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Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Measurement of the Speed of Sound in Near-Critical and Supercritical n‑Heptane at Temperatures from (513.40 to 650.90) K and Pressures from (2.5 to 10.0) MPa Ying Zhang, Yutian Chen, Taotao Zhan, 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
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ABSTRACT: The speed of sound in n-heptane was measured by the Brillouin light scattering (BLS) method. The examined region is T = (513.40 to 650.90) K along seven isobaric lines at p = (2.5, 3.0, 4.0, 5.0, 6.0, 8.0, and 10.0) MPa, which was near the critical point of n-heptane. The relative expanded uncertainty (k = 2) of BLS experimental system is estimated to be 0.990 filtered through the membrane filters B
DOI: 10.1021/acs.jced.8b00212 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Figure 2. Typical count rate variation with time.
to the principle of Doppler frequency shift, the frequency shift of the scattered light can be determined by the speed of sound wave in the directions of the scattered light and the incident light ij Δω yz ij c yz ij ΘS yz jj z j z jj ω zzz = ±2njjj c zzz sinjjj 2 zzz k 0{ k 0{ k {
in which Δω is the frequency shift of scattered light, ω0 is the frequency of incident light, c is the speed of sound in sample and c0 is the speed of light in vacuum. Combining eqs 1 and 2, the relationship between the speed of sound in sample and the frequency shift of scattered light can be expressed as eq 3
Figure 3. BLS experimental setup for the speed of sound measurement.
electric susceptibility is a function of the thermodynamic variables and the macroscopic transport properties of bulk fluid, and the corresponding microscopic fluctuation relaxation processes follow the same governing equation. So the thermophysical properties can be related to the spectrum of the scattered light. The thermal motion of fluid molecules induces thermal excited waves, which can be considered as the mixing of sound waves. As a diffraction grating, these sound waves periodically modulate the scattered light. According to Bragg’s law, the modulus of the sound wave vector can be calculated by 4nπ sin iΘ y q = 2|kI| sinjjjj S zzzz = λ0 k 2 {
ΘS 2
( ) ≈ 2π sin Θ λ0
(2)
Δω = c·q
(3)
Equation 3 implies that the Brillouin frequency shift of scattered light equals the frequency of the sound wave, and the speed of sound in sample can be calculated as the frequency shift of Brillouin peak is measured. The photon counter PMT and the Fabry−Perot interferometer were employed to determine the frequency shift of Brillouin peak. Figure 2 shows a typical count rate variation with time, which can also be regarded as the scattered light spectrum. For a more detailed description of the fundamentals and methodological principles, the reader is referred to specialized literatures and the authors’ previous papers.26−30 The optical setup and the temperature and pressure control and measure units employed in this work are shown in Figures 3 and 4, which have been introduced in detail in the authors’ previous paper.30 A continuous wave diode pumped solid-state laser (Cobolt Samba, 532 nm, 300 mW) adopting single longitudinal mode is used as the light source. A Glan−Taylor prism for improving the polarization of the probing beam is
Ex
(1)
in which kI is the wave vector of the incident light, ΘS is the scattering angle in the sample, n is the refractive index of the fluid, λ0 is the wavelength of the incident light in vacuum, and ΘEx is the incident angle in air. The typical scattered light spectrum of BLS includes the central Rayleigh peak and the symmetrical Brillouin peak and anti-Brillouin peak. According
Figure 4. Temperature and pressure control and measurement units. C
DOI: 10.1021/acs.jced.8b00212 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 3. Experimental Speeds of Sound in Near-Critical and Supercritical n-Heptane
