Speed-of-sound measurements for liquid n-pentane and 2,2-dimethylpropane under pressure

O-369 J. Chem. Thermodynamics 1990, 22, 937-948

Speed-of-sound liquid n-pentane 2,2-dimethylpropane A. LAINEZ,“

J. A. ZOLLWEG,

School of Chemical Engineering, Ithaca, NY 14853. U.S.A. (Received 5 March

measurements for and under pressure and W. B. STREETT Cornell

University,

1990; in final form 3 May 1990)

Speeds of sound c have been measured on isotherms between 263 K and 433 K and at pressures to 210 MPa for n-pentane and to 54 MPa for 2,2-dimethylpropane. Measurements were carried out at 3 MHz using a pulse-echo-overlap technique. Rational polynomials were used to fit the (p, c, T) results, with root-mean-square deviations of 0.036 and 0.046 per cent for n-pentane and 2,2-dimethylpropane, respectively.

1. Introduction Speed-of-sound values under high pressures can be determined experimentally with high accuracy, and are therefore suitable for the precise determination of a number of thermodynamic properties. The speed of sound c is related to a derivative of the (p, V,, S) surface by c = (vJJcSMp2,

(1)

K~= - v,-yav~ap),,

(2)

where V, is the molar volume, M is the molar mass, kS is the isentropic compressibility, and p is the pressure. The speed of sound and other measurable properties may be used in a multiproperty fit (I) to obtain a more accurate equation of state than that based on (p, V,, T) alone. In previous papers we reported speeds of sound at high pressures for tetrachloromethane’2) and trichlorofluoromethane. (3) In this work, measurements for n-pentane and 2,2-dimethylpropane are reported. Both substances are very interesting from the practical and theoretical point of view, and experimental measurements of (p, I’,,, T) and the formulation of an equation of state have been investigated over wide ranges of temperature and pressure, mainly for n-pentane.‘4’ Recent (p, I$,, T) results for this substance include those of Easteal and Woolf,“’ who measured ratios of molar volumes on isotherms in the range 278 K to 338 K and at ‘Permanent address: Departamento Complutense, 28040 Madrid, Spain. 0021-9614/90/010937 + 12 %02.00/O

de Quimica

Fisica, Facultad

de Quimicas,

Universidad

c 1990 Academic Press Limited

938

A. LAINEZ,

J. A. ZOLLWEG.

AND

W. B. STREETT

pressures up to 280 MPa; Kratzke et ill.,“’ who reported liquid densities up to 60 MPa. Vasil’ev,‘7’ who studied the density of the liquid phase in the interval 173 K to 448 K up to 150 MPa; and Gehrig and Lentzc8’ who measured (p, V,, T) from 313 K to 643 K and 5 MPa to 250 MPa. Recent (p, r/,, T) values for 2,2-dimethylpropane are scarce, and earlier results are summarized by Das et ~1.‘~’ A multiproperty fit for n-pentane should also include the recent heat-capacity results of Czarnota”” at 299 K and up to 1022 MPa and of Grigor’ev et al.(“) in the range 293 K to 698 K and 0.5 MPa to 60 MPa. Speeds of sound for n-pentane and 2,2-dimethylpropane have been measured in the gas phase by Ewing et ~1.“’ I’) at different temperatures and pressures. Measurements along the (liquid + vapor) equilibrium line include those of Chavez et ~1.“~’ in the temperature range 203 K to 308 K, Sachdeva and Nanda’16’ between 283 K and 303 K, and Golik et al. (17) who present their results only graphically. Only measurements for n-pentane could be found for comparison in the liquid phase. Otpushchennikov et al.” ‘) measured speed of sound in the range of 303 K to 393 K at pressures up to 200 MPa, and at fixed densities between 439 kg. m A and 624 kg.mp3 and temperatures of 303 K to 473 K. Houck”” measured speeds of sound as well as densities to 2400 MPa at 295 K. The study of speed-of-sound variation with temperature and pressure by Melikhov’20’ covered the range from 303 K to 433 K and pressures to 600 MPa, but his results are presented only

1000

100

10

5 ‘4

1

0.1

0.01

0.001 200

250

300

350

400

450

TIK FIGURE 1. (p, T) diagram showing ranges where measurements of speed of sound have liquid n-pentane. The study by Ismagilov and Ermakov included measurements on metastable states. ps is the (liquid + vapor) equilibrium locus. q . Otpushchennikov E, Ismagilov and Ermakov;tz2’ !$& Belinskii and Ikramov;“” q , This work. as11 , Houck;“” I# , Golik et a1.;“” .:\~Lx , Sachdeva and Nanda;“” m, Chavez

been made in the liquid in er (I!.;(~~) . Melikhov;‘z”l er al.“”

c(T,

p) FOR

PENTANE

ISOMERS

939

graphically. Other measurements include those of Belinskii and Ikramov’2r’ at 293 K, 303 K, and 313 K and pressures from 1 MPa to about 800 MPa, and Ismagilov and Ermakov(22’ between 383 K and 438 K at pressures below 2.5 MPa. Figure 1 is a pressure-against-temperature diagram showing the regions over which speed-of-sound measurements have been made in liquid n-pentane.

