Thermal volume

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.

A number of investigations on the thermal volume transition of PNIPAM have been performed [201-208]. PNIPAM chains carry two types of bound... 

The correct derivation of the remaining working equations involves replacing equation 13.1, which only takes into account the thermal volume increase, with equation 13.10, where both contributions are considered. The thermal volume change in equations 13.1 and 13.2 was renamed A v to distinguish it from the intrinsic (or chemical ) volume change Ac lcmv. 

Delaminations can occur during cure as a result of high internal stresses. These stresses develop due to resin shrinkage and thermal volume changes. The level of stresses depend on several material properties, such as the Young s modulus, Poisson s ratio, and thermal expansion coefficients of both resin and fibers. In addition, the level of stresses also depends on several conditions, such as fiber orientation, fiber volume fraction, and part geometry. 

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 general condition for the stability of equilibrium state with respect to thermal, volume, and fluctuations in the numbers of moles is obtained by combining Eqs. (12.7), (12.9), and (12.12)... 

Block Data for the Mean-Square-Fluctuation (MSF) and the Coefficient of Thermal Volume... 

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. 

Equations (2)-(4) show that elucidation of the rate constant requires prior knowledge of the residence time, t (the time the reacting solution spends in the calorimetric vessel) and hence the thermal volume, i.e. the operational volume of the calorimeter). Determination of reliable values for rate constants and enthalpy changes from experimental data (power, time data) for reacting systems, studied by flow microcalorimetry therefore, it requires an accurate and precise value for t at any given flow rate. This is determined from Equation (5) through knowledge of F and K. 

Flowing reacting systems necessarily result in transport of heat from the detection area. Thus, whilst the physical volume of the cell can be known, this volume may not be the effective or thermal volume nor indeed the zero-flow-rate volume of the cell. Figure 3. 

Studies using the base-catalysed hydrolysis of methyl paraben (BCHMP) test and reference reaction have been conducted with a variety of different solution-phase flow calorimeters. The results obtained from these studies have shown that the flow rate dependency of the thermal volume is different for each of the instruments used and indeed for each experimental arrangement e.g. sample and reference cell set-up). The determined value for can differ by as much as 15% (over a range of experimental flow rates) from the nominal engineered volume (typically approximately 1ml). This effect can be minimised by careful design of the flow cell and also by careful consideration of the sample and reference cell arrangements (more details can be found in ref. 22 and references therein). 

Knowledge of how thermal volume varies with flow rate allows the physical characteristics of the flow cell to be investigated. For example, it is possible to simulate... 

It must be emphasized that this analysis is not possible without prior knowledge of the thermal volume of the calorimetric cell and therefore the validation routine described above must be conducted if accurate values for the enthalpy in particular are to be obtained. 

Calculational methods for the accurate determination of thermodynamic parameters (particularly for solution-phase calorimetry) have only recently become available through the BCHMP chemical test and reference reaction. It is likely therefore that values reported for enthalpy, for example, are likely to be significantly in error for some of the earlier work using flow calorimetry. These errors can be rectified, however, through the calculation of the thermal volume and relevant adjustment of the calorimetric data. 

Although the H-Oil reactor is loaded with catalyst, not all of the reactions are catalyzed some are thermal reactions, like thermal cracking, which depend on liquid holdup and not on how much catalyst is present. Thus, the material balance equations need to be divided into two categories, one set for the noncatalytic thermal reactions and another set for the catalytic reactions. A convenient parameter to use is the thermal volume/catalytic volume ratio, T/C, which is the ratio of liquid holdup to catalyst volume. In a commercial ebullated bed, this ratio is close to 1.0 under ebullation conditions. Consequently, the material balance equations for the catalytic reactions with no recycle are given in Eq. (17) ... 

Taking the hard sphere colloids as a reference state, the mean-square displacement (MSD) in dilute suspensions is associated with the particle self-diffusion whereas at finite volume fractions the onset of interactions marks the alteration of the dynamics. The latter can be probed by the intermediate scattering function C(, t) which measures the spatiotemporal correlations of the thermal volume fraction fluctuations [91]. Figure depicts two representations (lower inset and main plot) of the non-exponential for a nondilute hard sphere colloidal... 

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]. 

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