Measurement of the Speed of Sound in Hexane and Heptane at

Article pubs.acs.org/jced

Measurement of the Speed of Sound in Hexane and Heptane at Temperatures from (303.15 to 536.15) K and Pressures from (1.0 to 8.5) MPa Xiong Zheng, Ying Zhang, and Maogang He* †

Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, P. R. China ABSTRACT: The speed of sound in hexane and heptane (mass purity > 0.990, GC) was measured using the Brillouin light scattering method at T = (300.15 to 506.15) K for hexane, (302.15 to 536.15) K for heptane), and p = (1.0 to 8.5) MPa, including saturated liquid, saturated vapor, and compressed liquid. The expanded relative uncertainty (k = 2) of the speed of sound was estimated to be less than 1.0% over the whole investigated range of states. Polynomial representations for the speed of sound in hexane and heptane were fitted to the experimental results. A comparison of the speed of sound data with the correlation shows that, for hexane, the AAD is 0.67% for the saturated liquid, 0.36% for the saturated vapor and 0.57% for the compressed liquid respectively, and for heptane, the AAD is 0.46% for the saturated liquid, 0.38% for the saturated vapor and 0.41% for the compressed liquid, respectively. Hawley et al.19 reported the data at ambient temperature as a function of pressure. Data sets covering an extended temperature and pressure range in the liquid region were reported by Daridon et al.,20 Ball et al.,21 Boeltouwer et al.,22 and Khasanshin and Shchemelev.23 For heptane, the experimental data in saturated liquid were only reported by Zotov et al.12 Togo et al.,15 Boeltouwer et al.,22 Iglesias et al.,17 and Artigas et al.18 reported the data in liquid or gas heptane at ambient pressure as a function of temperature. The large part of these measurements was presented by Daridon et al.,20 Boeltouwer et al.22 Wang et al.,24 Sachdeva et al.,25 Freyer et al.,26 Banos et al.,27 Muringer et al.28 and Dzida et al.29 covering a large pressure and temperature range. The distribution of the literature data and our measurements in the p, T plane is shown in Figures 1 and 2. They show that previous studies were focused on the measurements at high pressure and in low or moderate temperature, but experimental data in the high temperature region are scarce. We measured the speed of sound in hexane and heptane, including saturated liquid/vapor and compressed liquid, from (300.15 to 506.15) K for hexane and (302.15 to 536.15) K for heptane and pressure up to 8.5 MPa using Brillouin light scattering method.

1. INTRODUCTION As members of the low logous series of n-alkanes, hexane and heptane are important fluids with a wide range of applications. For example, they are the major components of gasoline and raw materials in the chemical industry. Besides, they are also widely used as solvents to extract some organic fluids, such as soybean oil, safflower seed oil, etc.1,2 Thus, accurate knowledge of the thermophysical properties of hexane and heptane is required. The speed of sound is a very important thermophysical property, which is useful in modeling the thermodynamic properties of real fluids, such as virial coefficients, heat capacity, etc.3 And it is also useful in engineering areas, for example, it is an important parameter in the estimation of fuel injection timing.4 For the measurement of the speed of sound, the acoustic method is a traditional method researched, and it was studied by many authors.5−8 There are two types of resonators, one is a spherical resonator, the other is a cylinder resonator. In the comparison of these two instruments, a spherical resonator shows better precision in the measurement than a cylinder resonator, while the manufacture of a cylinder resonator is easier than that of a spherical resonator. Recently, the Brillouin light scattering (BLS) method has been regarded as a promising method, and this method has been used to measure the speed of sound of many organic fluids, such as R227ea,9 R365mfc,10 and toluene,11 etc. Experimental data for the speed of sound in hexane and heptane were published by many authors. For hexane, Zotov et al.12 and Bolotnikov et al.13,14 measured the speed of sound of saturated liquid. Tojo et al.,15 Sastry,16 Iglesias et al.17 and Artigas et al.18 reported the measurements of the sound of speed in liquid hexane at ambient pressure as a function of temperature. © XXXX American Chemical Society

2. EXPERIMENT SECTION 2.1. Material. The hexane and heptane samples were provided by Aladdin Reagent, Inc. The manufacturer specified mass fraction is higher than 0.990 (GC) for both of them. Received: December 7, 2014 Accepted: December 3, 2015

A

DOI: 10.1021/je501106d J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 2. Comparison of Speed of Sound of Saturated Liquid Toluene with the Data in Literaturea cThis work

T

−1

K 323.15 423.15 523.15 a

cLemmon −1

m·s

m·s

1200.8 806.0 425.5

1198.0 810.8 422.5

cWill m·s−1 1195.1 798.8 420.6

Expended uncertainty U is U(T) = 0.02 K and Ur(c) = 0.016.

