Volume measurement, specific

As noted above, not all techniques which provide information regarding crystallinity are useful to follow the rate of crystallization. In addition to sufficient sensitivity to monitor small changes, the method must be rapid and suitable for isothermal regulation, quite possibly over a range of different temperatures. Specific volume measurements are especially convenient for this purpose. We shall continue our discussion using specific volume as the experimental method. 

In discussing Fig. 4.1 we noted that the apparent location of Tg is dependent on the time allowed for the specific volume measurements. Volume contractions occur for a long time below Tg The lower the temperature, the longer it takes to reach an equilibrium volume. It is the equilibrium volume which should be used in the representation summarized by Fig. 4.15. In actual practice, what is often done is to allow a convenient and standardized time between changing the temperature and reading the volume. Instead of directly tackling the rate of collapse of free volume, we shall approach this subject empirically, using a property which we have previously described in terms of free volume, namely, viscosity. 

Pressure. Standard atmospheric pressure is defined to be the force exerted by a column of mercury 760-mm high at 0°C. This corresponds to 0.101325 MPa (14.695 psi). Reference or fixed points for pressure caUbration exist and are analogous to the temperature standards cited (23). These points are based on phase changes or resistance jumps in selected materials. For the highest pressures, the most rehable technique is the correlation of the wavelength shift, /SX with pressure of the mby, R, fluorescence line and is determined by simultaneous specific volume measurements on cubic metals... 

Also, in cases where the dimensions of a regular particle vary throughout a bed of such particles or are not known, but where the fractional free volume and specific surface can be measured or calculated, the shape factor can be calculated and the equivalent diameter of the regular particle determined from Figure 2. 

Figure 13.6 shows the influence of temperature on specific volume (reciprocal specific gravity). The exaet form of the eurve is somewhat dependent on the crystallinity and the rate of temperature change. A small transition is observed at about 19°C and a first order transition (melting) at about 327°C. Above this temperature the material does not exhibit true flow but is rubbery. A melt viseosity of 10 -10 poises has been measured at about 350°C. A slow rate of decomposition may be detected at the melting point and this increases with a further inerease in temperature. Processing temperatures, exeept possibly in the case of extrusion, are, however, rarely above 380°C. 

It is seen that in order to measure retention volumes with a precision of 0.1%, the temperature control must be +/- 0.04°C. This level of temperature control on a thermostat bath is not difficult to achieve but it is extremely difficult, if not impossible, to return to a specific temperature to within +/- 0.04°C after prior change. To achieve a precision of retention volume measurement of 1%, the temperature control must be +/- 0.4°C. This is far more practical as most column oven temperature can be set to a given temperature to within +/-0.25°C. Although the data was obtained for three specific solutes, the results can be taken as reasonably representative for all solutes and phase systems. In most practical analyses, the precision limits of retention volume measurement will be about 1% but this will not include the reproducibility of the flow rate given by the pump. As... 

The volume measured at a specific pressure is directly related to the number of pores with that radius. 

Systematic errors usually arise from specific shortcomings in the measuring instrument, the observer, or the way in which the measurement is taken. Sources of systematic error include a badly calibrated measuring device, a faulty instrument movement, an incorrect action by the experimenter (e.g., misreading a volume measurement), or the parallax effect when incorrectly viewing a scale. Repeating the measurement does not necessarily help, because the error may be repeated, and the analyst may... 

Kell and Whalley (26) fit the results of their pure water specific volume measurements to the polynomial... 

Density or specific gravity (relative density) is used whenever conversions must be made between mass (weight) and volume measurements. This property is often used in combination with other test results to predict oil quality, and several methods are available for measurement of density (or specific gravity). However, the density (specific gravity) (ASTM D1298 IP 160) is probably of... 

Any characteristic of a system is called a property. The essential feature of a property is that it has a unique value when a system is in a particular state. Properties are considered to be either intensive or extensive. Intensive properties are those that are independent of the size of a system, such as temperature T and pressure p. Extensive properties are those that are dependent on the size of a system, such as volume V, internal energy U, and entropy S. Extensive properties per unit mass are called specific properties such as specific volume v, specific internal energy u, and specific entropy. s. Properties can be either measurable such as temperature T, volume V, pressure p, specific heat at constant pressure process Cp, and specific heat at constant volume process c, or non-measurable such as internal energy U and entropy S. A relatively small number of independent properties suffice to fix all other properties and thus the state of the system. If the system is composed of a single phase, free from magnetic, electrical, chemical, and surface effects, the state is fixed when any two independent intensive properties are fixed. 

The fresh and spent catalysts were characterized with the physisorption/chemisorption instrument Sorptometer 1900 (Carlo Erba instruments) in order to detect loss of surface area and pore volume. The specific surface area was calculated based on Dubinin-Radushkevich equation. Furthermore thermogravimetric analysis (TGA) of the fresh and used catalysts were performed with a Mettler Toledo TGA/SDTA 851e instrument in synthetic air. The mean particle size and the metal dispersion was measured with a Malvern 2600 particle size analyzer and Autochem 2910 apparatus (by a CO chemisorption technique), respectively. 

The bulk (or volume) specific resistance p is one of the most useful electric properties that can be measured. Specific resistance is a physical quantity that may differ by more than 1023 in readily available materials. This unusually wide range of conductivity is basic to the wide use of electricity and many electric devices. Conductive materials, such as copper, have p values of about 10-6 ohm cm, while good insulators, such as polytetrafluoroethylene (PTFE) and low-density polyethylene (ldpe), have p values of about 1017 ohm cm. 

