Magnitude Volume

Clerk Maxwell (South Kensington Conferences, 1876), in discussing the work of Willard Gibbs, remarked that the existence of a system depends on the magnitudes of the system, which are the quantities of the components, the volumes, the entropies, as well as on the intensities of the system, viz., the temperature and the potentials of the components (cf. 143). In his Theory of Heat he also refers to a separation of the variables in terms of which the state can be defined into two classes, one of which includes what are called intensities (pressure, temperature), and the other magnitudes (volume, entropy). 

The goal of this research is to develop a new class of bioresponsive materials that undergo rapid, large-magnitude, volume-phase transitions in response to specific biological stimuli. Our approach to these materials is based on two fundamental aspects of hydrogels (1) hydrogel solvation/desolvation thermodynamics can be perturbed... and... 

When, for a one-component system, one of the two phases in equilibrium is a sufficiently dilute gas, i.e. is at a pressure well below 1 atm, one can obtain a very usefiil approximate equation from equation (A2.1.52). The molar volume of the gas is at least two orders of magnitude larger than that of the liquid or solid, and is very nearly an ideal gas. Then one can write... 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

Spanning, accompHshed using a sample gas containing a known volume concentration of impurity, is performed at levels that are the same order of magnitude as the required detection. The actual span concentration is selected so that the majority of expected measurements fall at or within its value. 

The cables designed for use at voltages over 49 kV require that the conductor and insulation shields be firmly bonded to the insulation in order to avoid any possibiUty of generating corona at interfaces strippable insulation shields are not accepted. The A ETC specifications for cables rated for 59—138 kV require a volume resistivity of one order of magnitude lower than for the medium voltage cables. 

The Hildebrand Solubility Parameter. This parameter, 4 can be estimated (10) based on data for a set of additive constants, E, for the more common groups ia organic molecules to account for the observed magnitude of the solubiHty parameter d = EE/V where Erepresents molar volume. SolubiHty parameters can be used to classify plasticizers of a given family ia terms of their compatibihty with PVC, but they are of limited use for comparing plasticizers of differeat families, eg, phthalates with adipates. 

Reasons for these trends are clearly related to the polarity of the plasticizer and its abiUty to impart free volume by chain separation. Differences in polarity affect the temperature at which the plasticizer can penetrate the polymer matrix and the magnitude of the interaction with the polymer chain that results. 

The diametei of average mass and surface area are quantities that involve the size raised to a power, sometimes referred to as the moment, which is descriptive of the fact that the surface area is proportional to the square of the diameter, and the mass or volume of a particle is proportional to the cube of its diameter. These averages represent means as calculated from the different powers of the diameter and mathematically converted back to units of diameter by taking the root of the moment. It is not unusual for a polydispersed particle population to exhibit a diameter of average mass as being one or two orders of magnitude larger than the arithmetic mean of the diameters. In any size distribution, the relation ia equation 4 always holds. 

Prefixes. In SI, 20 prefixes are used and are direcdy attached to form decimal multiples and submultiples of the units (see the introduction to this volume, p. xvi). Prefixes indicate the order of magnitude, thus eliminating nonsignificant digits and providing an alternative to powers of 10 eg, 45 300 kPa becomes 45.3 MPa and 0.0043 m becomes 4.3 mm. 

In hydrological studies, the transfer of water between reservoirs is of primary interest. The magnitudes of the main reservoirs and fluxes (volume per time) are given in Figure 7. The oceans hold ca 76% of all the earth s water. Most of the remainder, ie, ca 21%, is contained in pores of sediments and in sedimentary rocks. A Httle more than 1% (or 73% of freshwater) is locked up in ice. The other freshwater reservoir of significant size is groundwater. Lakes, rivers, and the atmosphere hold a surprisingly small fraction of the earth s water. 

Population density (n) has dimensions number/(volume)(length) it is a key quantity in the discussion of CSD, a function of the characteristic crystal dimension E, and it is defined so that it is independent of the magnitude of the system. When a total population density is used, the symbol is n and the units are number/length. Population density is defined by letting AiVbe the number of crystals per unit system volume in a size range from E to L + AL, so that... 

If the gas volume is not isothermal and is zoned, an additional magnitude, the gas-to-gas total-exchange area QGj, arises (see Hottel and Sarofim. Radiative Tran.sfer, McGraw-Hill, New York, 1967, chap. 11). Space does not permit derivations of special cases only the single-gas-zone system is treated here. 

The large variety of displacement-type flmd-transport devices makes it difficult to list characteristics common to each. However, for most types it is correct to state that (1) they are adaptable to high-pressure operation, (2) the flow rate through the pump is variable (auxiliary damping systems may be employed to reduce the magnitude of pressure pulsation and flow variation), (3) mechanical considerations limit maximum throughputs, and (4) the devices are capable of efficient performance at extremely low-volume throughput rates. 

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