Table 3. Standard Uncertainty in Temperature, Pressure, Impurity, and Speed of Sound platinum resistance, u1 temperature stability, u2 resistance measurement circuits, u3 standard uncertainty, uc

Figure 1. Distribution of our measurements and literature data for the speed of sound in hexane in the p, T plane: The gray area denotes the region of our measurements; blue ▶, this work: green ▽, Zotov et al.;5 gray ◁, Bolotnikov et al.;6 red ⬠, Bolotnikov et al.;7 Togo et al.;8 red crossed triangle, Sastry;9 blue +, Iglesias et al.;10 blue ×, Artigas et al.;11 red ◇, Hawley et al.;12 red ○. Daridon et al.;13 blue △, Ball et al.;14 ⬡, Boeltouwer;15 purple ☆, Khasanshin and Shchemelev.16

pressure transmitter, u1 pressure measurement circuits, u2 pressure control system, u3 standard uncertainty, uc impurity, u1 standard uncertainty, ur(i) wavelength, ur(λ0) incident angle, ur(ΘEx) Brillouin frequency shift, ur(Δω) impurity, ur(i) relative standard uncertainty, ur(c)

When filling the sample cell, the samples were filtered through membrane filters with 0.22 μm pore size to prevent dust and particles from entering the cell. 2.2. Measurement Method and Apparatus. The Brillouin scattering method (BLS) was used to measure the speed of sound in this work. A complete and more detailed description of the measurement principle can be found in various fundamental studies.30−33 Here only a brief description is presented in the following. The thermal motion of molecules via fluid induces thermal excited waves which can be considered as the mixing of a myriad of sound waves. These sound waves modulate the scattered light periodically as a diffraction grating. According to Bragg’s law, we can calculate the modulus of the sound wave vector as

Figure 2. Distribution of our measurements and literature data for the speed of sound in heptane in the p, T plane: The gray area denotes the region of our measurements: blue ▲, this work; purple ☆, Zotov et al.;5 red crossed triangle, Togo et al.;8 blue +, Iglesias et al.;10 blue ×, Artigas et al.;11 blue △, Daridon et al.;13 ⬡, Boeltouwer et al.;15 green ▽, Wang et al.;17 red ◇, Sachdeva et al.;18 gray ◁ Freyer et al.;19 red ⬠, Banos et al.;20 red ○, Muringer et al.;21 red ∗, Dzida et al.22

q≈

Table 1. Specifications of the Samples Used in This Paper material

CAS number

toluene

108-88-3

hexane

110-54-3

heptane

142-82-5

supplier Tianjin Baishi Chem. Eng. Co. Ltd. Aladdin Reagent Inc. Aladdin Reagent Inc.

mass purity

purification method

> 0.995

filtered through the membrane filters

> 0.990

filtered through the membrane filters filtered through the membrane filters

> 0.990

Temperature/K 0.005 0.008 0.002 0.01 Pressure/MPa 0.001 (p < 5.0 MPa)/0.007 (p > 5.0 MPa) 0.001 0.015 (p < 5.0 MPa)/0.03 (p > 5.0 MPa) 0.015 (p < 5.0 MPa)/0.03 (p > 5.0 MPa) Impurity 0.006 0.006 Speed of Sound 3.76 × 10−5 0.001 0.005 0.006 0.0078

2π sin ΘEx λ0

(1)

in which ΘEx is the incident angle in the air on the side of the incident, and λ0 is the wavelength of the incident light in vacuum. When a beam transmits the fluid, it will induce the sample radiating the scattered light. The spectrum of the scattered light is composed of three peaks, which are the central Rayleigh peak and the symmetrical Brillouin and anti-Brillouin peaks. According to principle of the light scattering, the frequency shift between the Brillouin peak and the Rayleigh peak is related to the speed of sound of the sample as

The samples were not further purified in order to prevent sample alterations. The specifications of the sample are listed in Table 1.

Δω = cq B

(2) DOI: 10.1021/je501106d J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 4. Experimental Speed of Sound in Hexane and Heptane along the Saturation Linea T/K

