Ultrasonic speed in compressed liquid by a sing-around method

M-21 19 J. Chrm.

Thertwdvmmics

1987,

19.

1299- 1304

Ultrasonic speed in compressed liquid by a sing-around method TOSHIHARU

TAKAGI

and HIROSHI

TERANISHI

Department of Chemistry, Faculty of Engineering and Des@, Kyoto Institute of Technology.” Matsugasaki, Sakyoku. Kvoto 606. Japan i Received 12 January

1987: in.final,form

5 May 1987)

A new apparatus for the measurement of ultrasonic speed in compressed liquid was constructed. The reliability of this instrument was confirmed by measuring the speeds in pure benzene in the ranges from 283.15 to 323.15 K and pressures up to near freezing pressure, and by comparing the results with literature values. The isentropic compressibilities 4 were also determined using the experimental speeds and densities. and the results Q(U) were compared with those observed directly elsewhere KS(d) and those calculated thermodynamically h’s(c) from @. V,. 7). At atmospheric pressure, the present results, while agreeing with r~s(u) reported in the literature, show differences from r+(d) and as(c), while those for higher pressures close on a simple curve with Q(C).

1. Introduction The variation of the isentropic compressibility us for fluids with temperature and pressure is an important thermodynamic property which can be obtained from direct measurements, KS(d), by use of a piezometer; from u measurements. Q(U), derived from the ultrasonic speed u measured at low frequencies and small amplitudes with density p by use of the equation: KS = l/pu2;

(1)

and from (p. V,, T) measurements. K~(c), derived thermodynamically by combining with isothermal compressibilities J+, isobaric expansivities or, and isobaric heat capacities C, by K~ = rtT - Ta2 V/C,.

Among these, the second method is commonly used today to determine Q; a number of values for pure liquids’1-4’ and liquid mixtures’5-9’ under several conditions have been provided. However, under high pressures measurements of the speed of sound usually involve difficulties, and have therefore seldom been reported. This paper describes a new apparatus for measuring readily and accurately the ultrasonic speeds in compressed liquids covering pressures up to 200 MPa. We a Recently, the official English-language name of our University was changed from Kyoto Technical University to that above. 0021-9614/87/121299+06

$02.00/O

,(‘I 1987 Academic Press Inc. (London) Limited

1300

T. TAKAGI

AND

H. TERANISHI

present new ultrasonic speeds in pure benzene, for which a number of values of II and some thermodynamic properties under various conditions exist in the literature. The measurements were carried out over the ranges of temperature from 293.15 to 323.15 K and pressures up to near the freezing pressure. From the experimental results, isentropic compressibilities ks were calculated from equation (1) by combining with (p, V,, T), and the results were compared with those determined directly elsewhere and with those derived thermodynamically from (p, V,, T).

2. Experimental The method used for measurement of ultrasonic speed was a sing-around technique”’ (model UVM-2, Cho-onpa Ind. Co.) with fixed-path ultrasonic interferometer with a single transducer employing a gated amplifier. The interferometer is shown in figure 1. The transducer and reflector were maintained in a parallel position in a cylinder made of SUS 316 stainless steel. A short acoustic pulse, excited by the transducer (lead zircontitanate, PZT, 20 mm in diameter, 2 MHz), travelled over the known distance L in the sample. When the wave, after reflection, returned to the transducer, the signal was detected by the same transducer through the gate which had been opened in anticipation electrically by a gated amplifier. An automatic gain controller and a delay line were employed in a sing-around unit to avoid the distortion of signals caused by absorption of the acoustic wave and the interference of multiple echoes. The next acoustic short pulse was generated a definite time: delay time r = (511272 f 1.6) ns, after the arrival of the reflected wave. In the present work, the repetition period r including the delay time 7, observed using an universal counter (model TR-5822, Takeda Riken Ind. Co.) with a resolution of 0.1 ns, was from 545 to 560 us as the average value of 1000 periods. The ultrasonic speed u was obtained by the equation: u = h!,/(t - 7).

