> 0.995c high puritye

< 0.5 % < 0.05 %

a Dynamic light scattering. bSaturated gas and liquid. cVolume fraction. dSpherical resonator. eAnalysis carried out by a gas chromatography-mass spectrometry-infrared spectrometry method.

Table 5. Results for the Speed of Sound in Liquid HFC365mfca T/K

p/MPa

c/m·s−1

249.9964 249.9964 249.9963 249.9961 249.9961 249.9960 249.9957 249.9958 249.9961 249.9962

1.10524 2.10581 3.10629 4.10688 5.10739 6.10831 7.10889 8.10814 9.10881 10.1095

921.654 926.727 931.741 936.695 941.591 946.435 951.224 955.954 960.643 965.279

259.9980 259.9980 259.9974 259.9976 259.9984 259.9980 259.9971 259.9970 259.9972 259.9966 259.9971 259.9965 259.9964

1.10431 2.10481 3.10532 4.10593 5.10633 6.10790 7.10917 8.10995 9.11074 10.1116 12.6133 15.1148 17.6166

881.567 886.957 892.275 897.525 902.702 907.823 912.886 917.883 922.822 927.709 939.678 951.341 962.702

279.9955 279.9955 279.9953 279.9958 279.9956 279.9958 279.9961 279.9963 279.9954 279.9958 279.9956 279.9959 279.9959

1.10439 2.10488 3.10541 4.10601 5.10656 6.10780 7.10851 8.10928 9.11025 10.1109 12.6126 15.1142 17.6159

803.308 809.414 815.422 821.335 827.157 832.893 838.546 844.119 849.619 855.044 868.295 881.135 893.599

299.9969 299.9971 299.9970 299.9968 299.9970 299.9970 299.9979 299.9981 299.9981 299.9974 299.9976 299.9973 299.9974

1.10450 2.10502 3.10550 4.10600 5.10700 6.10762 7.10715 8.10781 9.10842 10.1102 12.6120 15.1138 17.6157

727.097 734.062 740.902 747.608 754.188 760.648 766.961 773.205 779.340 785.368 800.064 814.225 827.906

T/K

p/MPa

c/m·s−1

249.9962 249.9963 249.9963 249.9965 249.9965 249.9964 249.9963 249.9953 249.9955 249.9955

12.6112 15.1128 17.6145 20.1163 25.1197 30.1232 35.1267 40.1298 45.1332 50.1367

976.667 987.778 998.623 1009.23 1029.77 1049.47 1068.44 1086.73 1104.43 1121.55

259.9958 259.9963 259.9969 259.9971 259.9972 259.9971 259.9974 259.9966 259.9963 259.9975 259.9974 259.9967

20.1183 25.1218 30.1258 35.1292 40.1326 45.1360 50.1395 60.1464 70.1533 80.1603 90.1673 100.174

973.795 995.213 1015.72 1035.40 1054.35 1072.64 1090.32 1124.06 1155.90 1186.11 1214.88 1242.39

279.9960 279.9959 279.9958 279.9963 279.9967 279.9973 279.9970 279.9973 279.9975 279.9974 279.9971 279.9973

20.1176 25.1210 30.1245 35.1280 40.1313 45.1349 50.1383 60.1452 70.1522 80.1592 90.1662 100.172

905.714 929.005 951.169 972.336 992.623 1012.14 1030.93 1066.64 1100.18 1131.86 1161.95 1190.62

299.9975 299.9975 299.9982 299.9982 299.9982 299.9983 299.9983 299.9985 299.9984 299.9983 299.9983 299.9985

20.1174 25.1210 30.1251 35.1286 40.1320 45.1355 50.1390 60.1459 70.1529 80.1598 90.1668 100.174

841.146 866.442 890.344 913.064 934.735 955.482 975.384 1013.06 1048.27 1081.40 1112.74 1142.54

T = 250 K

T = 260 K

T = 280 K

T = 300 K

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Article


p/MPa

c/m·s−1

320.0053 319.9934 319.9931 319.9924 319.9903 319.9904 319.9905 319.9904 320.0004 320.0005 320.0006 320.0005 320.0005

