Volume, units for

The osmotic second virial coefficient A2 is another interesting solution property, whose value should be zero at the theta point. It can be directly related with the molecular second virial coefficient, expressed as B2=A2M /N2 (in volume units). For an EV chain in a good solvent, the second virial coefficient should be proportional to the chain volume and therefore scales proportionally to the cube of the mean size [ 16]. It can, therefore, be expressed in terms of a dimensionless interpenetration factor that is defined as... 

Notice that density will always have two units a mass unit divided by a volume unit. For example, water has a density of 1.0 g/mL. Density can have a different combination of units, though. For example, water also has a density of 1000 kg/m3 and 8.33 pounds/gallon. By the way, the density of water as 1.0 g/mL is a useful quantity to remember. Since the mass of 1 mL of water has a mass of 1 g, we can interchange grams and milliliters of water (as long at the temperature is close to 25°C). 

The amount of permeated substance can be expressed in mass, mole or volume units. For gases, volume is preferred, expressed as the amount permeating under conditions of standard temperature and pressure (STP), which corresponds to the standard temperature of 273.15 K and standard pressure of 1.01325 105 Pa. The corresponding dimensions for D and S are obtained at the same time from Eq. (9-4). The standard ambient temperature and pressure (SATP) are set at p°= 1 bar= 105 Pa = 0.9678 atm and T = 298.15 K. The data in handbooks however is still mostly expressed with p = 1 atm as standard pressure. For practical purposes the difference between these two conventions is insignificant compared to the variability of the materials themselves. 

For describing the rate of conversion changes in a volume unit the author simplified eqn. (72) (substituting volume units for the total volumes M V and PV) tot... 

The apparatus used is a modification of the equipment employed by Lev is et al. (6). For pure components, it is a constant-volume unit for gas mixtures, it operates at constant total pressure (nearly constant volume). It utilizes an internal recirculation device to expose the adsorbent continuously to a gas mixture of approximately known composition, and thus avoid localized concentration variations which could arise as a result of diiferences in the diffusivities of the various species. 

If the analyte is a hquid dissolved in another liquid, the results may be expressed on a volume/volume basis, but you will hkely encounter this formula only in rare simations. You would handle the calculations in the same manner as those above, using the same volume units for solute and sample. Gas analyses may be reported on a weight/weight, weight/volume, or volume/volunie basis. 

Fig. 2. Production volumes and prices for volume units for thermoplastics considered in this compilation. The dashed line represents an arbitrary border between engineering and high performance thermoplastics. In some cases, reinforced resins have been considered, ie, PPS 10% glass fibers (GF) PSU, PAll 30% GF PAS 40% GF. Acronyms are those listed in Table 1.

R, = R / Qc - total number of chain scissions per unit volume normalised by the initial number of ester units of aU the chains per unit volume. Unit for all the concentrations mol/m. ... 

Cp is tire number of elasticity active chains per volume unit. The comparison between experimental data and tire prediction by (C2.1.20) shows a reasonable agreement up to large defonnation (figure C2.1.16). For large values of X, strain hardening arises because of tire limited extensibility of tire chains or because of shear-induced crystallization. 

A stock solution is prepared by weighing out an appropriate portion of a pure solid or by measuring out an appropriate volume of a pure liquid and diluting to a known volume. Exactly how this is done depends on the required concentration units. For example, to prepare a solution with a desired molarity you would weigh out an appropriate mass of the reagent, dissolve it in a portion of solvent, and bring to the desired volume. To prepare a solution where the solute s concentration is given as a volume percent, you would measure out an appropriate volume of solute and add sufficient solvent to obtain the desired total volume. 

As in osmotic pressure experiments, polymer concentations are usually expressed in mass volume units rather than in the volume fraction units indicated by the Einstein equation. For dilute solutions, however, Eq. (8.100) shows that

partial molar volume of the polymer in solution, and M is the molecular weight of the polymer. Substituting this relationship for (pin Eq. (9.9)gives... 

For the moment, let us define a/47teQ as Oy, where the subscript V reminds us that the polarizability is being expressed in volume units. Multiplying the numerator and denominator of Eq. (10.33) by (4 ) gives... 

As noted at the end of the last section, it is fluctuations in concentration 5c2 rather than density which act as the scattering centers of interest for solutions of small molecules. There is nothing in the forgoing theory that prevents us from placing 6p by 6c2, the solute concentration in mass volume" units. Therefore we write for a solution of small molecules... 