p/MPa

c/m·s−1

T/K

300.15 313.15 328.15 343.15 353.15 363.15 373.15 383.15 393.15

0.014 0.063 0.094 0.122 0.161 0.214 0.260 0.331 0.413

1073 993.0 926.8 882.7 838.8 794.9 751.0 707.2 663.4

403.15 413.15 423.15 433.15 443.15 448.15 453.15 458.15 463.15

383.15 393.15 403.15 413.15 423.15 433.15 443.15

0.331 0.413 0.512 0.627 0.762 0.924 1.113

178.6 176.6 174.3 171.6 168.3 164.2 159.4

448.15 453.15 458.15 463.15 468.15 473.15 478.15

302.15 318.15 333.15 348.15 363.15 378.15 393.15 408.15 418.15 428.15

0.012 0.031 0.050 0.084 0.116 0.152 0.204 0.286 0.352 0.441

1108. 1042. 981.5 921.1 861.2 801.6 742.3 683.1 643.5 603.9

438.15 448.15 453.15 458.15 463.15 468.15 473.15 478.15 483.15 488.15

408.15 418.15 428.15 438.15 448.15 453.15 458.15 463.15

0.286 0.352 0.441 0.535 0.654 0.711 0.780 0.853

170.3 168.1 165.9 163.4 160.5 158.8 157.0 155.0

468.15 473.15 478.15 483.15 488.15 493.15 498.15 503.15

p/MPa Hexane Saturated Liquid 0.512 0.627 0.762 0.924 1.113 1.210 1.322 1.447 1.563 Saturated Vapor 1.210 1.322 1.447 1.563 1.700 1.843 1.992 Heptane Saturated Liquid 0.535 0.654 0.711 0.780 0.853 0.935 1.022 1.114 1.203 1.307 Saturated Vapor 0.935 1.022 1.114 1.203 1.307 1.409 1.532 1.649

c/m·s−1

T/K

p/MPa

c/m·s−1

619.5 575.6 531.6 487.5 443.1 420.7 398.2 375.6 352.8

468.15 473.15 478.15 483.15 488.15 493.15 498.15 503.15 506.15

1.700 1.843 1.992 2.144 2.313 2.491 2.677 2.878 2.991

329.8 306.4 282.6 258.2 233.0 206.4 177.3 142.0 109.7

156.6 153.5 150.1 146.4 142.2 137.6 132.5

483.15 488.15 493.15 498.15 503.15 506.15

2.144 2.313 2.491 2.677 2.878 2.991

126.9 120.6 113.4 105.3 95.91 89.34

564.0 523.9 503.6 483.3 462.8 442.2 421.3 400.3 379.0 357.4

493.15 498.15 503.15 508.15 513.15 518.15 523.15 528.15 533.15 536.15

1.409 1.532 1.649 1.781 1.910 2.049 2.201 2.358 2.519 2.630

335.4 313.0 290.1 266.6 242.4 217.3 190.9 162.7 131.9 111.1

152.8 150.3 147.5 144.5 141.2 137.5 133.4 129.0

508.15 513.15 518.15 523.15 528.15 533.15 536.15

1.781 1.910 2.049 2.201 2.358 2.519 2.630

124.1 118.7 112.8 106.4 99.37 91.71 86.78

a

Expended uncertainties U are U(T) = 0.02 K, U(p) = 0.03 MPa for p = (0 to 5.0) MPa, U(p) = 0.06 MPa for p = (5.0 to 20) MPa, U(i) = 0.012 and Ur(c) = 0.016.

in which Δω is the frequency shift of the Brillouin peak and c is the speed of sound. Equation 2 implies that we can calculate the speed of sound of the fluid if the frequency shift of the Brillouin peak is measured. The experimental setup is the same as used in our previous paper.23 In this system, we use a continuous wave diode pumped solid state laser (Cobolt Samba, 532 nm, 300 mW) with a single longitudinal mode as the laser supplier. When the laser irradiates the sample, it will induce the scattering light. And then, the scattering light is filtered by Fabry−Perot interferometer (FPI, Thorlabs SA200-5B), and we use the photon counting head (Hamamatsu H8259-01) to detect the scattering light and convert the light signal into the TTL signal. A data acquisition card (DAQ card, NI-PCI6221) is used to record the TTL signal. In this way we can get the spectrum of the scattering light. 2.3. Experimental System Calibration. To verify the reliability of the experimental system, we have measured the

speed of sound of toluene in saturated liquid and compared our data with other authors, and the results are shown in Table 2. The specifications of toluene sample used in this work are listed in Table 1. In 1998, Will et al.11 measured the speed of sound of saturated liquid toluene using the Brillouin light scattering method; the absolute average deviation is 0.85%. Recently, Lemmon et al.34 also developed the fundamental equation of state for toluene with uncertainty of 1% below 500 K and 2% above 500 K. Compared with the value calculated by EOS, the absolute average deviation is 0.51%. It shows that the accuracy and stability of this system is good. 2.4. Assessment of Experimental Uncertainties. The expanded uncertainties in temperature and pressure can be determined by