a
T
p
c
T
p
c
(K)
(MPa)
(m·s−1)
100Ur(c)
(K)
(MPa)
(m·s−1)
100Ur(c)
513.92 525.23 528.93 534.12 538.13 544.09 547.02 552.59 559.91 564.02 572.57 584.19 590.48 601.60 612.58 620.87 632.18 640.72 650.07 513.59 523.83 528.41 532.76 538.36 544.95 549.04 553.93 559.74 563.09 574.33 582.39 591.77 602.84 612.37 623.42 632.04 641.53 650.90 513.65 524.25 528.90 533.55 537.58 541.47 549.16 553.43 560.41 563.94 575.28 584.60 591.62 603.68 612.08 621.22 631.85 641.95 515.23 521.41 534.45
2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 5.0 5.0 5.0
266.7 196.3 167.0 121.4 101.3 100.7 107.6 118.7 129.2 135.5 144.5 156.3 161.6 170.4 179.2 183.8 189.4 192.9 195.8 293.6 242.6 218.6 193.8 152.7 115.6 105.3 110.6 116.0 119.8 134.5 143.0 152.9 161.4 167.6 174.6 180.0 186.2 189.4 333.8 291.4 269.0 252.2 231.1 208.3 178.4 160.1 132.6 124.5 113.6 122.6 127.8 143.9 149.8 157.3 163.2 173.3 363.9 337.0 294.0
2.7 2.3 2.1 1.9 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.1 2.1 2.1 2.2 2.2 2.2 2.3 2.3 2.9 2.6 2.4 2.3 2.1 1.9 1.8 1.9 1.9 1.9 2.0 2.0 2.1 2.1 2.1 2.2 2.2 2.2 2.2 3.2 2.9 2.7 2.6 2.5 2.3 2.2 2.1 2.0 1.9 1.9 1.9 1.9 2.0 2.0 2.1 2.1 2.2 3.4 3.2 2.9
574.87 577.04 582.31 588.17 592.28 597.48 602.30 607.65 615.11 623.25 632.29 643.51 513.58 524.62 529.10 533.77 539.09 543.60 548.98 553.05 557.86 563.84 574.85 583.18 592.57 604.10 613.73 622.48 632.41 643.04 513.40 524.62 528.95 533.57 538.84 542.55 548.66 553.19 557.81 563.58 574.41 583.10 593.19 604.67 613.93 620.20 632.86 642.59 515.30 523.19 533.40 543.16 553.20 563.03 573.39 579.18 582.86 587.85 592.71
5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0
160.5 154.2 142.7 139.9 136.4 135.4 135.3 136.7 142.6 150.6 156.6 165.4 394.2 357.7 344.2 332.0 316.7 300.6 284.0 270.3 255.8 236.5 211.9 191.5 176.1 161.8 158.5 158.8 159.4 164.7 451.7 417.8 403.6 391.3 376.3 364.4 346.4 335.8 325.5 312.8 287.4 270.7 249.2 226.0 218.0 211.6 201.0 195.7 481.2 459.3 437.1 413.3 388.9 363.9 345.2 331.9 325.0 315.8 307.5
2.1 2.1 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.1 2.1 3.6 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.1 2.1 2.1 2.1 4.0 3.8 3.6 3.6 3.5 3.4 3.2 3.2 3.1 3.0 2.8 2.7 2.6 2.5 2.4 2.4 2.3 2.3 4.2 4.1 3.9 3.7 3.5 3.4 3.2 3.1 3.1 3.0 3.0
D
DOI: 10.1021/acs.jced.8b00212 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 3. continued T
p
c
T
p
c
(K)
(MPa)
(m·s−1)
100Ur(c)
(K)
(MPa)
(m·s−1)
100Ur(c)
543.50 553.42 565.65
5.0 5.0 5.0
262.3 225.2 187.9
2.7 2.4 2.2
603.51 614.03 623.13
10.0 10.0 10.0
291.2 272.9 260.7
2.9 2.7 2.7
a
Ur(c) is the relative expanded uncertainty for a state point. Expended uncertainties are U(T) = 0.032 K and U(p) = 0.036 MPa. The level of confidence is 0.95 (k = 2).
adopted. The probing beam passing through the sample will induce it to radiate the scattered light spontaneously. With diameters of 1 and 0.5 mm, respectively, two pinholes are used, of which the distance is ∼1 m for limiting the scattered light in a coherent area and determining the scattering angle. The scattered light is filtered by a Fabry−Perot interferometer (FPI, Thorlabs SA200-5B) and becomes weak. A photon counting head (Hamamatsu H8259-01) can convert the weak scattered light into TTL signals. With a focal length of 400 mm, the lens placed between the two pinholes is used to form the beam waist in the center of the FPI cavity and increase the resolution of the FPI. The data acquisition card (DAQ card, NIPCI6221) can record the TTL signals. Finally, the spectrum of the scattered light can be obtained. The temperatures were measured with the platinum resistance thermometer (PRT, Fluke Corporation; uncertainties are T = 0.01 K). The pressures were measured with the pressure transmitter (Rosemount, 3051S, 0−20 MPa) with an uncertainty of 5 kPa. The relative expanded uncertainty of the speed of sound is estimated to be