2. Experimental The ultrasonic apparatus used for measurement of speed of sound was based on the pulse-echo overlap method described previously by Papadakis.‘23’ The technique and the apparatus are described in detail elsewhere. (24. 2. 3, Measurements were made by using a (lead zirconate + lead titanate) electrostrictive crystal (PZT-5A from Valpey-Fisher Corporation) with a fundamental frequency of 1 MHz to generate and receive the sound waves. The apparatus was operated at a frequency of 3 MHz to avoid the propagation of modes other than the zeroth-order mode.“” The speed of sound was measured by determining the round-trip travel time between the crystal and a reflector of a 12 us radio-frequency pulse. The acoustic path length of about 0.1 m was calibrated at 3 MHz using the sound-speed value of 1004.38 rn. s ’ reported by Benson and Handa (*w for pure n-pentane at 298.15 K and atmospheric pressure. The path length for each experimental point was corrected for the variation of the length of the 99.99 mass per cent copper spacers with pressure and temperature using the isobaric expansivity’27’ and the isothermal compressibility.‘28’ Appropriate corrections were also applied to the measured values to take into account the effects of diffraction. (29) Those corrections were never larger than 0.019 m-s--‘. The speed of sound was measured in the pressure range from near the vapor pressure to about 210 MPa for n-pentane and to 54 MPa for 2,2-dimethylpropane. The maximum pressure for 2,2-dimethylpropane was limited by the freezing of the liquid in the lines outside the temperature bath. The measurements were carried out along isotherms in the temperature range between 263 K and 433 K. The acoustic cell was placed inside a pressure vessel of i.d. 38.1 mm thermostatted in a liquid bath whose short-time temperature was maintained to within +2 mK with a proportional controller. Temperatures from 263 K to 340 K were maintained in a (water + antifreeze) bath, while an oil bath was used for higher temperatures. Temperature was measured at the outer wall of the pressure vessel on IPTS-68 with a platinum resistance thermometer and Mueller resistance bridge. Reading precision was &- 1 mK but absolute accuracy was around fO.O1 K. The pressure in the system was generated by either a screw pump, for pressures to 53 MPa, or by an oil-activated intensifier for higher pressures. The pressure was measured by means of a triplerange (10, 20, 34) MPa sensor (T-Hydronics) for pressures up to 34 MPa, and a (68, 136, 204) MPa triple-range sensor (T-Hydronics) for higher pressures. These transducers were accurate to about 0.15 per cent of the full scale reading according to specifications. The calibration provided by the manufacturer was checked against a dead-weight tester in our laboratory. The accuracy of speed-of-sound measurements on both liquids was estimated to be about 0.05 per cent.

940

A. LAINEZ,

J. A. ZOLLWEG,

AND

W. B. STREETT

The n-pentane was Fisher Spectranalyzed grade. No impurity was detected by g.1.c. It was not purified further except for degassing under vacuum. The 2,2-dimethylpropane was supplied by Matheson as their C.P. grade, with a purity of about 99 mass per cent. It was purified by fractional crystallization until no impurity was detected by g.1.c. The detection limit of the g.1.c. is believed to be 0.02 mass per cent. The purified material was degassed before use.

3. Results and discussion The measured speeds of sound c in n-pentane and 2,2-dimethylpropane as a function of pressure and temperature are given in tables 1 and 2, and plotted in figures 2 and 3. The experimental results have been fitted to a ratio of two polynomials: c2/(m2

‘Se2)

= 2 i=O

f ai,j{(p/MPa)-

lO}‘{(T/K)-350)’

j=O

i

$

f

k=O

I=0

b,,,{(p/MPa)-10}k{(T/K)-350}‘.

(3)

The ratio is normalized to make the leading term in the denominator b,,, = 1. The VdlleS Of Ui, j and bk, 1 for the two liquids, from a least-squares analysis of the

FIGURE 2. Speeds of sound c at different A,298.11K;0,313.16K;.,353.15K;A,393.17K;~,433.23K.

pressures

p for liquid

n-pentane.

