Adiabatic bulk compression

This isothermal bulk modulus (Kj) measured by static compression differs slightly from the aforementioned adiabatic bulk modulus (X5) defining seismic velocities in that the former (Kj) describes resistance to compression at constant temperature, such as is the case in a laboratory device in which a sample is slowly compressed in contact with a large thermal reservoir such as the atmosphere. The latter (X5), alternatively describes resistance to compression under adiabatic conditions, such as those pertaining when passage of a seismic wave causes compression (and relaxation) on a time-scale that is short compared to that of thermal conduction. Thus, the adiabatic bulk modulus generally exceeds the isothermal value (usually by a few percent), because it is more difihcult to compress a material whose temperature rises upon compression than one which is allowed to conduct away any such excess heat, as described by a simple multiplicative factor Kg = Kp(l + Tay), where a is the volumetric coefficient of thermal expansion and y is the thermodynamic Griineisen parameter. 

Often the compressibility ( t ) is used rather than the bulk modulus (K). These quantities are simple reciprocals for isotropic materials, i.e., x = Ultrasonic methods for measuring elastic properties are inherently adiabatic processes. Compressibility, on the other hand, is frequently determined by hydrostatic pressurization techniques which are isothermal in nature. Conversion of isothermal values ( t) to adiabatic values ( s) is accomplished via the following relation ... 

K by the internal friction method as shown in fig. 8.47. The shear modulus decreased almost linearly from 293 to about 673 K where a sudden change in slope occurred the investigators attributed this to grain boundary relaxation effects. Bridgman (1954), Evdokimova and Genshaft (1965) and Frolov et al. (1969) have determined isothermal compressibilities. For the sake of comparison, these isothermal compressibilities have been converted to adiabatic bulk moduli (See table 8.11). 

The frequency ranges of the two devices described above are such that they measure primarily isothermal and adiabatic moduli respectively (Chapter 5) and the difference between the two will be larger for bulk compression than for any other type of deformation. For a soft polymeric solid with a = 6 X 10 deg and Kis = 3 X 10 0 dynes/cm, Kad would be higher than Kjs by about 20% (Chapter 5, equation 41). 

R. ZwanzigandR. D. Mountain, J. Chem. Phys. 43,4464 (1965) show that the modulus Goo and the isothermal compressibility are determined by similar integrals containing the pair correlation function and the interparticle potential for simple Lennard-Jones fluids. The adiabatic (zero frequency) bulk modulus Ko equals —y(0P/0P) j, which clearly is a kind... 

Thus a measurement of the ultrasonic velocity and density can be used to determine the adiabatic compressibility (or bulk modulus) of the material. For homogeneous solids measurements of the compression and shear velocities can be used to determine the bulk and shear moduli (see section 2.4). The Young s modulus of rod-like materials (e.g. spaghetti) can be determined by measuring the velocity of ultrasound. 

The bulk density of ANFO ranges from 0.80 to 0.87 g/cc. So, clearly about half of the ANFO is air or void space. All explosives require a certain amount of entrained void space in order to detonate properly. These void spaces also play a major role in the detonation reaction by creating hot spots under adiabatic compression in the detonation front.39 The amount of void space in any given explosive and the resultant change in density have a significant impact on the detonation properties like detonation velocity, sensitivity, and even energy release. 

Jjet us consider as an example the case of a saturated vapor which has been suddenly and adiabatically compressed to a vapor pressure P which is in excess of its equilibrium vapor pressure Po at the final temperature T. In order for liquid to form, it must grow by the growth of small droplets. If, however, we consider a very small droplet of the liquid phase present in the vapor, it will have an excess free energy, compared to bulk liquid, that is due to its extra surface. The magnitude of the excess surface energy is 4irrV, where surface tension and r is the radius of the drop. In order for the drop and vapor to be in equilibrium, the vapor pressure P must exceed the saturation vapor pressure Po by an amount which can be calculated from the Gibbs-Kelvin equation... 