U = kuc = k C

∑ u i2



Article

Table 5. Experimental Speed of Sound in Hexane and Heptane for Compressed Liquida c/m·s−1

p/MPa

c/m·s−1

p/MPa

p/MPa

c/m·s−1

Hexane T = 300.15 1.00 2.50 T = 313.15 1.00 2.50 T = 328.15 1.00 2.50 T = 343.15 1.00 2.50 T = 353.15 1.00 2.50 T = 363.15 1.00 2.50 T = 373.15 1.00 2.50 T = 383.15 1.00 2.50 T = 393.15 1.00 2.50 T = 403.15 1.00 2.50 T = 413.15 1.00 2.50 T = 423.15 1.00 2.50 T = 433.15 1.00 2.50 T = 443.15 2.50 4.00 T = 448.15 2.50 4.00 T = 453.15 2.50 4.00 T = 458.15 2.50 4.00 T = 463.15 2.50 4.00 T = 468.15 2.50 4.00 T = 473.15 2.50 4.00

K 1080 1090

4.00 5.50

1102 1115

7.00 8.50

1129 1140

1027 1038

4.00 5.50

1049 1062

7.00 8.50

1077 1092

964.1 975.9

4.00 5.50

988.6 1002

7.00 8.50

1017 1032

900.3 913.8

4.00 5.50

927.8 942.3

7.00 8.50

957.3 972.8

857.0 872.0

4.00 5.50

887.1 902.5

7.00 8.50

918.1 934.0

813.22 829.9

4.00 5.50

846.4 862.9

7.00 8.50

879.3 895.7

768.8 787.4

4.00 5.50

805.6 823.4

7.00 8.50

840.9 857.9

723.8 744.7

4.00 5.50

764.8 784.1

7.00 8.50

802.8 820.7

678.3 701.6

4.00 5.50

723.8 744.9

7.00 8.50

765.0 783.9

632.1 658.2

4.00 5.50

682.8 705.9

7.00 8.50

727.5 747.7

585.4 614.5

4.00 5.50

641.7 667.0

7.00 8.50

690.4 711.9

538.1 570.5

4.00 5.50

600.6 628.3

7.00 8.50

653.7 676.7

490.1 526.2

4.00 5.50

559.3 589.7

7.5 8.50

617.3 642.0

481.5 518.0

5.50 7.00

551.3 581.2

8.50

607.8

459.1 497.4

5.50 7.00

532.1 563.3

8.50

590.9

436.6 476.7

5.50 7.00

513.0 545.4

8.50

574.1

414.0 456.0

5.50 7.00

493.9 527.7

8.50

557.4

391.3 435.2

5.50 7.00

474.8 510.1

8.50

540.9

368.5 414.5

5.50 7.00

455.8 492.5

8.50

524.5

345.7 393.7

5.50 7.00

436.8 475.0

8.50

508.2

K

K

K

K

K

K

K

K

K

K

K

K

K

K

K

K

K

K

K

D



Article

Table 5. continued c/m·s−1

p/MPa

p/MPa

c/m·s−1

p/MPa

c/m·s−1

Hexane T = 478.15 2.50 4.00 T = 483.15 4.00 5.50 T = 488.15 4.00 T = 493.15 4.00 T = 498.15 4.00 T = 503.15 4.00 T = 506.15 4.00

K 322.8 372.9

5.50 7.00

417.9 457.6

8.50

492.1

352.1 399.0

7.00

440.3

8.50

476.1

331.3

5.50

380.1

310.5

5.50

361.3

289.6

5.50

342.5

268.8

5.50

323.7

256.2

5.50

K

K K K K K 312.5 Heptane

T = 302.15 1.00 2.50 T = 318.15 1.00 2.50 T = 333.15 1.00 2.50 T = 348.15 1.00 2.50 T = 363.15 1.00 2.50 T = 378.15 1.00 2.50 T = 393.15 1.00 2.50 T = 408.15 1.00 2.50 T = 418.15 1.00 2.50 T = 428.15 1.00 2.50 T = 438.15 1.00 2.50 T = 448.15 1.00 2.50 T = 453.15 1.00 2.50 T = 458.15 1.00 2.50 T = 463.15