0,263.15

K;

q ,283.06 K,

c(T, p) FOR TABLE

1. Experimental

PIMPa 263.164 263.163 263.158 263.154 263.145 263.152 263.157 263.163 263.156 263.166 263.154 263.151 263.155 263.150 263.155 263.155 263.158 263.158 263.149 263.154 283.057 283.054 283.057 283.057 283.066 283.066 283.046 283.050 283.065 283.044 283.061 283.050 283.060 283.049 283.056 283.055 283.060 283.056 298.093 298.099 298.094 298.118 298.120 298.123 298.100 298.107 298.107 298.130 298.121 298.121 298.122 298.117 298.118 298.117

0.63 1.50 2.67 5.39 8.19 10.94 15.33 20.03 24.93 29.95 35.59 41.06 47.09 146.27 155.77 166.17 176.19 186.95 196.62 208.83 0.29 2.95 5.25 7.64 10.19 14.15 18.37 109.13 117.34 125.72 134.00 142.87 151.80 161.58 171.47 181.78 194.29 205.41 2.55 4.39 6.61 100.35 110.38 118.00 128.66 134.82 139.85 147.81 155.28 164.28 172.41 177.99 184.95 191.16

speeds of sound

c/(m.s-I) 1180.7 1187.1 1195.9 1215.5 1235.3 1253.5 1281.9 1310.8 1339.3 1367.4 1396.2 1424.3 1453.5 1822.4 1850.3 1880.3 1908.0 1937.2 1962.5 1993.7 1079.8 1102.5 1121.2 1140.0 1159.0 1187.7 1216.4 1643.1 1671.6 1700.5 1727.4 1756.7 1784.2 1813.7 1842.3 1871.4 1905.5 1934.9 1027.6 1044.3 1063.7 1567.8 1605.3 1632.7 1669.7 1691.1 1707.5 1732.8 1756.2 1783.6 1807.6 1823.8 1843.3 1860.7

PENTANE

941

ISOMERS

c in liquid n-pentane: from equation (3)

6 = 102(c,,,C-c)/c,

6

T/K

PiMPa

-0.017 -0.005 - 0.006 0.009 - 0.002 0.016 0.010 - 0.002 - 0.002 - 0.022 0.059 0.028 0.03 1 -0.051 - 0.028 - 0.030 -0.011 -0.004 0.010 0.021 -0.012 -0.006 - 0.002 - 0.008 0.011 0.007 0.020 0.019 0.045 0.029 0.051 0.000 0.015 0.010 0.021 0.022 0.027 0.028 0.024 0.015 0.014 -0.017 - 0.006 0.002 0.009 -0.033 -0.021 -0.012 -0.011 -0.014 -0.015 -0.019 - 0.008 -0.016

263.147 263.149 263.152 263.152 263.150 263.145 263.153 263.145 263.155 263.158 263.148 263.156 263.150 283.062 283.056 283.058 283.054 283.050 283.062 283.053 283.061 283.050 283.056 283.048 283.059 283.045 283.058 298.086 298.087 298.092 298.094 298.106 298.116 298.119 298.122 298.127 298.133 298.138 298.111 298.114 298.114 313.140 313.140 313.162 313.173 313.162 313.162 313.159 313.159 313.173 313.186 313.157 313.156 313.165

52.61 59.32 65.62 65.68 72.79 80.12 87.27 94.88 102.80 111.11 119.41 128.42 137.39 22.78 27.22 32.06 37.31 42.56 48.18 53.81 59.87 66.13 72.79 79.34 86.54 93.71 101.42 8.96 11.29 14.99 18.80 23.11 28.76 35.24 41.80 48.66 56.39 64.75 72.72 81.50 90.62 0.63 0.64 2.59 4.57 4.76 6.79 8.67 12.05 13.62 13.62 15.48 19.23 23.18

where

c/(m.s-‘) 1479.6 1509.5 1537.1 1537.1 1566.3 1596.0 1623.2 1651.9 1680.0 1709.2 1736.8 1766.4 1794.4 1245.2 1272.8 1301.6 1329.8 1358.4 1386.9 1415.2 1443.4 1472.4 1500.7 1528.7 1557.4 1585.9 1614.6 1083.5 1102.0 1130.4 1158.2 1187.9 1225.4 1264.1 1301.5 1338.6 1378.0 1418.1 1454.2 1492.2 1529.7 937.2 937.3 958.0 976.8 979.4 998.7 1016.0 1045.0 1057.1 1057.1 1073.3 1102.3 1131.0

cCSIC is obtained

6 0.004 0.008 - 0.022 -0.006 0.010 - 0.022 -0.004 - 0.029 -0.010 -0.033 -0.011 -0.025 -0.004 0.000 -0.019 -0.038 0.057 0.018 0.043 0.000 0.027 -0.012 0.038 0.009 0.038 0.016 0.039 0.005 0.022 0.016 0.000 -0.009 -0.082 -0.032 - 0.028 -0.047 -0.055 -0.055 - 0.036 -0.032 -0.024 0.013 0.020 - 0.027 0.058 -0.012 -0.009 - 0.030 0.003 0.090 0.079 -0.017 - 0.029 -0.014