1.10313 2.10492 3.10553 4.10630 5.10770 6.10864 7.10932 8.11003 9.11117 10.1119 12.6137 15.1154 17.6172

652.277 660.367 668.239 675.918 683.411 690.741 697.912 704.932 711.767 718.523 734.862 750.505 765.527

339.9992 339.9990 339.9989 339.9987 339.9986 339.9989 339.9989 339.9989 339.9986 339.9986 339.9987 339.9989 339.9989

1.10582 2.10643 3.10695 4.10749 5.10805 6.10906 7.10973 8.10887 9.10942 10.1099 12.6114 15.1129 17.6144

578.155 587.648 596.831 605.733 614.361 622.752 630.920 638.859 646.622 654.203 672.434 689.742 706.243

360.0022 360.0016 360.0014 360.0010 360.0009 360.0010 360.0011 360.0013 360.0011 360.0011 360.0014 360.0012 360.0006

1.10209 2.10272 3.10333 4.10397 5.10479 6.10619 7.10694 8.10767 9.10839 10.1091 12.6109 15.1127 17.6149

503.740 515.201 526.145 536.638 546.727 556.452 565.844 574.937 583.754 592.319 612.735 631.924 650.069

379.9935 379.9931 379.9931 379.9931 379.9930 379.9931 379.9932 379.9930 379.9935 379.9935 379.9934 379.9935 379.9933

1.10078 2.10166 3.10207 4.10271 5.10345 6.10471 7.10549 8.10627 9.10751 10.1083 12.6101 15.1119 17.6137

427.276 441.660 455.118 467.802 479.824 491.269 502.214 512.709 522.809 532.542 555.505 576.814 596.763

400.0017 400.0013 400.0011 400.0015

1.60521 2.10565 3.10643 4.10725

355.522 364.944 382.376 398.307

T/K

p/MPa

c/m·s−1

320.0006 320.0003 320.0001 320.0001 319.9993 319.9992 319.9994 319.9991 319.9992 319.9996 319.9995 319.9998

20.1190 25.1226 30.1261 35.1297 40.1336 45.1372 50.1406 60.1476 70.1547 80.1617 90.1688 100.176

779.984 807.438 833.194 857.515 880.586 902.594 923.632 963.245 1000.07 1034.59 1067.14 1098.00

339.9990 339.9987 339.9989 339.9985 339.9985 339.9982 339.9982 339.9982 339.9973 339.9973 339.9975 339.9974

20.1160 25.1192 30.1225 35.1242 40.1277 45.1311 50.1346 60.1416 70.1500 80.1571 90.1643 100.171

722.034 751.783 779.466 805.417 829.931 853.186 875.341 916.858 955.265 991.116 1024.81 1056.68

360.0004 360.0006 360.0007 360.0010 360.0004 360.0003 359.9996 359.9994 359.9997 359.9997 359.9997 359.9995

20.1166 25.1201 30.1235 35.1269 40.1304 45.1339 50.1369 60.1439 70.1509 80.1579 90.1649 100.172

667.308 699.501 729.186 756.831 782.776 807.276 830.523 873.891 913.800 950.908 985.685 1018.48

379.9938 379.9934 379.9935 379.9936 379.9930 379.9929 379.9933 379.9931 379.9930 379.9930 379.9930 379.9931

20.1155 25.1190 30.1226 35.1262 40.1302 45.1337 50.1373 60.1443 70.1514 80.1585 90.1656 100.173

615.559 650.335 682.079 711.417 738.790 764.514 788.832 833.968 875.312 913.604 949.388 983.052

