Measurements of the Speed of Sound in Liquid ... - ACS Publications

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Measurements of the Speed of Sound in Liquid Toluene K. Meier*,‡ and S. Kabelac§ Institut für Thermodynamik, Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg, Holstenhofweg 85, D-22043 Hamburg, Germany ABSTRACT: Comprehensive and accurate measurements of the speed of sound in liquid toluene have been carried out by a double-path-length pulseecho technique. The measured data cover the temperature range from (240 to 420) K with pressures up to 100 MPa. The measurement uncertainties amount to 3 mK for temperature, 0.01 % for pressures below 10 MPa, and 0.005 % for pressures between (10 and 100) MPa, and 0.03 % for speed of sound. Comparisons with literature data and equation of state models show that our data are more accurate than all presently available literature data for the speed of sound in liquid toluene.

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INTRODUCTION Toluene (methylbenzene, C7H8) is an important fluid with a wide range of applications. For example, it is a basic ingredient in many production processes in the chemical industry, and it is applied as solvent in adhesives, paints, furniture care products, or printing inks. Because of its wide liquid region, relatively low toxicity, and easy availability, it is also used as reference fluid for calibration of viscometers,1,2 thermal conductivity sensors,3 and densimeters.4,5 Speed of sound data are particularly useful in modeling the thermodynamic properties of real fluids.6 Although the speed of sound in toluene has been measured by numerous workers, only few studies report measurements in the liquid phase over wide temperature and pressure ranges. In this work we report new accurate speed of sound measurements in liquid toluene in the temperature range between (240 and 420) K with pressures up to 100 MPa. These measurements form part of a larger program in our laboratory to measure the speed of sound in several pure fluids.7 In previous papers, measurements in propane,8 the refrigerants HFC227ea and HFC365mfc,9 and propene10 were reported. We expect that our speed of sound data are useful to develop a new wide ranging fundamental equation of state for toluene.

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 with an estimated uncertainty of 3 mK, which was located in the wall of the pressure vessel and calibrated on the ITS-90 scale. The pressure in the pressure vessel was measured with two nitrogen-operated gas pressure balances with measurement ranges of 5 MPa and 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 MPa and 100 MPa. These measurement uncertainties refer to a 95 % confidence level.

EXPERIMENTAL PROCEDURE The speed of sound measurements were carried out with a double-path-length pulse-echo instrument, which has been described in detail in ref 11. Our sensor employs a piezoelectric quartz crystal as a sound emitter and receiver, which is operated at its resonance frequency of 8 MHz. Before the measurement campaign, the acoustic path length in the sensor and the thermal expansion coefficient of the sensor 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

MATERIALS The toluene sample was purchased from Riedel-de Haën with a manufacturer specified volume purity better than 99.7 % (see Table 1). A gas chromatograph analysis revealed two peaks with 0.025 % and 0.045 % in area fraction besides the main toluene peak. The first peak was identified as water and the second peak as nitrogen or oxygen. Since according to the manufacturer’s

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© XXXX American Chemical Society

Received: February 20, 2013 Accepted: March 30, 2013

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dx.doi.org/10.1021/je4001697 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Chemical Sample Description

a

chemical name

source

initial volume fraction purity

purification method

final volume fraction purity

analysis method

toluenea

Riedel-de Haën

0.997

degassing

0.99975

GCb

b

Methylbenzene. Gas chromatography.