942

A. LAINEZ,

J. A. ZOLLWEG, TABLE

T/K

PIM Pa

313.161 313.172 313.172 313.173 313.173 313.176 313.157 313.156 313.177 313.156 313.180 313.157 313.156 313.173 313.154 353.155 353.155 353.154 353.154 353.155 353.154 353.154 353.155 353.158 353.158 353.159 353.160 353.159 353.157 353.148 353.147 353.147 353.148 353.149 393.192 393.193 393.194 393.193 393.190 393.187 393.185 393.183 393.183 393.158 393.158 393.160 433.212 433.214 433.217 433.223 433.227 433.231 433.237 433.246 433.251 433.226

0.22 31.59 36.26 41.04 45.84 46.01 51.30 56.59 56.60 62.35 68.13 68.17 74.54 80.80 87.26 0.45 1.10 1.76 3.14 4.54 6.11 8.49 11.16 13.91 16.92 20.10 23.96 28.04 32.46 154.61 165.66 175.29 187.12 205.45 1.14 4.46 7.55 10.92 13.92 17.38 21.10 24.88 29.08 182.56 195.30 211.09 4.47 6.07 11.56 15.29 19.56 24.66 30.36 37.19 44.63 52.17

c/(m.s-‘) 933.1 1188.3 1216.5 1245.2 1272.7 1273.9 1302.2 1330.0 1330.5 1358.9 1387.4 1387.1 1416.0 1444.4 1471.6 741.5 751.1 760.7 779.9 798.4 818.2 846.3 875.2 903.5 932.7 961.5 994.2 1026.9 1060.2 1624.7 1660.6 1690.7 1726.4 1779.1 552.2 620.5 672.2 720.3 758.9 799.3 838.3 875.3 913.3 1636.0 1674.9 1720.9 437.0 480.0 589.4 646.7 703.2 761.2 818.7 877.2 936.2 990.3

AND

W. B. STREETT

I-continurd

6

T/K

p/M Pa

-0.030 - 0.064 0.014 0.001 -0.008 - 0.025 0.019 0.010 - 0.034 0.005 - 0.044 -0.001 0.039 0.000 0.041 - 0.004 -0.003 0.002 -0.002 - 0.005 -0.002 0.005 0.057 0.050 0.029 0.016 0.015 -0.015 -0.057 -0.003 -0.014 -0.017 -0.032 - 0.059 0.092 -0.115 - 0.076 0.046 0.057 0.038 0.065 0.012 - 0.039 -0.011 -0.035 - 0.066 0.151 -0.149 -0.017 0.048 0.021 0.027 - 0.068 0.104 0.026 -0.032

313.173 313.158 313.154 313.158 313.153 313.155 313.153 313.154 313.153 313.154 313.152 313.153 313.153 313.153 313.153 353.157 353.154 353.159 353.153 353.160 353.153 353.160 353.151 353.160 353.150 353.158 353.149 353.149 353.147 393.181 393.157 393.174 393.156 393.178 393.155 393.176 393.156 393.157 393.155 393.155 393.156 393.161 393.158 433.226 433.226 433.225 433.226 433.232 433.235 433.235 433.237 433.241 433.217 433.232 433.222 433.235

27.40 95.28 101.29 108.93 116.58 125.47 132.40 141.06 149.17 159.10 168.27 177.66 187.57 197.86 206.17 42.38 53.28 59.38 65.63 71.93 78.66 86.32 93.75 101.20 109.46 1 17.54 126.65 135.64 145.39 33.98 38.84 45.10 49.63 55.81 62.03 69.08 76.20 91.77 108.78 127.79 147.97 158.93 170.71 60.91 70.56 81.13 92.35 103.69 116.01 129.23 142.24 154.87 167.86 183.16 196.71 212.77

c/(m.s 1 160.4 1505.2 1528.7 1558.5 1586.6 1618.8 1642.5 1672.7 1698.9 1730.4 1758.3 1786.2 1814.7 1843.5 1866.1 1126.7 1193.4 1227.3 1261.6 1292.7 1326.2 1361.2 1394.9 1426.2 1460.5 1491.8 1526.6 1558.8 1593.9 952.6 990.2 1034.9 1065.6 1104.8 1142.1 1180.9 1719.0 1295.2 1370.6 1447.0 1521.9 1559.5 1598.h 1047.4 1104.5 1162.3 1218.8 1271.8 1325.7 1379.6 1430.4 1476.2 1520.9 1567.7 1613.3 1661.0

‘)