K 1112.9 1126.4

4.00 5.50

1139 1152

7.00 8.50

1163.2 1174.3

1054.1 1066.6

4.00 5.50

1079 1091

7.00 8.50

1102 1113

997.8 1010

4.00 5.50

1022 1034

7.00 8.50

1045 1057

940.3 952.9

4.00 5.50

965.3 977.6

7.00 8.50

989.7 1002

881.6 895.3

4.00 5.50

908.8 922.0

7.00 8.50

934.9 947.6

821.8 837.2

4.00 5.50

852.2 866.8

7.00 8.50

881.0 894.7

760.8 778.7

4.00 5.50

795.8 812.2

7.00 8.50

827.9 842.9

698.6 719.6

4.00 5.50

739.4 758.2

7.00 8.50

775.8 792.2

656.6 680.0

4.00 5.50

701.9 722.4

7.00 8.50

741.5 759.1

614.0 640.1

4.00 5.50

664.4 686.9

7.00 8.50

707.6 726.4

570.9 600.0

4.00 5.50

626.9 651.6

7.00 8.50

674.0 694.3

527.2 559.7

4.00 5.50

589.5 616.6

7.00 8.50

640.9 662.6

505.2 539.5

4.00 5.50

570.8 599.1

7.00 8.50

624.5 647.0

483.1 519.2

4.00 5.50

552.1 581.7

7.00 8.50

608.2 631.4

K

K

K

K

K

K

K

K

K

K

K

K

K

K E



Article

Table 5. continued p/MPa

c/m·s−1

p/MPa

c/m·s−1

p/MPa

c/m·s−1

498.9 533.4

5.50 7.00

564.4 592.0

8.50

616.0

478.5 514.7

5.50 7.00

547.2 559.8

8.50

600.8

458.0 496.0

5.50 7.00

530.0 543.9

8.50

570.6

437.5 477.4

5.50 7.00

512. 528.1

8.50

555.7

416.9 458.7

5.50 7.00

495.7 512.3

8.50

540.9

396.3 440.0

5.50 7.00

478.7 496.7

8.50

526.3

375.7

4.00

421.4

5.50

461.7

354.9

4.00

402.8

5.50

444.8

334.2

4.00

384.1

5.50

428.0

313.3

4.00

365.5

5.50

411.2

292.4

4.00

346.9

5.50

394.5

271.5

4.00

328.3

5.50

377.8

309.7

5.50

361.2

291.1

5.50

344.6

Heptane 2.50 4.00 T = 468.15 2.50 4.00 T = 473.15 2.50 4.00 T = 478.15 2.50 4.00 T = 483.15 2.50 4.00 T = 488.15 2.50 4.00 T = 493.15 2.50 T = 498.15 2.50 T = 503.15 2.50 T = 508.15 2.50 T = 513.15 2.50 T = 518.15 2.50 T = 523.15 4.00 T = 528.15 4.00

K

K

K

K

K

K K K K K K K K

a

Expanded uncertainties U are U(T) = 0.02 K, U(p) = 0.03 MPa for p = (0 to 5.0) MPa, U(p) = 0.06 MPa for p = (5.0 to 20) MPa, U(i) = 0.012 and Ur(c) = 0.016.

in which ui is the uncertainty in each influence factor, uc is the standard uncertainty which is composed of uncertainties of all influence factors, and k is the coverage factor, it is usually considered to be 2 or 3 when the degree of confidence is 95% or 99%, respectively. The standard uncertainty in speed of sound is estimated by u r (c ) =

The results listed in Table 3 show that the expanded uncertainties in temperature, pressure, impurity, and speed of sound are estimated to be less than 0.02 K, 0.03 MPa for p = (0 to 5.0) MPa, 0.06 MPa for p = (5.0 to 20) MPa, and 0.012 and 0.016 over the whole examined p−T region with a coverage factor of k = 2, respectively.

0.00152 + ur2(Δω) + ur2(λ 0) + ( − 1)2 ur2(ΘEx )

3. RESULTS The measurements of speed of sound in hexane and heptane were both carried out along the saturated line and in the compressed liquid. During the measurements along the saturation line, the sample fluid was maintained in the two-phase region to satisfy the saturated conditions. Each experimental point was independently measured six times at three different scattering angles. The repeatability of the results was better than 0.2% and the average value was adopted in the measurements. To enable a fair comparison of our data with literature data and to facilitate the use of our data, the experimental data of speed of sound along the saturated line were correlated by least-squares fit to the polynomial function,11

(4)

in which ur(Δω), ur(λ0), and ur(ΘEx) are the standard uncertainties in the Brillouin frequency shift, the wavelength of the incident light, and the incident angle, respectively. A constant 0.0015 results from the approximate calculation of the scattering vector modulus as shown in eq 1. A more detailed description of the measurement uncertainties in speed of sound has been proposed in ref 33. The expanded uncertainty in speed of sound can be calculated from Ur(c) = k·ur(c). The uncertainty caused by the impurity is also significant, so in this paper we also analyze the uncertainty of impurity according to ref 35. With a purity of 0.99, the standard uncertainty caused by purity ur (i) = 0.01/ 3 ≈ 0.006

i ⎛ TC − T ⎞a4 ⎛T ⎞ ⎜ ⎟ + a a ⎟ ∑ i⎝ ⎠ 3⎜ K ⎝ TC ⎠ i=0 2

c= (5) F



Article

Table 6. Fitted Coefficients of Equation 6 and 7a

a

saturated liquid

saturated vapor

a0 a1 a2 a3 a4

2.09435 × 103 −4.81077 × 10° 8.38444 × 10−4 3.72578 × 102 7.99991 × 10−2

Hexane 3.87673 × 10−3 −1.21141 × 101 9.15230 × 10−3 −3.44499 × 103 1.53256 × 10°

AAD/% MD/% Bias/%

0.67 0.82 0.0008

a0 a1 a2 a3 a4

−9.28718 × 102 3.60361 × 10−2 3.37195 × 10−3 3.47441 × 103 8.59199 × 10−1

0.33 1.11 0.0017 Heptane −4.21563 × 103 1.77235 × 101 −1.80899 × 10−2 5.83389 × 103 2.52757 × 10°