specification the sample should not contain nitrogen or oxygen and it was degassed before it was used, it is assumed that the nitrogen or oxygen impurities were accidentally introduced when the sample was injected with a syringe into the injector of the gas chromatograph. Thus, the nitrogen or oxygen is not considered as an impurity, and the volume purity of the sample is estimated to be 99.975 %. For the water impurity, an additional allowance of 0.01 % is added to the uncertainty of the speed of sound. The reproducibility of the speed of sound, when repeating measurements at the same state point after pressure and temperature cycles was within 0.002 %, which is well within the uncertainty contribution due to the temperature and pressure measurement uncertainties described below. Thus, it does not contribute to the uncertainty of the speed of sound. After refilling the apparatus with a new sample, repeated measurements at the same state point showed small deviations of up to 0.0055 % to speeds of sound measured with the first filling. It is assumed that this is partially due to the temperature and pressure measurement uncertainty described below and partially caused by small movements of the quartz crystal when the apparatus is refilled with a new sample. Only the difference between 0.0055 % and the temperature and pressure measurement uncertainty, that is 0.0025 %, is considered as an additional contribution to the uncertainty of the speed of sound measurement. Refilling the apparatus with new samples was necessary between the 360 K and 380 K isotherms, between the 380 K and 400 K isotherms, and after the measurement at 25.1 MPa on the 400 K isotherm. Including the reproducibility and the additional contribution due to sample impurities, the total uncertainty of the speed of sound measurement is given by U(c) = (2.0·10−4 + 2.5·10−7·p/MPa)·c. The uncertainty contributions to the speed of sound due to the uncertainties of temperature and pressure measurements were estimated by the toluene equation of state of Lemmon and Span.12 They amount to 15 ppm each. Taking these additional contributions into account, the combined uncertainty of the speed of sound measurement becomes Uc(c) = (2.3·10−4 + 2.5·10−7·p/MPa)·c. The uncertainty estimates are for a 95 % confidence level.

Figure 1. Distribution of our measurements and literature data at high pressures for the speed of sound in liquid toluene in the p,T plane. The gray area denotes the region of our measurements: × , this work; △, ref 13; ◊, ref 37; +, ref 39; □, ref 42; ⋈, ref 43; ▽, ref 47; −, vapor pressure.

and pressure was developed. As a functional form, the 35-term polynomial 4 6 ⎛ p/MPa ⎞i ⎛ T /K ⎞ j ⎟ ⎟⎜ c(p , T )/m·s−1 = 1000 ∑ ∑ aij ⎜ ⎝ 100 ⎠ ⎝ 1000 ⎠ j=0 i=0

suggested by Okhotin et al.13 was chosen. The coefficients aij were determined by a least-squares fit to our data with the software package ODRPACK.14 The numerical values of the coefficients are reported in Table 3. The correlation represents our data with an average absolute deviation of 0.002 % and a maximum absolute deviation of 0.011 %, which occurs at (420 K, 1.1 MPa).

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DISCUSSION In this section our speed of sound data are compared with literature data and equation of state models. Experimental data for the speed of sound in toluene were published by many groups. Details of these literature data sets are summarized in Table 4. Ten works report measurements of the speed of sound in liquid toluene at ambient pressure as a function of temperature. In the larger part of these studies, that is, the works of Deshpande and Bhatgadde,15,16 George and Sastry,19 Kononenko and Yakovlev,21 Nath and Tripathi,22 Reddy,24 Tamura et al.,25 and Tardajos et al.,26 only a few data near ambient temperature are reported. Fortin et al.,17 Freyer et al.,18 Heine and Snyder,20 and Okhotin et al.23 report data in extended temperature ranges. Saturated liquid or vapor speeds of sound were published by Kireev and Otpushchennikov,27 Lednewa,28 Rudenko et al.,29 Will et al.30 and Zotov and coworkers.31−33 Allegra et al.,34 Hawley et al.,38 Swanson,44 and Takagi and Teranishi45,46 measured the speed of sound in the single phase liquid under pressure on isotherms near ambient temperature. Data sets covering an extended temperature and pressure range in the single phase liquid region were reported

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RESULTS The distribution of our measurements in the p,T plane is shown in Figure 1. Our data cover a part of the subcritical liquid region from (240 to 420) K with pressures up to 100 MPa. The measurements were carried out along isotherms in steps of 20 K. The initial pressure on each isotherm was either ambient pressure or, when the vapor pressure was higher than ambient pressure, a pressure in the liquid region near the vapor pressure. The measurement results are reported in Table 2. Figure 2 depicts the speed of sound data for the 10 measured isotherms as a function of pressure. In the measured state region, the speed of sound ranges from about 820 m s−1 at the lowest pressure at 420 K to 1880 m s−1 at 100.2 MPa on the 240 K isotherm. To enable a fair comparison of our data with literature data, a correlation for the speed of sound as a function of temperature B