J

---0.039 0.010 0.045 0.020 0.05 1 0.029 0.054 -0.005 0.014 0.001 0.009 0.002 - 0.003 -0.017 -0.021 0.038 -0.005 0.028 - 0.034 0.048 - 0.002 0.044 0.003 0.04 1 0.012 0.048 0.026 0.050 -0.013 0.079 0.037 0.014 -0.027 -0.051 ~ 0.078 -0.021 - 0.036 - 0.025 -0.004 0.019 -0.015 0.005 -0.010 -0.071 -0.041 -0.019 0.006 0.030 0.057 0.017 0.028 0.043 0.043 0.016 -0.013

c(T. p) FOR TABLE

2. Experimental

T/K 263.133 263.133 263.132 263.132 ‘63.131 163.132 263.132 263.131 263.130 263.128 263.128 263.129 283.065 283.062 283.063 283.065 283.063 283.063 298.121 298.122 ‘98.118 298.116 298.115 298. I 19 298.120 298.118 298.121 298.119 298.119 313.180 313.180 313.182 313.183 313.183 313.182 313.180 313.180 313.180 313.178 313.180 313.178 333.148 333.149 333.150 333.150 333.150 333.150 333.149 333.149 333.149 333.148 333.147 333.147 333.148

piMPa 0.78 1.41 2.22 2.94 3.76 4.64 5.60 6.49 7.40 8.33 9.39 10.44 0.48 26.39 29.06 31.92 34.79 31.36 0.48 1.77 2.74 3.77 4.72 5.58 7.13 8.50 10.46 49.49 53.08 0.50 I .63 2.71 3.72 4.81 5.99 7. I9 8.44 10.24 12.01 13.99 16.05 1.68 2.63 3.63 4.77 6.03 7.33 8.65 10.28 12.00 14.01 16.16 18.10 20.27

PENTANE

speeds of sound c in liquid 2,2-dimethylpropane; obtained from equation (3) r/(m.s-‘) 1036.1 1042.0 1049.5 1056.2 1063.5 1071.4 1079.7 1087.4 1095.1 1103.0 1111.7 1120.3 928.7 1153.2 1171.8 1191.1 1209.8 1226.2 851.1 866.9 878.4 890.3 900.9 910.2 926.7 940.8 960.2 1245.9 1266.4 775.1 790.9 805.1 818.3 831.9 846. I 860.1 874.2 893.8 912.1 931.8 951.6 692.3 707.6 722.9 739.8 757.4 174.8 791.8 811.6 831.6 853.9 876.5 896.0 916.8

943

ISOMERS

6

T/K

-0.007 -0.003 0.001 -0.008 -0.003 - 0.003 0.002 0.004 0.010 0.001 0.007 0.008 0.019 0.010 0.004 -0.002 -0.002 -0.009 0.043 0.037 0.030 0.016 0.019 0.018 0.003 0.000 -0.005 - 0.024 -0.051 -0.044 -0.042 -0.014 -0.025 -0.023 -0.022 - 0.020 - 0.030 -0.030 -0.027 - 0.023 - 0.028 -0.025 - 0.007 0.02 1 0.012 0.020 0.022 0.015 0.037 0.037 0.038 0.038 0.042 0.047

283.066 283.065 283.065 283.066 283.063 283.062 283.062 283.062 283.065 283.065 283.061 283.058 283.062 298.119 298.119 298.115 298.117 298. I22 298.116 298. I20 298.117 298.117 298.119 298.118 298.125 298.125 298.119 313.177 313.176 313.178 313.177 313.177 313.177 313.177 313.176 313.176 313.176 313.176 313.176 313.176 333.146 333.147 333.149 333.147 333.149 333.149 333.149 333.149 333.147 333.148 333.148 353.134 353.134 353.132

6 = 10z(c,,,,-c)/c,

p/MPa 1.25 2.88 3.86 4.81 6.33 7.82 9.78 Il.92 14.11 16.47 18.81 ‘1.31 23.8 I 12.41 14.48 16.74 19.05 21.38 23.96 26.36 28.97 31.69 34.43 37.24 40.15 43.33 46.40 18.18 20.40 22.96 25.89 28.86 32.06 35.16 38.09 40.93 43.72 46.44 49.43 53.05 0.60 25.30 28.28 31.61 35.01 38.13 41.18 44.13 46.97 49.90 53.16 1.09 1.19 3.48

c/(m.s~‘) 937.2 954.4 964.5 974.0 989.0 1003.2 1021.2 1040.2 1058.8 1078.2 1096.9 1116.1 1134.6 978.8 997.9 1017.5 1037.1 1056.0 1076.3 1094.6 1113.8 1133.2 1 152.0 I 170.6 1189.3 1209. I 1227.7 971.1 990.7 1012.4 1036.1 1059.3 1083.1 1105.1 I 125.2 1144.0 1162.0 1179.1 1197.3 1218.7 674.0 962.1 987.1 1013.8 1039.8 1062.4 1083.6 1103.5 1122.0 1140.7 1160.7 578.4 601.2 626.5

where

ccalr is

6 0.003 0.001 - 0.002 -0.001 -0.009 -0.013 -0.014 - 0.02 I -0.008 -0.002 0.000 0.006 0.007 -0.007 - 0.003 0.006 0.004 0.010 0.016 0.008 0.009 0.003 0.004 0.008 0.003 0.000 -0.010 -0.019 -0.018 -0.013 - 0.006 - 0.009 -0.007 0.007 0.012 0.015 0.018 0.008 -0.002 -0.023 -0.041 0.045 0.047 0.045 0.033 0.047 0.057 0.060 O.Oh 1 0.050 0.037 0.074 0.093 0.018