(3)

For pure water, u had been measured in detail by Wilson’i”’ and correlated by Kell and Whalley. (il) Thus 3 the acoustic path length L, difficult to obtain directly, was calibrated by measuring the periods in water from 283.15 to 323.15 K and pressures up to 200 MPa. It was (31.483+0.003)mm at 303.15K and 0.1 MPa. This length was distorted by temperature: by -0.0115 mm at 283.15 K, and pressure: by -0.0515 mm at 200 MPa, from its initial length. The strain thus observed is larger Electrode

Sample

inlet

O-Ring

(0.3 mm in thickness) q

Insulator FIGURE

Transducer 1. Fixed-Dath

Refiector ultrasonic

interferometer

ULTRASONIC

FIGURE 2. Schematic drawing

1301

SPEED IN LIQUID

of the new apparatus

for measurements

of the ultrasonic

speed.

than those for construction materials having lower expansitivity and compressibility. (r2) It may be altered by other electrical and/or mechanical factors. Figure 2 is a functional diagram of the whole apparatus. The interferometer was placed in a high-pressure vessel made of SUS 630 stainless steel, used up to 300 MPa, and this vessel was immersed in a water bath controlled within +0.02 K. The temperature in the bath and the difference in temperature between sample chamber and bath were observed by thermocouples (Thl to Th3) of T type calibrated by a 25 Q platinum resistance thermometer (model R800-1, Chino Works Ltd.) and precise bridge (model 5840, Tinsley Co. Ltd.) with a precision of 5 mK on IPTS-68. The pressure was generated by means of a hand oil-pump which combined with the intensifier (model KP-SR, Hikari High Pressure Ind. Co., maximum 500 MPa), and transmitted to the sample through a Teflon capsule in the highpressure vessel. Under each experimental condition, the pressure was measured by a precise strain gauge (model HT-2000. Toyo Baldwin Co., Ltd.) of full scale 300 MPa. The gauge was calibrated by a deadweight tester (model P-3, Nagano Keiki Ltd.) within kO.08 MPa up to 70 MPa and within +0.13 MPa in the range from 70 to 200 MPa. All the electric signals, measured by a universal counter and by a digital voltmeter (DVM), were recorded by a microcomputer to yield the respective experimental values. The measurements for each pressure were started at regular time intervals (about 30 min) after the thermostat had been stabilized at each experimental temperature. Water was distilled 2 times by using an all-Pyrex glass distillation column, and used to calibrate the pathlength with temperature and pressure. Benzene was a “chromatograph reagent” supplied by Dojin Chemical Ltd.; its purity was better than 99.9 mass per cent. 3. Results and discussion The experimental ultrasonic speeds u in benzene at various temperatures T and pressures p are listed in table 1. The u value is found to be 1299.3 m . s-r at

1302

T. TAKAGI

AND

11. TERANISHI

298.15 K and atmospheric pressure. At this condition, u values reported recently are: 1298.90 rn. s-’ by Kiyohara et LI~.,‘~’ 1299.08 m ‘s- ’ by Tamura rt u/.,‘~’ and 1299.40 rn. s- ’ by Tardajos er al. (4) These results agree with the present values to within 0.4m.s’; the difference between that in this work and Tardajos et ~11:s value, which is the most recent, is only 0.1 rn. s-‘. On the other hand. for benzene at high pressures, the speeds were measured by Bobic”’ in ranges of temperatures from 283 to 463 K and pressures up to about 60 MPa by a pulse-echo technique with an uncertainty less than ?0.5 rn. s- ‘. Richardson and Tait”“’ also measured the u values in benzene at several temperatures and pressures. These reported values are also shown in table 1. The results of Bobic agree very closely with our results from 10 to 20 MPa, while those at atmospheric pressure and near 40 MPa are slightly higher. The results of Richardson and Tait show nearly the same values at first, but similarities of our or Bobic’s results were not good under high pressures. At each experimental condition, the values of u were reproduced within an accuracy of +0.3 m.s-’ in repeated runs. The uncertainties of speed caused by the observed errors of temperature and pressure are at most i 0.1 and & 0.6 rn. so ‘. respectively. Consequently, the probable uncertainty in the measurements of speed is estimated, taking into account the observed errors and the influence on distance L caused by temperature or pressure change, to be less than kO.6 rn. s- I at atmospheric pressure and less than F 1.8 m . s- ’ under high pressures. TABLE

T

1. Ultrasonic

P

speeds u in benzene u/(m.s-I)

MPa

obs.