Article a

Table 2. Results for the Speed of Sound in Liquid Toluene T/K

p/MPa

c/m·s−1

239.9957 239.9960 239.9963 239.9958 239.9957 239.9960 239.9964 239.9959 239.9961 239.9960 239.9961 239.9966 239.9966

0.103321 1.10421 2.10494 3.10574 4.10628 5.10743 6.10767 7.10838 8.10915 9.10983 10.1105 12.6122 15.1138

1571.05 1574.99 1578.90 1582.79 1586.66 1590.51 1594.31 1598.11 1601.89 1605.65 1609.38 1618.62 1627.73

260.0012 260.0022 260.0017 260.0015 260.0016 260.0023 260.0020 260.0022 260.0018 260.0026 260.0021 260.0031 260.0032

0.102528 1.10338 2.10399 3.10483 4.10561 5.10649 6.10682 7.10753 8.10828 9.10901 10.1098 12.6118 15.1136

1476.76 1481.10 1485.39 1489.66 1493.90 1498.11 1502.29 1506.45 1510.58 1514.67 1518.75 1528.82 1538.73

280.0006 280.0002 280.0007 280.0009 280.0009 280.0007 280.0008 280.0005 280.0006 280.0008 280.0010 280.0008 280.0013

0.103617 1.10453 2.10531 3.10624 4.10705 5.10765 6.10814 7.10879 8.10945 9.11012 10.1108 12.6125 15.1142

1385.49 1390.25 1394.98 1399.66 1404.31 1408.92 1413.50 1418.04 1422.55 1427.02 1431.46 1442.42 1453.19

299.9999 300.0001 300.0001 299.9996 300.0049 300.0063 300.0066 300.0068 300.0068 300.0069 300.0071 300.0074 300.0080 300.0084 300.0084

0.102327 1.10324 2.10405 3.10469 0.103332 1.10424 2.10488 3.10558 4.10636 5.10704 6.10745 7.10808 8.10873 9.10936 10.1100

1297.15 1302.40 1307.60 1312.74 1297.13 1302.37 1307.56 1312.70 1317.80 1322.86 1327.87 1332.83 1337.75 1342.63 1347.47

320.0036 320.0031

0.102820 0.102830

1211.56 1211.57

p/MPa

c/m·s−1

239.9963 239.9962 239.9963 239.9965 239.9966 239.9967 239.9969 239.9970 239.9971 239.9971 239.9982 239.9976 239.9977

17.6155 20.1171 25.1206 30.1240 35.1274 40.1308 45.1342 50.1376 60.1444 70.1514 80.1582 90.1652 100.172

1636.72 1645.58 1662.98 1679.95 1696.50 1712.69 1728.51 1743.99 1774.01 1802.89 1830.74 1857.63 1883.64

260.0029 260.0022 260.0022 260.0023 260.0020 260.0026 260.0025 260.0025 260.0023 260.0017 260.0021 260.0023 260.0022

17.6154 20.1172 25.1207 30.1241 35.1276 40.1310 45.1345 50.1382 60.1454 70.1525 80.1595 90.1665 100.174

1548.49 1558.10 1576.92 1595.21 1613.03 1630.39 1647.33 1663.87 1695.85 1726.52 1755.96 1784.35 1811.73

280.0012 280.0012 280.0012 280.0015 280.0017 280.0015 280.0023 280.0023 280.0029 280.0029 280.0030 280.0034 280.0030

17.6160 20.1180 25.1215 30.1250 35.1285 40.1320 45.1350 50.1385 60.1453 70.1523 80.1591 90.1658 100.173

1463.78 1474.18 1494.49 1514.18 1533.29 1551.88 1569.95 1587.57 1621.55 1653.99 1685.08 1714.93 1743.69

300.0089 300.0069 300.0071 300.0069 300.0075 300.0076 300.0078 300.0082 300.0082 300.0085 300.0082 300.0078 300.0064 300.0065 300.0063

12.6117 15.1134 17.6152 20.1169 25.1203 30.1236 35.1269 40.1301 45.1333 50.1365 60.1431 70.1504 80.1585 90.1656 100.172