944

A. LAINEZ,

J. A. ZOLLWEG. TABLE

T/K 333.146 353.135 353.133 353.133 353.134 353.134 353.135 353.136 353.134 353.135 353.136 353.140 353.136 353.138 353.138 373.173 373.178 373.171 373.172 373.173 373.183 373.178 373.171 373.173 373.174 373.175 373.173 373.172 393.160 393.133 393.135 393.135 393.134 393.162 413.068 413.071 413.067 413.071 413.101 413.103 413.103 413.100 413.097 433.195 433.192 433.183 433.180 433.171

PIMPa 22.59 5.78 6.95 8.18 9.97 12.00 14.02 16.07 17.97 20.37 22.64 25.30 28.30 31.69 34.67 17.95 20.37 22.46 25.18 27.62 29.97 32.86 35.88 39.08 42.67 46.08 49.52 53.26 6.34 42.09 45.43 47.88 49.84 53.17 8.20 9.94 11.99 14.06 15.96 17.99 20.01 22.74 25.40 27.42 29.72 31.89 34.44 37.19

c/(m.s-‘) 938.3 666.3 684.8 703.1 728.4 755.2 780.0 804.9 826.0 851.2 873.8 899.0 926.0 955.0 978.4 760.1 787.6 810.2 837.8 861.5 882.7 908.0 933.1 958.6 985.9 1010.5 1034.5 1059.4 505.1 933.2 958.4 976.4 990.3 1013.3 467.4 506.3 545.7 581.2 611.4 640.5 667.3 700.9 731.4 707.3 732.1 754.0 781.4 806.6

AND

W. B. STREETT

Z-continued

6

TIK

0.045 0.027 0.043 0.070 0.08 1 0.068 0.087 - 0.045 -0.053 - 0.056 - 0.054 - 0.054 - 0.060 - 0.082 -0.012 - 0.036 - 0.039 - 0.048 -0.040 -0.055 -0.012 - 0.007 0.005 0.004 -0.001 0.001 -0.014 - 0.026 0.043 - 0.006 -0.005 -0.018 -0.018 -0.042 0.042 -0.017 0.094 0.120 0.047 0.071 0.113 0.130 0.129 -0.077 -0.091 -0.057 - 0.027 - 0.036

353.134 353.135 353.159 353.159 353.155 353.156 353.160 373.180 373.180 373.181 373.177 373.179 373.175 373.175 373.176 393.157 393.162 393.162 393.162 393.163 393.159 393.160 393.156 393.154 393.159 393. I26 393.124 393.128 393.130 413.098 413.080 413.080 413.082 413.098 413.077 413.097 413.091 413.096 433.206 433.203 433.199 433.199 433.200 433.172 433.178 433.183 433.189 433.192

piMPa 4.60 38.18 41.32 44.28 47.10 49.97 53.04 4.01 5.48 6.79 8.29 9.96 11.98 13.98 16.03 8.14 9.95 12.00 13.95 15.92 17.92 20.23 22.29 24.97 27.43 29.45 32.72 36.17 39.09 27.93 30.75 33.33 36.21 39.12 42.18 45.69 49.09 53.34 15.88 17.94 19.90 22.43 24.96 40.33 43.19 46.2 1 49.38 53.29

c/(m.s 646.6 1005.6 1028.6 1049.6 1068.9 1087.9 1107.6 543.2 574.0 598.9 625.8 652.6 683.0 710.5 736.8 543.6 578.1 612.8 643.5 671.3 697.8 726.5 750.3 779.7 805.0 825.0 855.5 885.2 909.4 758.6 787.4 812.0 837.6 862.7 887.7 915.2 940.5 970.7 553.8 586.2 614.1 648.2 679. I 834.0 857.6 881.6 905.7 932.0

‘)

