Temperature volumetric expansion

Djj. The Grashof number Nq, = Dj pgpAto/p" were is equivalent diameter, g is acceleration due to gravity, p is coefficient of volumetric expansion, p is viscosity, p is density, and Atg is the difference between the temperature at the wall and that in the bulk fluid. Nq, must be calculated from fluid properties at the bulk temperature. 

P = coefficient of volumetric expansion Atfj = the difference between the temperature at the wall and that in the bulk fluid... 

Under optimum conditions at this temperature, what fraction of the inlet benzene ends up as maleic anhydride What is the yield of maleic anhydride based on the amount of benzene reacted Neglect volumetric expansion. 

The volumetric expansion parameter S may thus be taken as 0.9675. The product distribution will vary somewhat with temperature, but the stoichiometry indicated above is sufficient for preliminary design purposes. (We should also indicate that if one s primary goal is the production of ethylene, the obvious thing to do is to recycle the propylene and ethane and any unreacted propane after separation from the lighter components. In such cases the reactor feed would consist of a mixture of propane, propylene, and ethane, and the design analysis that we will present would have to be modified. For our purposes, however, the use of a mixed feed would involve significantly more computation without serving sufficient educational purpose.)... 

Au is the difference between the liquid and glassy volumetric expansion coefficients and the temperatures are in kelvin. "The WLF equation holds between I], or / f 10 K and abftut 100 K above 7A,. Above this temperature, for thermally stable polymers, Berry and Fox (28) have shown that a useful extension of the WLF equation is the addition of an Arrhenius term with a low activation energy. 

TMA measures the mechanical responses of a polymer as a function of temperature. Typical measurements include (1) expansion properties, i.e., the expansion of a material leading to the calculation of the linear expansion coefficient (2) tension properties, i.e., the shrinkage and expansion of a material under tensile stress e.g., elastic modulus (3) dilatometric properties, i.e., the volumetric expansion within a confining medium e.g., specific volume ... 

With the method used here, the specimen is free to expand in only one direction, and this means that only a linear expansion can be determined. This is the same as volumetric expansion. If the system is above its glass temperature, 7g,... 

Instead of measuring the force-temperature dependence at constant volume and length, one can measure this dependence at constant pressure and length but in this case it is necessary to introduce the corresponding corrections. The corrections include such thermomechanical coefficients as iso-baric volumetric expansion coefficient, the thermal pressure coefficient or the pressure coefficient of elastic force at constant length 22,23,42). 

The solid so obtained was introduced in two different sealed refractory crucibles and immersed in a coke bed. One of the crucibles was submitted to the following thermal treatment in an electric furnace 20-1000 "C at 5"C/min. heating rate, followed by 3 h soaking time at this temperature, obtaining a porous solid composite called SC-100. The other crucible was treated in equal conditions but varying the final temperature to 1550 °C, obtaining in this case another porous composite called SC-155. The SC-155 showed a little volumetric expansion respect to the SC-100 material. (The names SC-100 and SC-155 means S= silica C= carbon and the number is the treatment temperature in °C/10). 

The data on the volume properties of PMS liquids (i.e. coefficient of volumetric expansion, relative volume variation, coefficient of isothermal compressibility) are essential for the performance characteristics of oli-godimethylsiloxanes in hydraulic systems, hydraulic shocks and dampers they allow one to determine the working characteristics of these systems with some brands of PMS liquids at different temperatures and pressures. 

Branched oligomethylsiloxanes PMS-lb - PMS-3b are soluble in aromatic hydrocarbons, do not corrode construction materials and alloys, are nontoxic. If heated above 200 °C, they form moderately toxic volatile substances, which excite the nervous system and cause conjunctivitis and inflammation of upper airways. The temperature of self-inflammation of these liquids exceeds 340 °C. Their coefficient of volumetric expansion ranges from 0.0013 to 0.0009 cm3/grad. 

When energy, e.g. in the form of heat, is supplied to the system under constant pressure, only a fraction of this energy serves to increase the internal energy of the system U. The remainder of the energy goes for expansion work (volumetric work) against the external pressure. The sum of V and the volumetric expansion work p-V s the enthalpy H. With entropy of a system defined as the ratio of the amount of heat q and temperature, S = q/T, the two quantities A = U - T S and G = H - T S are thus defined. 

The volumetric expansion of the liquid when it is contacted with the SCF plays the key role in the process. The behaviour reported by Yeo et al. [10] and by Kordikowski et al. [11] for the dymethylsulfoxide (DMSO)-CC>2 system at two temperatures shows that CO2 produces a remarkable volumetric expansion of DMSO near the mixture critical point. The increase of antisolvent amount in the mixed solvent and the evaporation of the organic liquid into the SCF eventually cause the precipitation of the solute. A cleaning step, carried out with pure antisolvent, is necessary after the precipitation, in order to remove completely the liquid solvent from the solid particles the antisolvent pushes the liquid out of the vessel, then it has to extract the residual solvent from the solid and the dry solid particles can be collected. 