AAD/% MD/% Bias/%

0.46 1.56 0.0013

0.38 1.10 0.0024

compressed liquid a00 a10 a20 a01 a11 a21 a02 a12 a22

1.94354 × 103 −1.73569 × 10° −3.87569 × 10−3 8.84079 × 101 −5.71635 × 10−1 9.88151 × 10−4 −1.13217 × 10° 1.29911 × 10−2 −2.72987 × 10−5 0.57 1.72 −0.0105

a00 a10 a20 a01 a11 a21 a02 a12 a22

1.84271 × 103 −1.32698 × 10° −3.70415 × 10−3 1.39436 × 102 −7.85930 × 10−1 1.17769 × 10−3 −6.33473 × 10° 3.64706 × 10−2 −5.28258 × 10−5 0.41 1.67 −0.0010

The coefficients a0−a3 and aij are in unit of m·s−1, while a4 is dimensionless.

in which c is the speed of sound in m·s−1, the ai are the fitted coefficients, T is the absolute temperature in K, and TC is the critical temperature. And the experimental data of compressed liquid were correlated by 2

liquid and vapor region from ambient temperature upward and extend up to the critical temperature with pressures to 8.5 MPa. For hexane, the measurement regions were carried out at T = (300.15 to 506.15) K for the saturated liquid, T = (383.15 to 506.15) K for the saturated vapor, and at T = (300.15 to 506.15) K for the compressed liquid along six isobaric lines p = (1 to 8.5) MPa. For heptane, the measurement regions were carried out at T = (302.15 to 536.15) K for the saturated liquid, T = (408.15 to 536.15) K for the saturated vapor, and at T = (302.15 to 536.15) K for the compressed liquid along six isobaric lines p = (1 to 8.5) MPa. The experimental speed of sound in hexane and heptane measured along the saturation line and six isobaric lines p = (1 to 8.5) MPa are presented in Tables 4 and 5, respectively. The experimental data were fitted to the polynomials in eq 6 and 7. The results for the coefficients are listed in Table 6. The critical temperatures of hexane and heptane are taken as TC = 507.79 K for hexane and TC = 540.14 K for heptane, as measured by He et al.36 We compared our experimental speeds of sound with the polynomial fit. For hexane, the AAD, MD, and Bias are 0.67%, 0.82%, and 0.0008% for the saturated liquid, 0.36%, 1.11%, and 0.0017% for the saturated vapor, and 0.57%, 1.72%, and −0.0105% for the compressed liquid, respectively. For heptane, the AAD, MD, and Bias are 0.46%, 1.56%, and 0.0016% for the saturated liquid, 0.38%, 1.10%, and 0.0024%, for the saturated vapor, and 0.41%, 1.67%, and −0.0010% for the compressed liquid, respectively. Figures 3 and 4 show the speed of sound data in hexane and heptane measured along the saturation line and six isobaric lines, respectively.

i

2

⎛ T ⎞ ⎛ p ⎞j ⎟ c = ∑ ∑ aij⎜ ⎟ ⎜ ⎝ K ⎠ ⎝ MPa ⎠ i=0 j=0

(7)

in which p is the pressure in MPa. The absolute average of the deviations (AAD), maximum deviation (MD), and average deviation (Bias) are introduced to assess the performances of the polynomial expressions, they are defined as AAD/% =

100 N

N

∑ i

cexp, i ccal, i

−1 (8)

⎞ ⎛ c exp, i MD/% = 100 max⎜⎜ − 1 ⎟⎟ ⎠ ⎝ ccal, i bias/% =

100 N

N

⎛ cexp, i

∑ ⎜⎜ i

⎝ ccal, i

⎞ − 1⎟⎟ ⎠

(9)

(10)

in which cexp,i is the ith experimental speed of sound datum, ccal,i is the ith speed of sound calculated from the polynomial expression. The distribution of our measurements in the p, T plane is shown in Figures 1 and 2. Our data cover the subcritical G



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Figure 5. Deviations of the speed of sound in saturated hexane: ■, this work for saturated liquid; blue ▼, this work for saturated vapor; red ●, Zotov et al.;5 green ▲, Bolotnikov et al.;6 , EOS of Span and Wagner31 for saturated liquid; ---, EOS of Span and Wagner31 for saturated vapor.