(i 0.003 -0.019 -0.021 ~ 0.025 ~ 0.029 - 0.042 - 0.052 -0.106 - 0.079 -0.053 -0.113 -0.061 -0.076 - 0.049 -0.041 0.024 0.004 0.032 - 0.044 - 0.008 ~ 0.003 -0.013 - 0.005 -0.015 -0.021 - 0.038 - 0.054 -0.001 -0.011 0.116 0.073 0.067 0.119 0.116 0.120 0.107 0.101 0.088 -0.088 -0.073 -0.008 -0.080 -0.067 - 0.043 -0.038 - 0.049 - 0.059 -0.070

experimental results, are listed in tables 3 and 4. All measurements were weighted according to an uncertainty determined by assuming that experimental errors derived primarily from two sources: the uncertainty in the pressure measurement, whose effect on speed of sound was determined by a preliminary fit of the results

c( T. p) FOR

PENTANE

945

ISOMERS

pIMPa FIGURE 3. Speeds of sound c at different pressures [7.283.06K: n.298.12K; 0.313.18K: W,333,15K; +. 413.09 K: n, 433.19 K.

p for liquid 2,2-dimethylpropane. l .353.14K; n .373.18K;

0. 263.13 K: A.393.15K:

along isotherms, and an assumed uncertainty of 0.1 of a cycle in the echo-overlap determination. Upper values m, = m2 = n, = n2 = 2 were selected for both substances to optimize the chi-square of the fit. The parameters given in tables 3 and 3 and equation (3) reproduce our experimental results with a root-mean-square TABLE +,,
= = = =

767067.1 -6296.313 13.748173

1 h 0. I = 9.4360917 h,,2 =-9,4268366x

x 10~~’ lo-’

TABLE 11”. o = i,<,, I = u,,. L = hxo = h 0. 1 =

549941.72 -5376.4835

13.618372 1 7.6164614

h 0.2 =-4,7744436x

x lo-~& lo-’

3. Parameters

of equation

u,,~ = 34981.489 Ul. I = 12.113121 u ,,2 = -0.3540286 h ,,. = 0.02104802 h 1.1 = 1.5249052x

h 1.2 = 3.3144059

4. Parameters

(3) for n-pentane u L,. = 281.49629 a,. 1 = 2.0583865 u 2,2 =0.0028709015 b 2.0 = 1.7055334x

10m4 x lo-’

of equation

h 2,, = 1.5076901 h *, z = 1.3302858

lo-’ x 10 ’ x 10 ”

(3) for 2.2-dimethylpropane

u ,,. = 40660.287 a,, 1 = -109.20074 l.z =-0.061045695 ;: ,.. =0.037828415 h 1, 1 = 1.3023041 x IO-“ h 1,z = 3.2219041x10~"

a z,. (I 2,1 u2,z h >,(, i2,, L,Z

= 624.196 = 1.0814811 =-o.cQ20405134

= 8.1498278 =4.006506x =-8,4933506x

x 10~’ lo-” lo-‘”

946

A. LAINEZ,

J. A. ZOLLWEG.

AND

I

W. B. STREET7

I

I

I

I IS0

I 200

n -

8

A

H

I SO

0 FIGURE n-pentane.

I loo pIMPa

4. Deviation plot of speeds of sound Symbols are the same as in figure 1.

c from

values

o’2r----0.1

I

-0.2 0

.

(3) for

l l

l * wwww w w w w w

l

w

1

”

”

n

n

n

.

I 10

equation

** l

2.

n

-

l

l

AB*wyw~c4~w a/l. a.*

-0.1

*

l

with

1

l o

0

2i,

l

l

.

of c,,,~ calculated

I 20

n

I 30 pIMPa

FIGURE 5. Deviation plot of speeds of sound c from values 2,2-dimethylpropane. Symbols are the same as in figure 2.

I 40 of cCHIC calculated

I SO with

60 equation

(3) for

c(T, p) FOR 0.2

I

PENTANE

947

ISOMERS I

I

I

(a)

-0.2 260

I

I

I

I

270

280

290

300

il(

T/K

1.2

-0.46

;&

3C (b) 0

I

I 50

I

I

100 pIMPa

I

I

I

I

150

200

-

FIGURE 6. Deviation plots of speeds of sound c measured by other investigators from values (‘ca,c calculated with equation (3) for n-pentane.. (a) Comparison with values of Chavez et a!.““’ at vapor pressure: 0. pulse-echo-overlap; n , pulse-echo-superposition. (b) Comparison with values 01 Otpushchennikov et ul.““: 3lf, 303.15 K: 0, 313.15 K; W , 333.15 K; 0. 353.15 K: n , 373.15 K; A. 393.15 K.

fractional error of 0.036 and 0.046 per cent for n-pentane and 2,2-dimethylpropane. respectively, within the estimated accuracy of the speed-of-sound measurements. Deviations 6 of experimental values of c from equation (3), 6 being defined as -c)Ic where c,,~~is the calculated value, are listed in tables I and 2. and are 1@XCCdC plotted in figures 4 and 5. Comparison with previous results shows that our results for n-pentane extrapolated to the vapor pressure are in good agreement with the measurementsof Chavez et u/.(~‘) with an average deviation from their results of only 0.014 per cent, but are mostly higher than those of Otpushchennikov et uL”*’ with deviations ranging from -0.4 per cent at low pressuresand temperatures to 1.0 per cent at the higher pressures.Deviation plots in figure 6 compare these results with equation (3). Our results are also in good agreement with those of Sachdeva and Nanda”” at 283 K, but their speed-of-sound results are significantly larger than ours at higher temperatures. Deviations between our results and those of Belinskii and Ikramov”” in the range below 200 MPa, where comparisons can be made, are similar to those shown in figure 6b.