Booster Pump. Use of a centrifugal booster pump avoids a low intake pressure, particularly for large, high volume units. A low pressure (>26.6 kPa (200 mm Hg)) on the iatake of a timing pump can cause vaporization of the product. The booster pump is ia the circuit ahead of the timing pump and operates only when the FDV is ia forward flow, the metering pump is ia operation, and the pasteurized product is at least 7 kPa (1 psi) above the maximum pressure developed by the booster pump (Fig. 8). 

Fig. 10. Log—log plot scale-up by power per unit volume where for A, constant blend time, = 2/3 B, same vortex, y = 1/6 C, dispersion, = 0 D,...

Dimensionless Quantities. Certain quantities, eg, refractive index and relative density (formerly specific gravity), are expressed by pure numbers. In these cases, the corresponding SI unit is the ratio of the same two SI units, which cancel each other, leaving a dimensionless unit. The SI unit of dimensionless quantities may be expressed as 1. Units for dimensionless quantities such as percent and parts per million (ppm) may also be used with SI in the latter case, it is important to indicate whether the parts per million are by volume or by mass. 

The solubihty coefficient must have units that are consistent with equation 3. In the hterature S has units cc(STP)/(cm atm), where cc(STP) is a molar unit for absorbed permeant (nominally cubic centimeters of gas at standard temperature and pressure) and cm is a volume of polymer. When these units are multiphed by an equihbrium pressure of permeant, concentration units result. In preferred SI units, S has units of nmol /(m GPa). 

Natural Gas. Natural gas, an abundant fuel resource in the United States, has sufficient reserves to fuel over 10 x 10 U.S. vehicles per year for the next 50 years (122). Natural gas is used in two forms as a transportation fuel compressed or Hquefied at low temperatures. Tanks for the storage of compressed natural gas are heavy and larger in volume than for Hquid fuels. However, the added cost is offset by an expected lower pump price compared to gasoline (123). Whereas the lack of pubHc natural gas fueling stations and other factors make natural gas more attractive for fleet vehicles in the United... 

Here g is the gravity vector and tu is the force per unit area exerted by the surroundings on the fluid in the control volume. The integrand of the area integr on the left-hand side of Eq. (6-10) is nonzero only on the entrance and exit portions of the control volume boundary. For the special case of steady flow at a mass flow rate m through a control volume fixed in space with one inlet and one outlet, (Fig. 6-4) with the inlet and outlet velocity vectors perpendicular to planar inlet and outlet surfaces, giving average velocity vectors Vi and V9, the momentum equation becomes... 

The quantity of a solute adsorbed can be given conveniently in terms of moles or volume (for adsorption) or ion-equivalents (for ion exchange) per unit mass or volume (dry or wet) of sorbent. Common units for adsorption are moV(m of fluid) for the fluid-phase concentration Cj and moV(kg of clean adsorbent) for adsorbed-phase concentration /ij. For gases, partial pressure may replace concentration. 

Mass concentration units for ambient measurements are mass (/xg) per unit volume (m ). Size classification involves the use of specially designed inlet configurations, e.g., PMjq sampling. To determine mass concentration, all the particles are removed from a known volume of air and their total mass is measured. This removal is accomplished by two techniques, filtration and impaction, described in Chapter 13. Mass measurements are made by pre-and postweighing of filters or impaction surfaces. To account for the absorption of water vapor, the filters are generally equilibrated at standard conditions T = 20°C and 50% relative humidity). 

The meli and mould temperatures and the value of the heal removed per gram on cooling are taken from the paper by Whelan and Goff. The values for the amount of heat required to raise the temperature to the melting point and the heat requirements per unit volume (both for heating and cooling) have been calculated from these data by the author. 

Mention should be made of the nomenclature for the polymer. Industrially the materially is invariably known in the English-speaking world as polypropylene. However, the lUPAC name for the monomer is propene and until 1975 the recommended lUPAC name was polypropene, a term very rarely used. The latest lUPAC rules base the name of a polymer on the constitutional repeating unit, which in this case is a propylene unit (c.f. a methylene unit for polyethylene) and this leads to the name poly(propylene) (i.e. with brackets). In this volume the more common, unbracketed but still unambiguous name will be used. 

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