Figure 3. Speed of sound in hexane: red ●, saturated vapor; ■, saturated liquid; red crossed hexagram, p = 1.0 MPa; blue crossed triangle, p = 2.5 MPa; pink crossed diamond, p = 4.0 MPa; green crossed star, p = 5.5 MPa; red ∗, p = 7.0 MPa; blue crossed pentagram, p = 8.5 MPa; , correction (eq 6 and 7).

Figure 6. Deviations of the speed of sound in saturated heptane: ■, this work for saturated liquid; blue ▲, this work for saturated vapor; red ●, Zotov et al.;5 , EOS of Span and Wagner31 for saturated liquid; ---, EOS of Span and Wagner31 for saturated vapor.

Figure 4. Speed of sound in heptane: red ●, saturated vapor; ■, saturated liquid; red crossed hexagram, p = 1.0 MPa; blue crossed triangle, p = 2.5 MPa; pink crossed diamond, p = 4.0 MPa; green crossed star, p = 5.5 MPa; red ∗, p = 7.0 MPa; blue crossed pentagram, p = 8.5 MPa; , correction (eq 6 and 7).

well with those of Zotov et al. below 360 K. With increasing temperature, the deviations become largeer in the negative direction. The largest deviations are observed at about 460 K. When reaching the critical point, the deviations increase strongly. Our results both for saturated liquid and vapor heptane at the low and moderate temperatures agree well with the EOS. The deviations are below 1% below 480 K, while they increase strongly with temperature. Figure 7 and Figure 8 show the deviations of our experimental speed of sound from literature data for compressed liquid hexane and heptane. The measurements of Daridon et al., Ball and Trusler for hexane, and Muringer et al. and Boelhouwer for heptane cover almost all measured regions in literatures, so we choose their results for comparison. For hexane, the differences between Daridon et al. and Span and Wagner are somewhat large, and our data lie between theirs and agree with the results of Ball and Trusler within 1%. At high temperatures, we can only

4. DISCUSSION In this section our experimental speed of sound data were compared with literature data and the equations of state (EOS) for hexane and heptane proposed by Span and Wagner.37 Figure 5 and Figure 6 show the deviations of our experimental speeds of sound and literature data for saturated hexane and heptane. For hexane, it is clear that our results agree well with those of Zotov et al. and Bolotnikov et al. at low temperatures, the relative deviations are about 0.5% below 400 K, while the deviations become larger at higher temperatures. Our data for saturated liquid and vapor hexane at moderate temperatures agree with the EOS within 1% between 370 and 430 K, while the deviations increase at lower and higher temperature regions, especially near the critical point. For heptane, our results agree H



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Figure 7. Deviations of the speed of sound in compressed liquid hexane: ■, Daridon et al.;13 red ●, Ball and Trusler;14 , EOS of Span and Wagner.31

below 1% in all measured regions, and our results also agree well with values calculated from the EOS of Span and Wagner at low and moderate temperatures, below 470 K the deviations are below 1%, while they increase strongly near the critical point.

compare our data with value calculated from the EOS of Span and Wagner. With increasing temperature, the deviations become smaller, while near the critical point up to 6% are observed. For heptane, our results agree within 1% with the data of Muringer et al. and of Boelhouwer, the deviations are I



Article

Figure 8. Deviations of the speed of sound in compressed liquid heptane: ■, Daridon etc.;13 red ●, Ball and Trusler.;14 , Eos of Span and Wagner.23

p = (1 to 8.5) MPa. For heptane, the examined region is T = (302.15 to 536.15) K for the saturated liquid, T = (408.15 to 536.15) K for the saturated vapor, and T = (302.15 to 536.15) K for the compressed liquid along six isobaric lines with p = (1 to 8.5) MPa. For the compressed liquid of hexane and heptane, the speed of sound increases slightly with pressure and decreases with temperature over the whole examined region. Polynomial

5. CONCLUSIONS Speeds of sound in hexane and heptane were measured using the Brillouin light scattering method (BLS). The examined region is T = (300.15 to 506.15) K for saturated liquid, T = (383.15 to 506.15) K for saturated vapor and T = (300.15 to 506.15) K for compressed liquid hexane along six isobaric lines with J



