Thermal volume expansivity

In the investigations carried out by one of the authors [56], an attempt was made to examine the conditions for the thermal volume expansivity of PET fibers. Within the framework of these investigations, aas was determined from the hydrostatic weight measurements using n-heptan as a liquid. The sought aas values have been calculated from the equation ... 

Table 11 Thermal Volume Expansivity (a2s) and Related Fine Structure Parameters of Differently Drawn PET Fibers...

Figure 7 Thermal volume expansivity coefficient ot25 of annealed PET fibers.

Fortunately, they are several species of low-loss dielectric ceramics with tailored temperature coefficient of dielectric constant, which can be made lower than 1 ppm/K for a certain temperature window around room temperature. Physically, this can be accomplished either by intrinsic compensation of the temperature dependence of thermal volume expansion V(T) and lattice polarizability a(T) via the Clausius-Mossotti relation ... 

The mean-square fluctuation in atomic positions (MSF) and the coefficient of thermal volume expansion (a ), calculated using the fluctuation formula [39], are presented in Table 3. The former varies little over the different data blocks, and the standard deviation is less than 1% of the average, indicating that this property has also converged by 20 ps. 

The coefficient of thermal volume expansion was found to increase with temperature, in general agreement with experiment. This behavior, which to our knowledge has not been demonstrated by earlier molecular dynamics studies, shall be treated in greater detail elsewhere [49]. 

Y. S. Touloulkian, R. K. Kirby, R. E. Taylor and D. P. Desai, Thermodynamical Properties of Matter, Plenum Press, New York, 1975 p. 77. The coefficient of thermal volume expansion is taken to be three times the coefficient of thermal linear expansion. 

The only stable form of sulfur at STP conditions is the well known orthorhombic ce-Sg modification which was already known in antiquity. No wonder that this allotrope is by far the best studied. Although there is a considerable amount of knowledge on the structural and physical as well as chemical properties of a-Sg, from the experimental and theoretical point of view there are also ambiguities. For example, the thermal volume expansion below 300 K was reported contradictorily [76, 77]. 

Fig. 34.13 shows the thermal volume expansion of the microcapsules with the hydrostatic pressure as the parameter, obtained by using the bellows vessel and a heating rate of 3 K min . For confirmation of the heating rate, the same results were obtained when the PVT test was carried out using 2 K min as the heating rate. The microcapsules start to expand dramatically around 60 °C both... 

Fig. 34.13 Variation of thermal volume expansion of microcapsules, with pressure as a parameter, measured using the bellows vessel.

Electrical resistivity comes in two different flavours resistivity at initial geometry (subscript IG, p/o), and resistivity including thermal volume expansion (subscript VE, py. The former can be directly determined from the electric signals by rationing the voltage and the current, whereas information about the volume expansion is needed to obtain the latter, by multiplying V/Vq and Physically, electrical resistivity with volume expansion considered is of greater interest because it can be directly compared with data from other measurement techniques, e.g., 4-point measurements. 

The observed temperature-pressure shift was found to he linear, while the concomitant hole hroadening can he described by a power law. The latter is clearly dominated by dynamical processes which are affected by the change in temperature. It is now assumed that, in analogy to pure pressure effects, the hole shift and the hole broadening due to the thermal volume expansion are linear functions of the temperature change. The function v Ri,Ap AT) in Eq. 5 can then be linearized to... 

Grashof number, Gr gp L pAT p,Lu - L characteristic length dimension density of liquid coefficient of thermal volume expansion / buoyancy force V viscous force / Free convention heat transfer... 

Rayleigh number, Ra p L Cp AT k fl coefficient of thermal volume expansion AT temperature different across film L characteristic length dimension heat transfer by convection heat transfer by conduction Free convection... 

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