1359.39 1371.09 1382.55 1393.79 1415.68 1436.82 1457.30 1477.14 1496.40 1515.12 1551.11 1585.36 1618.06 1649.39 1679.48

320.0010 320.0008

17.6149 20.1166

1304.82 1316.97

T/K T = 240 K

T = 260 K

T = 280 K

T = 300 K

T = 320 K

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Table 2. continued T/K

p/MPa

c/m·s−1

320.0033 320.0032 320.0031 320.0031 320.0027 320.0004 320.0004 320.0007 320.0010 320.0009 320.0011 320.0007

1.10361 2.10426 3.10503 4.10582 5.10665 6.10707 7.10778 8.10851 9.10916 10.1098 12.6115 15.1132

1217.34 1223.07 1228.73 1234.33 1239.88 1245.37 1250.80 1256.17 1261.50 1266.77 1279.74 1292.43

339.9989 339.9996 339.9999 339.9998 339.9999 339.9998 339.9999 339.9999 339.9998 339.9996 339.9995 339.9998 339.9998 340.0000 339.9998 339.9996

0.102944 1.10368 2.10432 3.10504 4.10583 0.103201 1.10411 2.10492 3.10578 4.10659 5.10725 6.10767 7.10835 8.10905 9.10973 10.1103

1128.51 1134.90 1141.21 1147.45 1153.61 1128.51 1134.90 1141.22 1147.45 1153.62 1159.71 1165.72 1171.67 1177.55 1183.36 1189.11

359.9960 359.9953 359.9955 359.9957 359.9956 359.9960 359.9956 359.9956 359.9957 359.9960 359.9960 359.9933 359.9957 359.9931

0.103401 1.10411 2.10483 3.10545 4.10644 5.10702 6.10739 7.10804 8.10872 9.10946 10.1101 10.1111 12.6119 12.6126

1047.63 1054.73 1061.73 1068.62 1075.42 1082.11 1088.72 1095.24 1101.68 1108.04 1114.32 1114.35 1129.68 1129.71

380.0004 380.0003 379.9997 380.0002 380.0004 380.0004 380.0002 380.0003 380.0005 380.0004 380.0004 380.0007 380.0008

0.101065 1.10250 2.10336 3.10410 4.10499 5.10571 6.10612 7.10684 8.10759 9.10831 10.1090 12.6108 15.1134

968.429 976.366 984.155 991.809 999.336 1006.74 1014.03 1021.20 1028.27 1035.23 1042.09 1058.83 1075.03

p/MPa

c/m·s−1

320.0008 320.0007 320.0006 319.9998 320.0000 319.9997 320.0000 320.0002 320.0001 320.0003 320.0003

25.1201 30.1235 35.1271 40.1309 50.1379 45.1344 60.1449 70.1520 80.1589 90.1659 100.173

1340.53 1363.20 1385.08 1406.22 1446.53 1426.68 1484.55 1520.59 1554.89 1587.66 1619.07

339.9999 339.9998 339.9999 340.0003 340.0004 340.0002 340.0003 340.0005 340.0002 340.0005 340.0005 340.0005 340.0005 340.0005 340.0005

12.6120 15.1137 17.6154 20.1171 25.1205 30.1240 35.1276 40.1312 45.1349 50.1388 60.1457 70.1526 80.1595 90.1665 100.174

1203.23 1216.98 1230.40 1243.50 1268.83 1293.10 1316.43 1338.91 1360.61 1381.60 1421.66 1459.49 1495.39 1529.58 1562.28

359.9933 359.9932 359.9942 359.9930 359.9929 359.9932 359.9936 359.9929 359.9932 359.9936 359.9928 359.9934 359.9944 359.9922

15.1140 17.6156 20.1173 25.1208 30.1242 35.1276 40.1311 45.1345 50.1379 60.1449 70.1520 80.1590 90.1660 100.173

1144.62 1159.13 1173.26 1200.47 1226.42 1251.26 1275.12 1298.07 1320.21 1362.33 1401.95 1439.41 1474.99 1508.93