Article

(15) Orge, B.; Rodriguez, A.; Canosa, J. M.; Marino, G.; Iglesias, M.; Tojo, J. Variation of densities, refractive indices, and speeds of sound with hexane, heptane, and octane. J. Chem. Eng. Data 1999, 44, 1041− 1047. (16) Sastry, N. V. Densities, Excess volumes, speeds of sound and excess isentropic compressibilities for 2-butoxyethanol + n-hexane and + n-heptane mixtures at 303.15 and 313.15 K. Fluid Phase Equilib. 1997, 128, 173−181. (17) Gayol, A.; Iglesias, M.; Goenaga, J. M.; Concha, R. G.; Resa, J. M. Temperature influence on solution properties of ethanol + n-alkane mixtures. J. Mol. Liq. 2007, 135, 105−114. (18) Alonso, E.; Guerrero, H.; Montano, D.; Lafuente, C.; Artigas, H. Thermophysical study of the n-hexane or n-heptane with 1chloropropane systems. Thermochim. Acta 2011, 525, 71−77. (19) Hawley, S.; Alleora, J.; Holton, G. Ultrasonic-absorption and sound-speed data for nine liquids at high pressures. J. Acoust. Soc. Am. 1970, 47, 137−143. (20) Daridon, J. L.; Lagourette, B. J.; Grolier, P. E. Experimental measurements of the speed of sound in n-hexane from 293 to 373 K and up to 150 MPa. Int. J. Thermophys. 1998, 19, 145−160. (21) Ball, S. J.; Trusler, J. P. M. Speed of sound of n-hexane and nhexadecane at temperatures between 298 and 373 K and pressures up to 100 MPa. Int. J. Thermophys. 2001, 22, 427−443. (22) Boelhouwer, J. W. M. Sound velocities in and adiabatic compressibilities of liquid alkanes at various temperatures and pressures. Physica 1967, 34, 484−492. (23) Khasanshin, T. S.; Shchemelev, A. P. Sound Velocity in Liquid nAlkanes. High Temp. 2001, 39, 60−67. (24) Wang, Z. J.; Nur, A. Ultrasonic velocities in pure hydrocarbons and mixtures. J. Acoust. Soc. Am. 1991, 89, 2725−2730. (25) Sachdeva, V. K.; Nanda, V. S. Ultrasonic wave velocity in some normal paraffins. J. Chem. Phys. 1981, 75, 4745−4746. (26) Freyer, E. B.; Hubbard, W. J. D.; Andrews, H. Sonic studies of the physical properties of liquids. I. The sonic interferometer. The velocity of sound in some organic liquids and their compressibilities. J. Am. Chem. Soc. 1929, 51, 759−770. (27) Banos, L. M.; Rivas, C.; Embid, J. M.; Otín, S. Excess molar volumes and speed of sound in bromotrichloromethane + n-heptane, dibromomethane + n-heptane, bromotrichloromethane + dibromomethane, and bromotrichloromethane + bromochloromethane at temperatures from (293.15 to 313.15) K. J. Chem. Eng. Data 2013, 58, 248−256. (28) Muringer, M. J. P.; Trappeniers, N. J. S.; Biswas, 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. (29) Dzida, M.; Cempa, M. Thermodynamic and acoustic properties of (heptane + dodecane) mixtures under elevated pressures. J. Chem. Thermodyn. 2008, 40, 1531−1541. (30) Mountain, R. D. Spectral distribution of scattered light in a simple fluid. Rev. Mod. Phys. 1996, 38, 205−213. (31) 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. (32) Kraft, K.; Leipertz, A. Sound velocity measurements by the use of dynamic light scattering: data reduction by the application of a Fourier transformation. Appl. Opt. 1993, 32, 3886−3893. (33) Wang, S.; Zhang, Y.; He, M. G.; Zheng, X.; Chen, L. B. Thermal diffusivity and speed of sound of saturated pentane from light scattering. Int. J. Thermophys. 2014, 35, 1450−1464. (34) Lemmon, E. W.; Span, R. Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 2006, 51, 785−850. (35) Guide to the expression of uncertainty in measurement, corrected and reprinted; ISO: Genevese, 1995. (36) Liu, Y.; Zhang, Y.; He, M. G.; Xin, N. Determination of the critical properties of C6-C10 n-alkanes and their binary systems using a flow apparatus. J. Chem. Eng. Data 2014, 59, 3852−3857. (37) Span, R.; Wagner, W. Equations of state for technical applications. II. Results for nonpolar fluids. Int. J. Thermophys. 2001, 24, 41−109.

representations for the speed of sound in hexane and heptane are proposed. For hexane, the ADD, MD, and Bias are 0.67%, 0.82%, and 0.0008% for the saturated liquid, 0.33%, 1.11%, and 0.0017% for the saturated vapor, and 0.57%, 1.72%, and −0.0105% for the compressed liquid, respectively. For heptane, the AAD, MD, and Bias are 0.46%, 1.56%, and 0.0016%, for the saturated liquid, 0.41%, 1.67%, and −0.0010% for the saturated vapor, and 0.41%, 1.67%, and −0.0010% for the compressed liquid, respectively.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86-29-8266-3863. Fax: +86-29-8266-8789. E-mail: [email protected]. Funding

This work was supported by the National Natural Science Fund for Distinguished Young Scholars of China (NSFC No. 51525604). Notes

The authors declare no competing financial interest.

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REFERENCES

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Measurement of the Speed of Sound in Hexane and Heptane at

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