Compare your answers with the laboratory measured specific volume of reservoir liquid at bubble point, 0.0353 cu ft/Ib. 13-18, The gas-liquid equilibrium calculations for a two-stage separation of a retrograde gas have been completed. Results are given below. 

The significance of such a difference between the partial specific volumes measured at constant chemical potential (v2,n3) and constant... 

For the denaturation of / -Lg in 40% 2-chloroethanol, the presently reported partial specific volume measurements result in a AV value of —590 ml/mole. This value is very close to that previously reported for the denaturation of this protein by 6.4M urea, —610 ml/mole (27). Although this similarity of AV values is striking, it might be the result of a fortuitous compensation of various effects. The change in volume calculated from the difference in partial specific volumes is the sum of a number of contributions (28), such as differences in electrostriction in the two media, changes in the density of solvent components when they interact... 

Specific surface area is dependent on the reciprocal of pore diameter. However, with a given pore diameter the measured specific surface may be different. A silicagel should be defined with mean particle diameter, specific surface area, pore diameter, and pore volume. 

The range of techniques discussed in this volume measure local elevation, local relief, erosion and several environmental variables including precipitation, temperature, seasonality, and enthalpy. Relief, erosion and environmental records are related to paleoaltimetry through (1) empirically and theoretically determined climate-elevation relationships, and (2) assumptions about how erosion and relief relate to elevation change. While reading this volume, the reader should consider the specific measurement provided by a particular technique and its sensitivities to other factors. A broad range of approaches provides the opportunity to be both circumspect and comprehensive with tectonic and geomorphic interpretations based on paleoaltimetry data. 

Fig. 1. Assay for progestin receptors in human breast cancer cytosol. A. Saturation analysis. Total ( — ) and aspecific (o—o) binding are measured Specific binding (solid line) is calculated by subtraction. B. Scatchard plot derived from the binding data by the method of Chamness and McGuire [8]. Numerical data protein concentration of cytosol. 1.8 mg/ml assay volume, 100 /d cytosol volume, 50 /ul. Calculated values Kd = 0.76 nmol/l progestin receptor content, 510 fmol/mg protein.

The interpretation of dilatometric volume measurements is complicated by the fact that the molten fat has a coefficient of thermal expansion (about 0.00084 mL/gK) more than twice that of solid fat (about 0.00038 mL/gK). This difference means that the melting dilation is temperature-dependent (Stauffer, 1996). In principle, this could be allowed for by measuring the specific volume of both the fully molten fat and the fully solid fat at the measurement temperature. However, while the specific volume of the molten fat is easily measured using the dilatometer, that of the solid fat is not. This difficulty is circumvented by assuming, by convention, that the temperature dependence of specific volume is the same for both the molten fat and the solid fat (thus making the melting dilation temperature independent), and that the melting dilation itself has a constant value, independent of fat type, of 0.1 mL/ g (= 0.1 L/kg). Thus (Hannewijk et al., 1964),... 

Internal energy (through the enthalpy, defined in Sec. 2.5) is useful for the calculation of heat and work quantities for such equipment as heat exchangers, evaporators, distillation columns, pumps, compressors, turbines, engines, etc., because it is a state function. The tabulation of all possible Q s and W s for all possible processes is impossible. But the intensive state functions, such as specific volume and specific internal energy, are properties of matter, and they can be measured and their values tabulated as functions of temperature and pressure for a particular substance for future use in the calculation of Q or W for any process involving that substance. The measurement, correlation, and use of these state functions is treated in detail in later chapters. 

These results may be tabulated along with the corresponding conditions of T and P existing at section 2 for a large number of runs. In addition, specific-volume measurements may be made for these same conditions, and these may be tabulated. Corresponding values of the internal energy of water may be calculated by Eq. (2.6), U = H - PV, and these numbers too may be tabulated. In this way tables of thermodynamic properties may be compiled over the entire useful range of conditions. The most widely used such tabulation is for H20 and is known as the steam tables, t... 

A variety of assays have been designed and validated to measure specific antibodies in the sera of treated animals. In addition efforts have been paid to minimizing the immunogenicity of therapeutic proteins. As these issues are addressed comprehensively in another chapter of this volume, the focus here will be on predicting problems that may ensue from the presence of such antibodies, namely hypersensitivity reactions. Presumably because allergic reactions have long been considered to be nonreproducible in animal models, limited efforts have been paid to designing predictive animal models until recently. Unexpectedly, the consequence is that no adequately standardized and validated model is available at the present time. 

One of the major reasons why outcome may not be correlated strongly with lesion volume is that volume measures do not take account of variations in lesion location or shape. Recently, evidence has been produced to suggest that the clinical consequences of an ischemic lesion can be predicted if damage and outcome are measured within a specific functional system (Fig. 23.1) (Binkofski et al. 1996 Pineiro et al. 2000). 

The true densities of crystalline and amorphous PTFE differ considerably, and 100% crystalline PTFE densities of 2.347 at 0°C (32°F) and 2.302 at 25°C (77°F) were calculated from x-ray crystallographic data [21]. The density decrease of about 2% between these temperatures includes the decrease of approximately 1% due to the transition at 19°C (66°F), which results from a slight uncoiling of the helical conformation of molecules on heating through the transition. By contrast, the density of amorphous PTFE is not affected by the transition at 19°C, and values around 2.00 have been reported from extrapolations of specific volume measurements to zero crystallinity [15]. 

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