400.0024 400.0024 400.0028 400.0029

20.1180 25.1215 30.1249 35.1283

566.858 604.312 638.139 669.157

T = 320 K

T = 340 K

T = 360 K

T = 380 K

T = 400 K

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Article


p/MPa

c/m·s−1

400.0009 400.0030 400.0031 400.0033 400.0029 400.0029 400.0026 400.0025 400.0023

5.10809 6.10781 7.10864 8.10938 9.11016 10.1109 12.6127 15.1145 17.6162

413.052 426.803 439.765 452.032 463.702 474.847 500.780 524.475 546.393

419.9940 419.9938 419.9936 419.9935 419.9934

2.10332 3.10280 4.10355 5.10427 6.10497

280.019 305.082 326.491 345.407 362.506

T/K

p/MPa

c/m·s−1

400.0028 400.0031 400.0026 400.0026 400.0026 400.0024 400.0025 400.0026

40.1318 45.1353 50.1380 60.1452 70.1523 80.1593 90.1664 100.174

697.922 724.825 750.161 796.979 839.661 879.055 915.765 950.225

T = 400 K

T = 420 K 419.9933 419.9934 419.9935 419.9933

7.10563 8.10635 9.10710 10.1078

378.198 392.762 406.402 419.256

a Uncertainty of temperature: u(T) = 3 mK. Relative uncertainty of pressure: ur(p) = 1·10−4 for p < 10 MPa, ur(p) = 5·10−5 for p > 10 MPa. Combined uncertainty of the speed of sound: Uc(c) = (3.6·10−4 + 2.5·10−7·p/MPa)·c (all uncertainties refer to a level of confidence = 0.95).

Figure 4. Speed of sound in HFC365mfc as a function of pressure. ○, 250 K; □, 260 K; △, 280 K; ▽, 300 K; ⋈, 320 K; ⧖, 340 K; ◊, 360 K; ×, 380 K; +, 400 K; ●, 420 K; , speed of sound obtained from the equation of state of McLinden and Lemmon; and ---, saturated liquid speed of sound obtained from the equation of state of McLinden and Lemmon.

apparatus. As already described in Section 3 for HFC227ea, this is probably due to interactions between HFC365mfc and a Viton O-ring used as a seal in a hand pump. For this reason, the sample was removed from the apparatus after two complete isotherms were measured (about up to 9 days), and the apparatus was refilled with a new sample. An additional allowance of 0.02 % is added to the uncertainty of the speed of sound to account for this effect. When the apparatus was evacuated after it had been filled with HFC365mfc, it took considerably longer than usual to reach 0.05 Pa, which is the lowest pressure indicated by the vacuum pressure gauge. Most likely the HFC365mfc dissolves the PTFE part of the pressure vessel sealing, which was employed in the HFC365mfc measurements, and the PTFE seals of the high pressure valves. Therefore, the apparatus was thoroughly evacuated before a new sample was filled in. Including the uncertainty contributions due to the sample purity and reproducibility, the uncertainty of the speed of sound is estimated to be u(c) = (3.1·10−4 + 2.5·10−7·p/MPa)·c. The uncertainty contributions to the speed of sound due to the

Figure 5. Fractional deviations Δc = c(expt.) − c(calc.) of measured speeds of sound c(expt.) in HFC227ea and literature data from speeds of sound c(calc.) obtained from the equation of state of McLinden and Lemmon as a function of pressure at 280 K, 300 K, and 320 K. ×, this work; □, ref 3; △, ref 4; and ○, ref 5.

uncertainties of the temperature and pressure measurement were determined from the fundamental equation of state of McLinden and Lemmon10 and amount to 0.002 % and 0.003 %, respectively. Near the vapor pressure, the influence of the uncertainty of the temperature measurement is larger, amounting to 0.005 %. Including these uncertainty contributions, the uncertainty of the 452



Article

Figure 8. Fractional deviations Δc = c(expt.) − c(calc.) of saturated liquid speed of sound data c(expt.) from ref 6 from speeds of sound c(calc.) obtained from the equation of state of McLinden and Lemmon as a function of temperature.

by 3.9·10−4. All uncertainty estimates are for a 95 % confidence level.