380.0003 380.0007 380.0008 380.0008 380.0003 380.0004 380.0011 380.0012 380.0016 380.0014 380.0015 380.0011 380.0013

17.6152 20.1169 25.1204 30.1239 35.1273 40.1308 45.1340 50.1375 60.1445 70.1516 80.1586 90.1656 100.173

1090.72 1105.95 1135.15 1162.87 1189.28 1214.55 1238.78 1262.09 1306.28 1347.66 1386.66 1423.62 1458.77

T/K T = 320 K

T = 340 K

T = 360 K

T = 380 K

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Table 2. continued T/K

p/MPa

c/m·s−1

400.0007 400.0005 400.0005 400.0008 400.0006 400.0006 400.0009 400.0008 400.0008 400.0011 400.0008 400.0015 400.0008 400.0011 400.0007

0.603007 1.10415 2.10460 3.10531 4.10600 5.10669 6.10736 7.10801 8.10866 9.10932 10.1099 12.6116 15.1133 17.6151 20.1168

894.984 899.421 908.149 916.697 925.074 933.288 941.350 949.265 957.044 964.687 972.207 990.479 1008.07 1025.05 1041.47

419.9963 419.9965 419.9963 419.9962 419.9965 419.9964 419.9964 419.9964 419.9963 419.9961 419.9962 419.9962 419.9960

1.10246 2.10316 3.10388 4.10456 5.10525 6.10594 7.10662 8.10732 9.10803 10.1087 12.6105 15.1123 17.6141

823.404 833.269 842.891 852.281 861.453 870.420 879.196 887.789 896.213 904.476 924.470 943.614 961.991

T/K

p/MPa

c/m·s−1

400.0005 400.0040 400.0031 400.0031 400.0030 400.0029 400.0016 400.0022 400.0017 400.0021 400.0018 400.0019 400.0019 400.0018

25.1202 0.608939 4.10508 15.1127 30.1232 35.1267 40.1304 45.1340 50.1375 60.1445 70.1515 80.1585 90.1656 100.173

1072.79 895.044 925.079 1008.09 1102.36 1130.40 1157.11 1182.65 1207.15 1253.40 1296.54 1337.05 1375.32 1411.65

419.9961 419.9959 419.9960 419.9959 419.9961 419.9960 419.9960 419.9957 419.9958 419.9955 419.9957 419.9959

20.1159 25.1194 30.1228 35.1263 40.1298 45.1332 50.1367 60.1439 70.1510 80.1580 90.1651 100.172

979.684 1013.26 1044.75 1074.47 1102.67 1129.52 1155.20 1203.50 1248.37 1290.36 1329.92 1367.39

T = 400 K

T = 420 K

a Uncertainty of temperature: U(T) = 3 mK; relative uncertainty of pressure: U(p) = 1·10−4·p for p < 10 MPa, U(p) = 5·10−5·p for p > 10 MPa; and combined uncertainty of speed of sound: Uc(c) = (2.3·10−4 + 2.5·10−7·p/MPa)·c (all uncertainties refer to a level of confidence = 0.95).

pressures up to 60 MPa. Only Pankevich and Zotov42 report data at supercritical temperatures. The distribution of these latter data sets in the p,T plane is shown in Figure 1. Equations of state for toluene were developed by Goodwin,48 Kiselev et al.,49 Lemmon and Span,12 and Polt et al.50 Goodwin48 published a nonanalytic equation of state, which consists of a set of equations, that has to be solved iteratively to calculate single phase properties. Although it provided the best representation of the thermodynamic properties of toluene at its time, modern explicit equations of state are much easier to apply. Therefore, it is not considered in the following discussion. The equation of state of Kiselev et al.49 is a crossover Helmholtz free energy model and describes the vicinity of the critical point in the temperature range between (593 and 680) K and density range from 100 kg·m−3 to 500 kg·m−3. Since our measurements extend only up to 420 K, it is also not considered in the discussion. Lemmon and Span12 developed a set of short fundamental equations of state in terms of the Helmholtz free energy with the same functional form and fixed exponents for a broad range of industrial fluids including an equation for toluene. Polt et al.50 published a thermal Bender-type equation of state. Together with an equation for the isochoric ideal gas heat capacity, this equation of state can be represented as a fundamental equation of state. The validity of the Polt et al. equation of state ranges from (298 to 673) K with pressures up to 25 MPa and covers only a small part of the state region of our measurements.

