Speed data, sound

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectmm an empirical approach based on the Bouguer-Lambert-Beerlaw (63) and a more fundamental or first-principle approach (64—66). The first-principle approach implies that no caHbration is required, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

Kieffer has estimated the heat capacity of a large number of minerals from readily available data [8], The model, which may be used for many kinds of materials, consists of three parts. There are three acoustic branches whose maximum cut-off frequencies are determined from speed of sound data or from elastic constants. The corresponding heat capacity contributions are calculated using a modified Debye model where dispersion is taken into account. High-frequency optic modes are determined from specific localized internal vibrations (Si-O, C-0 and O-H stretches in different groups of atoms) as observed by IR and Raman spectroscopy. The heat capacity contributions are here calculated using the Einstein model. The remaining modes are ascribed to an optic continuum, where the density of states is constant in an interval from vl to vp and where the frequency limits Vy and Vp are estimated from Raman and IR spectra. 

The pressure dependence of (3P/3v) can be tested by fitting [(3P/3v)P - (3P/3v) ]/P vs. pressure. It is clearly shown in Figure 14 that the values of [(3P/3v)p - (3P/3v) ]/P for pure water and 35 °/oo salinity seawater determined from sound speed data (112,123),increase almost linearly with pressure. This indicates that P or even higher order terms are needed to represent (3P/3v) over the pressure range of 0 to 1000 bars. In other words, the Tammann equation and the original Tait equation do not represent the PVT properties for pure or saline water within the accuracy of the data. 

Figure 13. (dP/dv)p determined from sound speed data ( 26) ((9) linear equation ( Q) quadratic equation)... 

Figure 14. Values of [(dP/Bv)p — (BP/3v)°]/P for pure water and 35%o salinity seawater determined from sound speed data (112, 123).

Li (142) published a variation of the Tait-Gibson equation for seawater from both compressibility and sound speed data... 

Unfortunately, at present, reliable PVT data for electrolytes at high pressures, temperatures and concentrations are not available to further test the applicability of these simple methods to natural waters. Reliable measurements of the speed of sound in aqueous electrolytes as a function of temperature, pressure and concentration should provide the data needed to test the postulation presented above. Since 1 atm measurements of vu and... 

Aminabhavi, T.M. and Banerjee, K. Density, viscosity, refractive index, and speed of sound in binary mixtures of dimethyl carbonate with methanol, chloroform, carbon tetrachloride, cyclohexane, and dichloromethane in the temperature interval (298.15-308.15) K, / Chem. Eng. Data, 43(6) 1096-1101,1998a. 

Chandrasekhar, G., Venkatesu, P., and Rao, M.V.P. Excess molar volumes and speed of sound of ethyl acetate and butyl acetate with 2-alkoxyethanols at 308.15 K, J. Chem. Eng. Data, 45(4) 590-593, 2000. 

Krishnaiah, A. and Surendranath, K.N., Densities, speeds of sound, and viscosities of mixtures of oxolane with chloroethanes and chloroethenes, J. Chem. Eng. Data, 41(5) 1012-1014, 1996. 

For our purpose, it is convenient to classify the measurements according to the format of the data produced. Sensors provide scalar valued quantities of the bulk fluid i. e. density p(t), refractive index n(t), viscosity dielectric constant e(t) and speed of sound Vj(t). Spectrometers provide vector valued quantities of the bulk fluid. Good examples include absorption spectra A t) associated with (1) far-, mid- and near-infrared FIR, MIR, NIR, (2) ultraviolet and visible UV-VIS, (3) nuclear magnetic resonance NMR, (4) electron paramagnetic resonance EPR, (5) vibrational circular dichroism VCD and (6) electronic circular dichroism ECD. Vector valued quantities are also obtained from fluorescence I t) and the Raman effect /(t). Some spectrometers produce matrix valued quantities M(t) of the bulk fluid. Here 2D-NMR spectra, 2D-EPR and 2D-flourescence spectra are noteworthy. A schematic representation of a very general experimental configuration is shown in Figure 4.1 where r is the recycle time for the system. 

Zafarani-Moattar, M.T. and Shekaari, H. Volumetric and speed of sound of ionic liquid, l-butyl-3-methylimidazolium hexafluorophosphate with acetonitrile and methanol at T = (298.15 to 318.15) K, /. Chem., Eng. Data, 50,1694,2005. Wang, J. et al.. Excess molar volumes and excess logarithm viscosities for binary mixtures of the ionic liquid l-butyl-3-methylimidazolium hexafluorophosphate with some organic solvents, /. Solution Chem., 34, 585, 2005. 

Since the compressibility is proportional to the pressure derivative of the volume, any experiment that establishes the P-V-T relation of a gas with sufficient accuracy also yields data for the isothermal compressibility. For obtaining the adiabatic compressibility from the P-V-T relation, some additional information is necessary see section (c). Tor instance specific heat data in the perfect gas slate of the substance considered. A more direct way of determining ihe adiabatic compressibility is by measuring the speed of sound i1. the two quantities being related by... 

First, speed of sound is determined from knowledge of temperature and molecular weight of the gas. For the selected range, this is illustrated in the following table, which provides approximate data. Note that we are only considering gaseous fluids. 

Takagi, T., Sawada, K., Urakawa, H., Ueda, M., Cibulka, I. (2004) Speeds of sound in dense liquid and vapor pressures for 1,1-difluoroethane. J. Chem. Eng. Data 49, 1652-1656. 

Table 14.5 shows the comparison of the values of the Ur and UH functions derived from experimental sound speed data with the values derived from the group contributions. It also shows a comparison between experimental sound speed values with those calculated purely from additive molar functions. The agreement is on the whole very satisfactory. 

The results of a typical crystallization experiment for a confectionery coating fat are shown as Figure 6. The speed of sound in the liquid fat decreased approximately linearly with decreasing temperature consistent with data reported in the literature for liquid vegetable oils (13). At the crystallization point, there was a rapid decrease in signal with the increasing solids content. The onset of crystallization was seen as a discontinuity in the ultrasonic velocity with respect to temperature... 

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