In non-scattering systems, ultrasonic properties and the volume fraction of the disperse phase are related in a simple manner. In practice, many emulsions and suspensions behave like non-scattering systems under certain conditions (e.g. when thermal and visco-inertial scattering are not significant). In these systems, it is simple to use ultrasonic measurements to determine 0 once the ultrasonic properties of the component phases are known. Alternatively, if the ultrasonic properties of the continuous phase, 0and p2 are known, the adiabatic compressibility of the dispersed phase can be determined by measuring the ultrasonic velocity. This is particularly useful for materials where it is difficult to measure jc directly in the bulk form (e.g. powders, granular materials, blood cells). 

Ultrasound propagation is adiabatic in homogeneous media at the frequencies typically used in US-based detection techniques. Therefore, although temperature fluctuations inevitably accompany pressure fluctuations in US, thermal dissipation is small and it is adiabatic compressibility which matters. As a second derivative of thermodynamic potentials, compressibility is extremely sensitive to structure and intermolecular interactions in liquids (e.g. the compressibility of water near charged ions or atomic groups of macromolecules differs from that of bulk water by 50-100%). 

If heat losses during compression are only slight then the bulk of the compressed gas will be at the core gas temperature. However, if heat losses during compression are very significant, as in slow compression, then a rather smaller fraction of the compressed charge will be at the core temperature. The extent to which heat losses during compression cause departures from the adiabatic ideal may be assessed from a comparison of (6.16) with the temperature (Tad) which is predicted on an ideal volumetric basis from knowledge of the dimensions of the RCM [50]. That is... 

The constant temperature process is a case when n=l, which is equivalent to isothermal compression, the constant pressure process n = 0 and the constant volume process n = Generally, it is impractical to build sufficient heat transfer equipment into the design of most compressors to convey the bulk of the heat of compression. Therefore most machines tend to operate along a poly tropic path that approaches the adiabatic. Most compressor calculations are based on the adiabatic curve [3]. 

Bulk modulus can be treated from the adiabatic as well as the isothermal point of view. Phenomenologically adiabatic compression or expansion are processes where heat is neither lost to nor gained from the environment. If the process occurs under equilibrium conditions, then we have the thermodynamically tractable case at zero entropy change and we define the bulk modalui as... 

Here Y denotes a general bulk property, Tw that of pure water and Ys that of the pure co-solvent, and the y, are listed coefficients, generally up to i=3 being required. Annotated data are provided in (Marcus 2002) for the viscosity rj, relative permittivity r, refractive index (at the sodium D-line) d. excess molar Gibbs energy G, excess molar enthalpy excess molar isobaric heat capacity Cp, excess molar volume V, isobaric expansibility ap, adiabatic compressibility ks, and surface tension Y of aqueous mixtures with many co-solvents. These include methanol, ethanol, 1-propanol, 2-propanol, 2-methyl-2-propanol (tert-butanol), 1,2-ethanediol, tetrahydrofuran, 1,4-dioxane, pyridine, acetone, acetonitrile, N, N-dimethylformamide, and dimethylsulfoxide and a few others. 

In thermally non-homogeneous supercritical fluids, very intense convective motion can occur [Ij. Moreovei thermal transport measurements report a very fast heat transport although the heat diffusivity is extremely small. In 1985, experiments were performed in a sounding rocket in which the bulk temperature followed the wall temperature with a very short time delay [11]. This implies that instead of a critical slowing down of heat transport, an adiabatic critical speeding up was observed, although this was not interpreted as such at that time. In 1990 the thermo-compressive nature of this phenomenon was explained in a pure thermodynamic approach in which the phenomenon has been called adiabatic effect [12]. Based on a semi-hydrodynamic method [13] and numerically solved Navier-Stokes equations for a Van der Waals fluid [14], the speeding effect is called the piston effecf. The piston effect can be observed in the very close vicinity of the critical point and has some remarkable properties [1, 15] ... 

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