Figure 2. The speed of sound in toluene as a function of pressure for all measured isotherms: ◊, 240 K; ⧫, 260 K; ▽, 280 K; ●, 300 K; △, 320 K; ▼, 340 K; □, 360 K; ▲, 380 K; ○, 400 K; ■, 420 K; −, speed of sound at the measured isotherms obtained from the speed of sound correlation.

by Gasanov et al.,37 Muringer et al.,39,40 Okhotin et al.,13 Pankevich and Otpushchennikov,41 Pankevich and Zotov,42 Shoitov and Otpushchennikov,43 and Verveiko et al.47 Among these studies, the work of Okhotin et al. covers the largest part of the liquid region, extending from (183 to 523) K with E



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Table 3. Coefficients aij of the Speed of Sound Correlation i

j=0

j=1

j=2

j=3

j=4

0 1 2 3 4 5 6

2.902 910 014 −0.003 235 339 383 1.559 583 093 −3.316 212 960 1.414 066 791 1.289 317 631 −0.807 633 1059

−5.880 665 929 0.917 217 565 1 −15.989 241 22 40.164 110 92 −28.179 957 01 −0.005 312 905 559 3.215 542 470

−1.374 596 878 8.445 283 898 44.635 045 902 −151.184 673 7 140.714 320 2 −48.094 893 42 9.621 136 798

15.523 175 39 −36.662 207 19 0.001 168 751 544 148.141 476 1 −185.140 670 6 110.036 573 7 −45.201 527 63

−16.975 095 49 59.816 687 22 −126.619 170 6 128.563 320 9 −88.035 771 17 11.098 406 12 24.536 610 77

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

year

method

Deshpande15,16 Fortin17 Freyer18 George19 Heine20 Kononenko21 Nath22 Okhotin23 Reddy24 Tamura25 Tardajos26

1968 2013 1929 2003 1984 1969 1983 1986 1986 1985 1986

OIa PEc IFe IF PE PE IF PE IF PE PE

Kireev27 Lednewa28 Rudenko29 Will30 Zotov31 Zotov32 Zotov33

1972 1956 1981 1998 1969 1969 1975

PE PE PE DLSg PE PE PE

Allegra34 Biquard35,36 Gasanov37 Hawley38 Muringer39,40 Okhotin13 Pankevich41 Pankevich42 Shoitov43 Swanson44 Takagi45 Takagi46 Verveiko47

1970 1938 2004 1970 1985 1988 1969 1976 1970 1934 1984 1985 1991

PE DLUi PE PE PE PE PE PE PE IF PE PE PE

T/K

data

Single Phase Liquid at Ambient Pressure 3 298 to 318 14 278 to 343 6 273 to 323 2 298, 308 5 283 to 323 4 294 3 298 to 308 21 183 to 383 2 303, 313 3 293 to 303 1 298 Saturated Liquid or Vapor 21 182 to 373 10 293 to 473 20 293 to 493 57 323 to 591 16 230 to 335 28 293 to 573 12 193 to 573 Single Phase Liquid 8 303 3 291, 293 73 298 to 523 13 303, 348 88 173 to 320 314 183 to 523 71 313 to 453 85 473 to 633 170 303 to 393 11 298 26 293 to 303 17 303 24 293 to 373

p/MPa

sample purity

0.1 0.83 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

high purityb SRM 211dd not reported not reported 0.99975f not reported high purityb high purityb not reported 0.9999f 0.99f

0.15 % 0.23 m·s−1 1.0 m·s−1 1.9 m·s−1 1.0 m·s−1 0.006 % 1.9 m·s−1 0.02 % 0.1 % 0.1 m·s−1 0.1 m·s−1

liquid liquid liquid liq/vap vapor liq/vap liquid

high purityb not reported not reported 0.999h not reported high purityb high purityb