948

A. LAINEZ,

.I. A. ZOLLWEG.

AND

W. B. STREETT

This work was supported by the U.S. Department of Energy under contracts DE-AC02-79ER10422 and DE-FG02-86ERl3623 and by the U.S.A. Spain Committee for Scientific Cooperation under grant CCB84-003. One of us, (A.L.) gratefully acknowledges a Fulbright fellowship during the years 1985-86. REFERENCES I. 2. 3. 4. 5. 6. I. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 21. 28. 29.

Hust, J. G.; McCarty, R. D. Cryogenics 1967, 7, 200. Lainez, A.; Miller, J. F.; Zollweg, J. A.; Streett, W. B. J. Chem. Thermodynomiu 1987, 19. 1251. Lainez, A.: Gopal, P.; Zollweg, J. A.: Streett. W. B. J. Chem. Thermodynamics 1989, 21, 773. Das, T. R.; Reed, C. 0.; Eubank. P. T. J. Chem. Eng. Data 1977, 22, 3. Easteal. A. J.; Woolf. L. A. In?. J. Thermoph.w. 1987, 8, 231. Kratzke. H.; Miiller. S.; Bohn, M.; Kohlen, R. J. Chem. Thermodynamics 1985, 17. 283. Vasil’ev. Yu. L. Icv. Vyssh. Uchehn. Zuved.. Neji Gaz 1984, 27( IO), 57. Gehrig, M.; Lcntz, H. J. Chem. Thermodynumics 1979, Il. 291. Das, T. R.; Reed, C. 0.; Eubank, P. T. .r. Chem. Eng. Durtl 1977, 22. 16. Czarnota. I. High Temp.-High Pressures 1985, 17. 543. Grigor’ev, B. A.: Gerasimov, A. A.; Kharin. V. E.; Rastorguev, Y. L. High Temp.-High Pressurc,s 1985, 17, 317. Ewing, M. B.; Goodwin, A. R. H.; Trusler, J. P. M. J. Chem. Thermo~vnamics 1989, 21. 867. Ewing, M. B.; McGlashan. M. L.: Trusler. J. P. M. J. Chem. Thermodynamics 1986, 18, 511, Ewing, M. B.; Goodwin. A. R. H.; McGlashan. M. L.; Trusler. J. P. M. J. Chem. Thermo&numics 1987, 19, 721. Chavez, M.; Palacios, J. M.; Tsumura, R. J. Chem. Eng. D&u 1982, 27, 350. Sachdeva, V. K.; Nanda. V. S. J. Chem. Phys. 1981, 75, 4145. Golik, A. Z.; Kuzovkov, Yu. I.; Tarasenko, 0. V. Ukr. Fi;. Zh. 1976, 21, 1492. Otpushchennikov, N. F.; Kir’yakov. B. S.; Panin, P. P. Izv. Vy.wh. Uchebn. Zuved., Nefi Gu: 1974, 17(4). 73. Houck, J. C. J. Res. Natl. Bur. Stand. A 1974, 78. 617. Melikhov, Yu. F. Ul’trazvuk Termodin. Svoitsva Veshcheslvu 1985, 8 I. Belinskii, B. A.; Ikramov, Sh. Kh. Akust. Zh. 1972, 18, 355. Ismagilov. R. G.; Ermakov, G. V. Teplojiz. Vys. Temp. 1982, 20. 677. Papadakis. E. P. J. Acoust. Sot. Am. 1967, 42, 1045. Miller. J. F. Ph.D. Thesis, Cornell University. Ithaca, New York. 1986 Del Grosso, V. A. U.S. Nuval Research Lab: Repl. 6133. Washington, D.C. 1965 Benson. G. C.: Handa. Y. P. J. Chem. Thermodvnumics 1981. 13. 887. White, G. K.; ‘Roberts; R. B. High Temp.-High Pressures 1980, 12, 31 I. ASM Metals Handbook, 9th Edition. American Society for Metals: Metals Park, Ohio. 1979. Del Grosso, V. A. U.S. Naval Reseurch Lab. Repr. 6026. Washington. D.C. 1964.