Sound thermal conductivity

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. 

Transport Properties. Viscosity, themial conductivity, the speed of sound, and various combinations of these with other properties are called steam transport properties, which are important in engineering calculations. The speed of sound (Fig. 6) is important to choking phenomena, where the flow of steam is no longer simply related to the difference in pressure. Thermal conductivity (Fig. 7) is important to the design of heat-transfer apparatus (see HeaT-EXCHANGETECHNOLOGy). The viscosity, ie, the resistance to flow under pressure, is shown in Figure 8. The sharp declines evident in each of these properties occur at the transition from Hquid to gas phase, ie, from water to steam. The surface tension between water and steam is shown in Figure 9. 

Other sohd-state apphcations of sihcon carbide include its use as an electroluminescent diode for use in sound recording equipment and photomultipliers and controllers. It has been studied as a reflective surface for lasers. By combining its excellent thermal conductivity and high electrical resistance, sihcon carbide has also found apphcation as an insulating material for integrated circuit substrates. 

Available data on the thermodynamic and transport properties of carbon dioxide have been reviewed and tables compiled giving specific volume, enthalpy, and entropy values for carbon dioxide at temperatures from 255 K to 1088 K and at pressures from atmospheric to 27,600 kPa (4,000 psia). Diagrams of compressibiHty factor, specific heat at constant pressure, specific heat at constant volume, specific heat ratio, velocity of sound in carbon dioxide, viscosity, and thermal conductivity have also been prepared (5). 

Extracted from U.S. Standard Atmosphere, 1976, National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration and tte U.S. Air Force, Washington, 1976. Z = geometric altitude, T = temperature, P = pressure, g = acceleration of gravity, M = molecular weight, a = velocity of sound, i = viscosity, k = thermal conductivity, X = mean free path, p = density, and H = geopotential altitude. The notation 1.79.—5 signifies 1.79 X 10 . ... 

Cp and Q are the specific heats, assumed here to be constant for simplicity q is the heat release rate per unit volume X is the thermal conductivity c is the local speed of sound... 

It is easy to check that sometimes k can exceed the Cu conductivity. The very high thermal conductivity of 4He n allows for the propagation of temperature waves (second sound) [42-48]. 

The bulk viscosity referred to here (pg) should not be confused with the so-called bulk viscosity of polymers which refers to the steady flow shear viscosity of the bulk undiluted polymer. Here it represents all the causes of sound absorption other than those produced by shear viscosity or thermal conductivity. Typically these may be ... 

DEELAGRATION A pyrotechnic event in which the flame front proceeds at less than the speed of sound in the material the velocity of deflagration being related to the thermal conductivity of the material. 

Vermiculites are formed by the decomposition of mica. They contain layers of water and magnesium ions in place the potassium ions. When heated to 800°C-1100°C, vermiculite expands because of the conversion of the water to gas. The expanded vermiculite has a low thermal conductivity and density, and is used as a thermal and sound barrier as well as an aggregate in lightweight concrete. It is also used as a moisture-retaining soil conditioner in planting. 

On account of its low heat conductivity solid sulphur breaks readily when warmed, the uneven expansion caused by the warmth of the hand being sufficient to cause an audible sound of cracking.1 The following values for the thermal conductivity of sulphur over the temperature range 20° to 210° C. have been obtained 3... 

When analyzing thermal processes, the thermal conductivity, k, is the most commonly used property that helps quantify the transport of heat through a material. By definition, energy is transported proportionally to the speed of sound. Accordingly, thermal conductivity... 

From Eq. (11), an obviously desirable characteristic for thermoelectric materials is to have low thermal conductivity k. The thermal diffusivity constant, Dt, of ErB44Si2 has been found to have small values of Dt < 1.1 x 10 2 cm 2/s (Mori, 2006c). These values are significantly smaller than what has been observed for boron carbide samples (Wood et ah, 1985). Although no data exists for the sound velocities of ErB44Si2, the velocities are probably high since borides are typically hard materials. Therefore, the small values of Dt indicate extremely short phonon... 

In Chap. 13 we have already discussed the use of sound speed measurements for the derivation of elastic parameters. We shall come back on that, more elaborately, in this chapter. We have also seen that sound speeds can be expressed in terms of additive molar functions these are of course basic for estimations, as well for mechanical properties as for thermal conductivity (Chap. 17). 

The following symbols are used in the definitions of the dimensionless quantities mass (m), time (t), volume (V area (A density (p), speed (u), length (/), viscosity (rj), pressure (p), acceleration of free fall (p), cubic expansion coefficient (a), temperature (T surface tension (y), speed of sound (c), mean free path (X), frequency (/), thermal diffusivity (a), coefficient of heat transfer (/i), thermal conductivity (/c), specific heat capacity at constant pressure (cp), diffusion coefficient (D), mole fraction (x), mass transfer coefficient (fcd), permeability (p), electric conductivity (k and magnetic flux density ( B) ... 

Thermal Conductivity and Thermal Expansion. Thermal conductivity of liquids (and gases to some extent) is still an empirical subject in any but the broadest sense. Kowalczyk (1144) reviewed the subject and the equations which relate thermal conductivity to viscosity, molar volume, melting point, and sound conductivity. Sakiadis and Goates (1776, 1777) tabulate values for a number of compounds and present correlation functions for thermal and sound conduction. 

Equation (3) has several other important implications which can be directly confirmed by finite-frequency probes. One example is the motion-narrowing effect in NMR experiments which is expected to disappear when l/r is below the chemical-shift-anisotropy (CSA) width. Indeed the NMR results of Tycko et al. [16] indicate that for a CSA width of 18.2 kHz the line broadens below 190 K and develops a powder pattern at lower temperature. This is in fair agreement with the 200 K calculated from Eq. (3). They also concluded that the thermal activation energy is around 260 meV below TV, again close to the values we calculated. The glassy dynamics can be probed by other experiments such as sound attenuation, microwave absorption, and thermal conductivity. In particular the characteristic temperature will depend on probe frequency. Such studies are essential to fully understand the low-temperature orientational dynamics. 

After we finished the manuscript we learned of recent experiments by X. Shi et ai on sound attenuation (to be published) and by R. Yu et ai on thermal conductivity (private communication). Their results indicate that there is a frequency-dependent glassy behavior at low temperature, in agreement with our predictions. 

Asbestos cement materials are widely used due to their good mechanical properties, low thermal conductivity and resistance to weathering, frost and rotting. The slurry of asbestos and cement can also be processed directly using a spray process, as so-called asbestos spray for fire-retarding layers as well as for thermal (hot and cold) and sound insulation. 

The uncertainties of the equation of state are 0.2% in density, 2% in heat capacity, and 2% in the speed of sound, except in the critical region. The uncertainty in vapor pressure is 0.2%. The uncertainty varies from 0.5% for the viscosity of the dilute gas phase at moderate temperatures to about 5% for the viscosity at high pressures and temperatures. The uncertainty in thermal conductivity is 2%. 

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