0.2 % not specified 0.1 % 0.45 % 1.0 % 2.0 m·s−1 3.0 m·s−1

981 39 58.9 523 263 60 81 32.7 155 304 160 160 250

not reported not reported 0.9992h 0.99f not reported high purityb high purityb not reported high purityb not reported not reported 0.996k high purityb

1.0 % not specified 0.03 % 0.3 % 0.01 % 0.05 % 0.5 % 0.5 %j 0.2 % 1.0 %j 3.0 m·s−1 0.3 % 0.3 %

uncertainty

Optical interference technique. bSample characterized by one or more of the following properties: density at 20 °C, index of refraction at 20 °C, and normal boiling point. cPulse-echo. dNIST Standard Reference Material 211d. eInterferometer. fMole fraction. gDynamic light scattering. hNot specified if reported sample purity is mole, mass, or volume fraction. iDiffraction of light by ultrasound. jAscribed uncertainty. kVolume fraction. a

our data by about 0.1 %. The older data of Freyer at al. show a different trend and deviate by up to 0.2 % from our data. The data of Heine and Snyder are very consistent, but lie by up to 0.55 % below our data and are probably too low. The recent data of Fortin et al. agree well with our data near 300 K, but deviate systematically by up to 0.13 % at lower and higher temperatures. This is probably due to the calibration procedure for the temperature dependence of the acoustic path length in their speed of sound sensor. Among the other data, the datum of Tardajos et al. and the data of Tamura et al. agree best with our data, while the other data sets scatter more and lie in part systematically by more than 0.1 % below or above our data. The

In the remainder of this section, our data are compared with the literature data and equation of state models of Lemmon and Span and Polt et al. Our speed of sound correlation is chosen as a baseline for this discussion. Figure 3 depicts percentage deviations of our data and literature data at ambient pressure from the correlation. Among the literature data sets, both data sets of Okhotin et al. and the data of Muringer et al. cover the largest temperature range. The data of Okhotin et al. agree with our data within 0.05 % at low temperatures, while larger differences up to 0.08 % are observed near 380 K. The Okhotin et al. data from ref 23 are more consistent than the data from ref 13. The Muringer et al. data are systematically higher than F



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Figure 3. Fractional deviations Δc = c(expt) − c(calc) of experimental speeds of sound c(expt) in toluene at ambient pressure, literature data at ambient pressure, and equation of state models from values c(calc) obtained from the speed of sound correlation as a function of temperature. Symbols: ···, triple point. Experimental data: ●, this work; △, ref 13; ⧓, ref 15, 16; ⧫, ref 17; black hourglass, ref 18; gray diamond; ref 19; gray triangle, ref 20; gray hourglass; ref 21; ⧖, ref 22; gray circle; ref 24; □, ref 25; gray square; ref 26; ▲, ref 34; ◊, ref 37; ▼, ref 38; +, ref 39; ⋈, ref 43; ■, ref 44; ○, ref 45, × , ref 46; and ▽, ref 47 Equations of state: , ref 12 and ----, ref 50.

Figure 5. Fractional deviations Δc = c(expt) − c(calc) of experimental speeds of sound c(expt) in toluene, literature data at nearby temperatures, and equation of state models from values c(calc) obtained from the speed of sound correlation as a function of pressure at 300 K, 320 K, 340 K, and 360 K. Experimental data: × , this work; ▲, ref 34 at 303 K and 348 K; ◊, ref 37 at 298 K, 323 K, and 348 K; ▼, ref 38 at 303 K; +, ref 39 at 298 K and 320 K; △, ref 13 at 303 K, 323 K, 343 K, and 363 K; ⋈, ref 43 at 303 K, 323 K, 343 K, and 363 K; ■, ref 44 at 298 K; ○, ref 45 at 298 K and 303 K; ●, ref 46 at 303 K; and ▽, ref 47 at 293 K and 323 K. Equations of state: −, ref 12 and ---, ref 50.