Ref. I

293.15

0.1 5 10

1323.2 1347.1 1369.9

1325.6 1348.3 1371.3

-

0.1 5 10 15

1299.3 1323.6 1347.3 1369.7

1301.1 1324.3 1347.8 1370.7

0.1 5 10 15 0.1 5 10 15 20 25 0.1 5 10 15 20 25 30

1276.3 1301.3 1325.2 1348.1 1228.7 1255.4 1280.5 1304.7 1327.9 1350.1 1183.1 1211.1 1237.7 1262.8 1287.2 1301.0 1332.1

1277.0 1300.9 1324.8 1348.1 1229.9 1255.2 1280.2 1304.5 1327.9 1350.6 1184.2 1211.1 1237.4 1262.7 1287.0 1310.5 1333.2

303.15

313.15

323.15

temperatures

Ref. 13

MPa

T and pressures

p with literature

values

u/(m,s-‘)

P

it

298.15

at several

obs.

Ref. 1

Ref. 13

1392.1 1413.2 1433.3

1393.8 1415.5 1436.3

~ --

30 40 50

1453.1 1490.9 1526.4

1456.3 1494.1 ~

-

-

15 20 25

1301 1349 -

20 25 30 40

1391.5 1412.4 1432.7 1470.8

1392.8 1414.1 1434.5 1473.3

1393

50 60 70

1506.8 1540.8 1573.1

1510.8 ~

1509 I543 1577

20 25 30 40

1370.5 1392.2 1412.6 1451.4

1370.7 1392.4 1413.3 1453.0

50 60 70 80

1488.4 1522.9 1556.0 1587.5

1490.9 ~ ~~

--

30 40 50 60 70 80 40 50 60 70 80 90 100

1371.7 1411.9 1450.0 1485.8 1519.7 1552.1 1374.7 1414.2 1451.0 1485.7 1518.7 1550.4 1580.4

1372.4 1413.7 1452.6 1489.8

90 100 110 120

1582.9 1612.6 1641.0 1668.4

--

1559 1581

110 120 130 140 150 160 170

1609.3 1637.3 1664.3 1690.1 1715.5 1740.1 1772.8

--

1229 1215 1319 -

1376.2 1416.2 --~ -

1434 1472

1361 1401 1439 1474 1505 1534 ~ --

~~ ~~

-

~~

ULTRASONIC

SPEED IN LlQUlD

1303

The isentropic compressibilities ICYfor benzene were derived from ultrasonic speed u and density p given by Ambrose and Lawrence.(14) The results at 0.1 MPa, presented in figure 3(a) with literature values, change smoothly with temperature. At 298.15 K the present value is (678.1 kO.5) TPa- ‘, and the uncertainty increases slightly with rise of temperature. Masood et a1.‘5) reported the values estimated, which have the overall precision within +O.l per cent. However, as shown in figure 3(a), their values are about 3 per cent higher than ours at all temperatures. Also the temperature dependence of ICYreported by Desphande and Bhatgadde”” was different from that presented here. As the most recent values at 298.15 K, results were obtained accurately by Kiyohara et aI.?’ (678.42+0.2), Tamurd and Murakami:“’ (678.26 +0.08), and Tardajos et al.: (4) 677.88 TPa- l. Our results are in good agreement with these, but our precision is not quite as good as the best in the literature. At high pressures, the values estimated from the experimental u values and Renuncio et d’s (p, V,, T) (16) decrease smoothly with increasing pressure as shown in figure 3(b). The K~(U)S thus obtained can readily be compared with those measured KS(d), and with those calculated isentropically by use of a piezometer, thermodynamically (p, V,, T), JC~(C),as a clue to the reliability of Q(U). The direct measurement, troublesome in general, is scarcely ever carried out at present. For pure benzene the KS(d) values reported in the literature are plotted as squares in figure 3(a). These KS(d) values, which appear to be in fairly good agreement among themselves except those by Apfel, increase along a nearly straight line with rise of temperature. As a whole the tiS(d) values are higher, by about 4 per cent at 298.15 K, than our Q(U) results. The thermodynamically calculated value tis(c) was obtained according to equation (2) via a and I+ derived from (p, V,, T). and the results at 0.1 MPa are also presented in figure 3(a). According to the review on (p, V,, T) for organic