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RESULTS The distribution of our HFC227ea measurements and literature data in the p,T plane is shown in Figure 1. Details of the literature data sets are summarized in Table 2. Our measurements cover the subcritical liquid region from 280 K upward and extend up to 420 K into the supercritical region with pressures to 50 MPa. Only the highest isotherm extends up to 90 MPa. During the HFC227ea measurements, the pressure vessel was sealed with an FEP encapsulated silicon O-ring. Since the sealing failed after it had been exposed to 100 MPa four times, the maximum pressure was decreased to 50 MPa starting from the lowest to the highest temperature. At 420 K, measurements were also taken at higher pressures up to 90 MPa. On subcritical isotherms, the lowest pressures at which measurements were carried out were chosen close to the vapor pressure. On supercritical isotherms, measurements were started at the lowest pressure where a clear signal cancellation could be observed. The measurement results are reported in Table 3. Figure 2 shows the speed of sound data for all measured isotherms as a function of pressure. In the range of our measurements, speeds of sounds lie between (240 to 780) m·s−1. Figure 3 depicts the distribution of our data for HFC365mfc, the data of Scott7 in the gas region, and the data of Fröba et al.6 on the saturation line in the p,T plane. Details of the two literature sets are reported in Table 4. Our measurements cover the liquid region in the temperature range between (250 and 420) K with pressures to 100 MPa. Initial starting measurements at 240 K were attempted. The sample was filled into the apparatus at 300 K. During the cooling process down to 240 K, the sample was kept at about 40 MPa, but froze before 240 K was reached. Therefore, the initial temperature was changed to 250 K. At this temperature, measurements were taken up to 50 MPa. Between 50 to 60 MPa the sample froze again. The measurements continued at 260 K, where it was possible to measure over the full pressure range of the apparatus up to 100 MPa. At the highest temperature of 420 K, measurements were only taken up to 10 MPa. The measurement results are reported in Table 5. Figure 4 shows the measured speeds of sound on all isotherms as a function of pressure. The speed of sound in HFC365mfc ranges from about 280 m·s−1 to about 1250 m·s−1 in our measurements.

Figure 6. Fractional deviations Δc = c(expt.) − c(calc.) of measured speeds of sound c(expt.) in HFC227ea and literature data from speeds of sound c(calc.) obtained from the equation of state of McLinden and Lemmon as a function of pressure between (340 and 420) K. Symbols in the top and center figures are the same as in Figure 5. Bottom figure: ×, this work, 380 K; ⧖, this work, 400 K; and ▽, this work, 420 K.

Figure 7. Fractional deviations Δc = c(expt.) − c(calc.) of measured speeds of sound c(expt.) in HFC365mfc from speeds of sound c(calc.) obtained the equation of state of McLinden and Lemmon as a function of pressure. ○, 250 K; □, 260 K; △, 280 K; ▽, 300 K; ⋈, 320 K; ⧖, 340 K; ◊, 360 K; ×, 380 K; +, 400 K; and ●, 420 K. −4

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DISCUSSION Our data have been used by McLinden and Lemmon10 to establish new fundamental equations of state for HFC227ea and

−7

speed of sound becomes Uc(c) = (3.6·10 + 2.5·10 ·p/MPa)·c. For pressures near the vapor pressure, 3.6·10−4 must be replaced 453



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HFC365mfc. Beside our data, the data sets of Benedetto et al.1 and Fröba et al.4 for HFC227ea and the data sets of Fröba et al.6 and Scott7 for HFC365mfc have been used in the optimization of the equations of state.10 In the following, our speed of sound data are compared with these equations of state and literature data for the speed of sound. Figures 5 and 6 show percentage deviations of our HFC227ea data and the data of Gruzdev et al.,3 Pires et al.,5 and Fröba et al.4 from the fundamental equation of state for HFC227ea. Between (280 and 400) K our data are generally represented by the equation of state within 0.02 % with only a few data showing larger deviations, while at 420 K the deviations increase up to 0.05 % at pressures above 50 MPa. They agree with the data of Gruzev et al. mostly within 0.5 %. Our data are very consistent, whereas the data of Gruzdev et al. scatter considerably. The data of Pires et al. at 280 K and 320 K are also consistent but are systematically lower than our data by about 0.8 %. This large systematic difference is probably due to the different calibration procedure employed by Pires et al. Their measurement technique is also a double-path-length pulse-echo method similar to ours, but they determined the acoustic path length in their sensor by a calibration measurement at 298.15 K and 10 MPa with pure CCl4, for which the speed of sound is not as accurately known as for water, which was used as the calibration fluid for our sensor. Our data agree with the Fröba et al. data within their quoted uncertainty of 0.5 %. Figure 7 compares our data for HFC365mfc with the fundamental equation of state for HFC365mfc, whereas percentage deviations of the Fröba et al. saturated liquid data from the equation of state are shown in Figure 8. The equation of state represents our data mostly within 0.02 %, and only few data at the highest measured temperature of 420 K show larger deviations up to 0.04 %. The Fröba et al. data are represented within 0.5 % in the temperature range of our measurements, but at higher temperatures the representation of the data is less good with deviations up to 1 %. One can conclude from this comparison that our data agree with the Fröba et al. data within their quoted uncertainty of 0.5 %.