These dimers are of interest because they serve as model compounds for a new class of phenolic materials, the polybenzoxazines, whose synthesis and characterization has been described by Ishida and coworkers.146-149 These polybenzoxazine resins were found to have a number of unusual, but commercially favorable, properties, in particular a near-zero shrinkage or volumetric expansion upon curing (polymerization) as well as low water absorption. In addition, the resins have high glass-transition temperatures even though they have been shown to have low crosslink densities. Explanations for these properties have been hypothesised in terms of favorable hydrogenbonding interactions.150... 

Fig. 5.24. The products of the temperature TL and volumetric expansion coefficient aw as functions of...

While TMA is one of the older and simpler forms of thermal analysis, its importance is in no way diminished by its age. Advances in DSC technology and the appearance of dynamic mechanical analysis (DMA) as a common analytical tool have decreased the use of it for measuring glass transitions, but nothing else allows the measurement of CTE as readily as TMA. In addition, the ability to run standardized material test methods at elevated temperatures easily makes TMA a reasonable alternative to larger mechanical testers. As the electronic, biomedical, and aerospace industries continue to push the operating limits of polymers and their composites, this information will become even more important. During the last 5 years a major renewed interest in dilatometry and volumetric expansion has been seen. Other thermomechanical techniques will also likely be developed or modernized as new problems arise. 

Figure 3 Volumetric expansion of C02-ethanol mixtures with pressure and temperature.

The decompositions of the three sillimanite minerals occur over different temperature ranges and with different volumetric expansions. As the sillimanites are formed at high pressures, it is natural that they exhibit large volumetric expansions when they decompose at 1 atm pressure. As expected, kyanite, the highest-pressure form, undergoes the largest volumetric expansion (about 15%). The P-T formation densities can be viewed as the driving force for the decompositions. Kyanite also initiates its decomposition at the lowest temperature of the three. 

Local anesthetics. Anesthetics interact with membranes and increase the gel to liquid-crystalline transition of fully hydrated bilayers. They induce a volume expansion which has the opposite effect of HHP and so they antagonize the effect of HHP on membranes fluidity and volume, making membranes more fluid and expanded. The application of HHP to membrane-anesthetic systems may even result in the expulsion to the aqueous environment. The local anesthetic tetracaine (TTC) can be viewed as a model system for a large group of amphiphilic molecules. From volumetric measiuements on a sample containing e.g. 3 mol% TTC, it has been found that the main tansition at ambient pressure shifts to a lower temperature. The expansion coefficient a drastically increases relative to that of the pure lipid system in the gel phase, and the incorporation of the anesthetic into the DMPC bilayer causes an about 15 % decrease of relative to that of the pure lipid system. The addition of 3 mol% TTC shifts the pressure-induced liquid-crystalline to gel phase transition towards somewhat higher pressures. Larger values for the compressibilities are found for both lipid phases by addition of 3 mol% TTC, and there is no apparent difference in the coefficient of compressibility between the gel and liquid-crystalline phases. Comparison of the IR spectra of DMPC and DMPC/TTC mixtures at pH 5.5 as a function of pressure shows an abrupt... 

Thermal diffusivity, kjpCp, m /h or ftVh also constant in Eq. (1Z58) Coeffident of volumetric expansion, 1/°R or 1/K also constant in Eq. (12.58) at mean film temperature Constant in Eq. (12.58)... 

Denote by 5 the stoichiometric expansion factor 8 nwi JiUjm. This equals the previously defined volumetric expansion factor 5v = (volume out)/(volume in) if there is no expansion due to heating or pressure change. In cases where there is expansion due to temperature or pressure changes, 8y= 8(TiyToP). 

The line for recycling the SCF is also indicated in Figure 2.3-7. Knowledge of the volumetric expansion of the liquid phase with pressure and of the precipitation pressure at the selected temperature are essential for performing any supercritical antisolvent precipitation experiment. The concentration of HC in the starting organic solution also affects the shape and dimensions of the product obtained. 

Other factors affecting the mechanism of oil extraction from the formation were also studied. Thermal expansion of oil also exerts an influence on the process of oil displacement from a porous medium. The volume of displaced oil essentially depends on the oil s properties and on the thermodynamic conditions of the formation. The changes in the displacement coefficients attributed to thermal expansion of oil were given in Table 8. At temperatures of 125, 150, and 2(X)°C, the percentage share of oil yield due to its volumetric expansion within the reservoir rocks is 5.4. 

The volumetric expansion ratio (expanded volume/original volume) of a volatile organic solvent upon exposure to compressed CO2 can be over 10 [33], but the ratio is far lower for liquid polymers. P EG-NPE-2500 at 50 °C reaches a ratio of only 1.17 and only when the CO2 pressure reaches as high as 16 MPa. At higher temperatures, greater expansion is observed (a ratio of 1.20 at 16 MPa and 70 °C) [34]. Liquid PDMS-308 000 expands considerably more, reaching a ratio of 1.7 at 50 °C and 20 MPa [31]. However, in the case of PDMS, the expansion is lower at higher temperatures. 

---