283

1

I

303 T/K

I

1

323 pIMPa

FIGURE 3. Isentropic compressibility us against (a), temperature and (b), pressure. 0, This work; 0, Desphandeand Bhatgadde;‘15) 0, Richardson and Tait:(13’ @. Masood et c11.;(~’0. Tamura et ~1.:“’ 0. Kiyohara et al.;@’ 0, Tardajos et ~1.‘~’ Cl, Tyrer:“” 0, Philip;“*’ 0, Staveley et a1.;‘19’ q , Apf~l.~zu~ --, Renuncio et ~l.;“~’ - - -, Gibson and Kincaid.“”

1304

T. TAKAGI

AND

H. TERANISHI

substances reported by Tekac et al., (2‘) for pure benzene about 50 papers have so far been published. Values measured at narrow intervals of temperature and pressure, needed to estimate accurately the c1and rcr, are unexpectedly limited. In this work, we adopt the results reported by Gibson and Kincaid”” and Renuncio et al.“” as a reliable indication of (p, V,, T). For the isobaric heat capacity, the values at 0.1 MPa were those derived from the equation given in the reference 23 and measured by Tanaka. (24) At room temperature, the Q(C) results derived from Renuncio et al.‘s (p, V,, T) are compatible with liS(u) obtained in this work, while for the high-temperature range they indicate a lower value than our k,(u). The temperature dependence of this Q(C) differs from that derived using Gibson and Kincaid’s (p, V,, T). The expansivities ~1, derived from several sets of (p, V,. T), behaved very differently from one another, especially in the higher-temperature region. This irregularity gives rise to the distortion of K~(c). At high pressures the am results at 298.15 and 323.15 K derived from two sets of (p, V,, T) are presented in figure 3(b). In this figure, the difference among kS results, shown at 0.1 MPa, shrinks almost to nothing with increasing pressure, and those for the higher-pressure region were found to fit on a simple curve. Further discussion would demand closer correlation of (p. V,, T) and C,.,. The comparison described, however, is useful for checking the precision of K,(U). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

Bobic, M. J. Chem. Thermodynamics 1978, 10. 1137. Takagi, T.: Teranishi, H. J. Sot. Mat. Sri. Jpn 1984, 33, 134. Muringer, M. J. P.; Trappeniers, N. J.; Biswas, S. N. Phys. C/rem. Liq. 1985, 14, 273. Tardajos, G.; Diaz-Peiia, M.; Aicart, E. J. Chem. Thermodynamics 1986, 18. 683. Masood, A. K. M.; North, A. M.; Pethrick, R. A.: Towland, M.; Swinton, F. L. J. Chem. Thermo&namics 1977, 9, 133. Kiyohara, 0.; Halpin, C. J.; Benson, G. C. J. Chem. Thermodynamics 1978, 10, 721. Tamura, K.; Ohomuro, K.; Murakami, S. J. Chem. Thermo&namics 1983, 15. 859. Takagi. T.; Teranishi. H. J. Chem. Thermodynamics 1984, 16, 1031. Takagi, T.; Teranishi, H. J. Chem. Thermodynamics 1985, 17. 1057. Wilson, W. D. J. Acousr. Sot. Am. 1959, 31, 1067. Kell. G. S.; Whalley, E. J. Chem. Phys. 1975, 62, 3496. Bridgman, P. W. The Physics qf High Pressure. G. Bell and Sons: London. 1949. Richardson, E. G.: Tait. R. I. Phil. Msg. 1957, 2, 441. Ambrose, D.; Lawrenson, 1. J. Process Technol. Int. 1972, 17. 968. Desphande, D. D.; Bhatgadde, L. G. J. Phys. Chem. 1968, 72, 261. Renuncio. J. A. R.; Freedveld, G. J. F.: Prausnitz. J. M. J. Phvs. Chem. 1977, 81. 324. Tyrer, D. J. Chem. Sot. 1914, 105. 2534. Philip, N. M. Proc. Indian Acad. Sci. 1939, A9, 109. Staveley. L. A. K.; Tupman. W. I.; Hart, K. R. Trans. Farada.v Sot. 1955, 51, 323. Apfel, R. E. J. Acousr. Sot. Am. 1976, 59. 339. Tekac, V.: Cibulka. 1.: Holub. R. Fluid Phase Equilibria 1985, 19. 33. Gibson, R. E.; Kincaid, J. K. J. Am. Chem. Sot. 1938, 60, 51 I. Weissberger, A.: editor. Techniques of Chemistry, Vol. II. Organic Solvents. Third Ed. Wiley: New York. 1970. Tanaka, R. J. Chem. Thermodynamics 1982, 14, 259.