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Article

REFERENCES

(1) Benedetto, G.; Gavioso, R. M.; Spagnolo, R.; Grigiante, M.; Scalabrin, G. Vapor-phase Helmholtz equation for HFC-227ea from speed-of-sound measurements. Int. J. Thermophys. 2001, 22, 1073− 1088. (2) Zhang, C.; Duan, Y.-Y.; Shi, L.; Zhu, M.-S.; Han, L.-Z. Speed of sound, ideal-gas heat capacity at constant pressure, and second virial coefficients of HFC-227ea. Fluid Phase Equilib. 2001, 178, 73−85. (3) Gruzdev, V. A.; Khairulin, R. A.; Komarov, S. G.; Stankus, S. V. Thermodynamic properties of HFC-227ea. Int. J. Thermophys. 2002, 23, 809−824. (4) Fröba, A. P.; Botero, C.; Leipertz, A. Thermal diffusivity, sound speed, viscosity, and surface tension of R227ea (1,1,1,2,3,3,3heptafluoropropane). Int. J. Thermophys. 2006, 27, 1609−1625. (5) Pires, P. F.; Esperanca, J. M. S. S.; Guedes, H. J. R. Ultrasonic speed of sound and derived thermodynamic properties of liquid 1,1,1,2,3,3,3heptafluoropropane (HFC227ea) from 248 K to 333 K and pressures up to 65 MPa. J. Chem. Eng. Data 2000, 45, 496−501. (6) Fröba, A. P.; Krzeminski, K.; Leipertz, A. Thermophysical properties of 1,1,1,3,3-pentafluorobutane (R365mfc). Int. J. Thermophys. 2004, 25, 987−1004. (7) Scott, J. Unpublished data. National Institute of Standards and Technology, Boulder, CO, 2000. (8) Meier, K. The pulse-echo method for high-precision measurements of the speed of sound in fluids; Habilitationsschrift, Fachbereich Maschinenbau, Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg: Hamburg, Germany, 2006. (9) Meier, K.; Kabelac, S. Thermodynamic properties of propane. IV. Speed of sound in the liquid and supercritical regions. J. Chem. Eng. Data 2012, 57, 3391−3398. (10) McLinden, M. O.; Lemmon, E. W. Thermodynamic properties of R-227ea, R-365mfc, R-115, and R-13I1. to be submitted to J. Chem. Eng. Data 2013. (11) Meier, K.; Kabelac, S. Speed of sound instrument for fluids with pressures up to 100 MPa. Rev. Sci. Instrum. 2006, 77, 123903. (12) Muringer, M. J. P.; Trappeniers, N. J.; Biswas, S. N. The effect of pressure on the sound velocity and density of toluene and n-heptane up to 2600 bar. Phys. Chem. Liq. 1985, 14, 273−296.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Addresses †

MTU Aero Engines GmbH, Dachauer Str. 665, D-80995 München, Germany. ‡ Institut für Thermodynamik, Leibniz Universität Hannover, Callinstr. 36, D-30167 Hannover, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is part of an international collaboration between the National Institute of Standards and Technology in Boulder and the Helmut-Schmidt-Universität/Universität der Bundeswehr in Hamburg. Discussions with Dr. Mark McLinden and Dr. Eric Lemmon of the National Institute of Standards and Technology, Boulder, are gratefully acknowledged. We thank Solvay Flour GmbH, Hannover, for providing the HFC227ea and HFC365mfc samples. All equation of state calculations were performed with the NIST Standard Reference Database 23 REFPROP Version 9.0. 454


Measurements of the Speed of Sound in the Refrigerants HFC227ea

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