equation of state of Lemmon and Span represents our data within 0.6 %, whereas the Polt et al. equation of state represents our data within 0.2 % in their restricted range of validity. Figures 4, 5, and 6 show percentage deviations of our data, literature data at nearby temperatures, and the two equation of state models from the speed of sound correlation for each measured isotherm as a function of pressure. Among the literature data sets, the data of Okhotin et al. agree with our data the best. Between (240 and 300) K the larger part of the data lies about 0.02 % to 0.03 % below our data. At 320 K and 340 K these deviations increase to 0.05 %, while above 360 K the Okhotin et al. data lie up to 0.02 % above our data. This behavior resembles the temperature dependent deviation pattern already observed for the ambient pressure data in Figure 2. At 360 K and 380 K, the Okhotin et al. data at high pressures agree much better with our data than the data at ambient pressure, where deviations of 0.06 % and 0.09 % are observed. Okhotin et al. reported an uncertainty from 0.02 % at high pressures to 0.05 % at ambient pressure for their data.

Figure 4. Fractional deviations Δc = c(expt) − c(calc) of experimental speeds of sound c(expt) in toluene, literature data at nearby temperatures, and equation of state models from values c(calc) obtained from the speed of sound correlation as a function of pressure at 240 K, 260 K, and 280 K. Experimental data: × , this work; +, ref 39 at 248 K and 274 K; and △, ref 13 at 241 K, 263 K, and 283 K. Equation of state: −, ref 12.

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CONCLUSION Comprehensive and accurate measurements of the speed of sound in liquid toluene have been carried out in the temperature range between (240 and 420) K with pressures up to 100 MPa. Comparisons with data of other workers demonstrate that our data are much more consistent and more accurate than all presently available data for the speed of sound in liquid toluene.

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AUTHOR INFORMATION

Corresponding Author

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

K.M.: MTU Aero Engines GmbH, Dachauer Strasse 665, D80995 München, Germany. § S.K.: Institut für Thermodynamik, Leibniz Universität Hannover, Callinstrasse 36, D-30167 Hannover, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Eric Lemmon for motivating this work and Dr. Arno Leasecke for sharing toluene speed of sound data prior to publication. Both provided some literature sources about the speed of sound in toluene. All equation of state calculations were performed with the NIST Standard Reference Database 19 Refprop.

Figure 6. Fractional deviations Δc = c(expt) − c(calc) of experimental speeds of sound c(expt) in toluene, literature data at nearby temperatures, and equation of state models from values c(calc) obtained from the speed of sound correlation as a function of pressure at 380 K, 400 K and 420 K. Experimental data: × , this work; ◊, ref 37 at 373 K, 398 K, and 423 K; and △, ref 13 at 383 K, 403 K, and 423 K; ⋈, ref 43 at 383 and 393 K; ▽, ref 47 at 373 K. Equations of state: −, ref 12 and ---, ref 50.

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REFERENCES

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Thus, both data sets agree among each other with some exceptions within their quoted combined uncertainties. The Muringer et al. data are also very consistent, but at 248 K, 274 K, and 298 K they are higher than our data by up to 0.15 %, and at 323 K they lie between 0.15 % to 0.25 % above our data. The data of Gasanov et al. between (300 and 360) K agree with our data within 0.35 %, while at 400 K and 420 K deviations up to 1.1 % are observed. The Shoitov and Otpushchennikov data and the Verveiko et al. data agree with our data mostly within 0.1 % at low pressures, but the deviations increase with pressure up to 0.5 % at 100 MPa. Among the data of Allegra et al.,34 Hawley et al.,38 Swanson,44 and Takagi and Teranishi45 near the 300 K isotherm, the data of Takagi and Teranishi46 at 298 K and 303 K agree best with our data. The deviations are within 0.16 % except for the data at ambient pressure. The data of the other authors show larger scatter and higher deviations from our data up to 1 % and lie partly outside of the figure. The equation of state of Lemmon and Span represents our data over almost the entire region of our measurements within 0.5 % or better. Larger deviations up to 0.9 % only occur between (240 and 280) K at the highest measured pressures and between (380 and 420) K near the vapor pressure. The older equation of Polt et al. provides only a fair representation of our data. Near the vapor pressure, our data are mostly represented within 0.2 %, but the deviations rapidly increase with pressure up to 1.7 % at 25 MPa. H



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