Volume corrected

The nth virial coefficient = < is independent of the temperature. It is tempting to assume that the pressure of hard spheres in tln-ee dimensions is given by a similar expression, with d replaced by the excluded volume b, but this is clearly an approximation as shown by our previous discussion of the virial series for hard spheres. This is the excluded volume correction used in van der Waals equation, which is discussed next. Other ID models have been solved exactly in [14, 15 and 16]. ... 

Equation 11 can be written where + V ). is often referred to as the volume-corrected response. A plot of versus... 

Multiplying each response and concentration by the initial volume of the sample, the so-called volume-corrected response equation ... 

After estimating iC, the vector of initial quantities can be obtained using the vector of volume-corrected initial responses by solving... 

Thermal expan sion of petroleum fuels can be estimated as volume change per unit volume per degree. ASTM-IP Petroleum Measurement Tables (ASTM D 1250 IP 200) are used for volume corrections in commercial transactions. 

The volume corrected to o° and 760 mm. will be given by the following expression —... 

Brake horsepower per 1 million ft /day measured at 14.7 psia and suction temperature using 75% overall compressor efficiency is given in Figure 12-68, and a volume correction factor is shown in Figure 12-69. 

Calculate the amount of boron present by reference to a calibration graph of absorbance against boron concentration (mg L 1). Multiply the result obtained by the appropriate volume correction factor arising from neutralisation of the sample. 

A volume correction is necessary, as can be seen from a numerical experiment similar to the preceding one If the increase in volume from VI to VI + V2 is ignored, a bias of about 7% is produced. 

ELECTRODEjcls Fig. 4.24 The operation of an ion-specific electrode with a slope of 59.16 mV per decade for mono-valent ions (29.58 mV/dec for di-valent ions) is simulated under the assumption that a digital volt meter with a resolution of, say, 0.1 mV is used. The sample volume and the concentration of the metered titration solution are known. Normally, one would add a few milliliters of the concentrated titration solution and do the calculation spelled out in lines 140-150 in Table 4.22 here, because the sample concentration is known, the result can be normalized to it. The operation of short-cuts (volume correction), unknowns (volume bias, deviation of true slope from theoretical), and equipment shortcomings (digitization) can be studied. 

Corrected Retention Volume V, Retention volume corrected for mobile phase compressibility V,- jv. 

The proceeding is simplified for such cases in which the volume of the added analyte amounts can be neglected in comparison with that of the initial sample (solution). Otherwise, a procedure using volume-corrected measurement values has to be applied (see Sharaf et al. [1986]). 

First-order estimates of entropy are often based on the observation that heat capacities and thereby entropies of complex compounds often are well represented by summing in stoichiometric proportions the heat capacities or entropies of simpler chemical entities. Latimer [12] used entropies of elements and molecular groups to estimate the entropy of more complex compounds see Spencer for revised tabulated values [13]. Fyfe et al. [14] pointed out a correlation between entropy and molar volume and introduced a simple volume correction factor in their scheme for estimation of the entropy of complex oxides based on the entropy of binary oxides. The latter approach was further developed by Holland [15], who looked into the effect of volume on the vibrational entropy derived from the Einstein and Debye models. 

Aguirre, R. M., De Paoli, A. L. (2002). Neutron star structure in a quark model with excluded volume correction. Phys.Rev.C68 055804. 

Note (0 To minimise the temperature variations between the titrant and the solution and also to obviate volume corrections, the concentration of the titrant is invariably maintained 10-100 times higher than that of the reactant, and... 

The data from the density (specific gravity) test method (ASTM D1298 IP 160) provides a means of identification of a grade of naphtha but is not a guarantee of composition and can only be used to indicate evaluate product composition or quality when used in conjunction with the data from other test methods. Density data are used primarily to convert naphtha volume to a weight basis, a requirement in many of the industries concerned. For the necessary temperature corrections and also for volume corrections, the appropriate sections of the petroleum measurement tables (ASTM D1250 IP 200) are used. 

Table I. Phase volume corrected second order rate constants (k .) as a function of phase volume (( )) for the reaction of cyanide with N-dodecyl-3-carbamoyl-pyridinium ion in CTAB and BriJ 96 microemulsions...

Figure 1. Phase volume corrected rate constant (ko ) phase volume ((f)) for the N-dodecylnicotinamide-cyanide reaction in (a) Brlj yE and (b) CTAB yE, Curves (c) and (d) are the ionic strength corrected Brij rate constants for Stern layer thicknesses of 4A and 2A, respectively (vide text).

As shown by Helgeson et al. (1978), satisfactory estimates of standard state molar entropy for crystalline solids can be obtained through reversible exchange reactions involving the compound of interest and an isostructural solid (as for heat capacity, but with a volume correction). Consider the generalized exchange reaction... 

Table I indicates good agreement between the molecular weight distribution statistics obtained by coupled GPC/Viscometer method and the nominal values for t BS 706. The discrepancy between the Mark-Houwink parameters obtained here and the reported values for polystyrene standard ( ) in THF at 25°C (i.e., a = 0,706 and k = 1.60 x 10 ) may in part be due to the uncertainty involved in the determination of the dead volume between DRI and viscometer detectors. Our simulation studies over a range of dead volume values (0 to 120u)l) showed that a and k are quite sensitive to the dead volume between the detectors. Larger dead volume results in smaller o and larger k values. This is a direct result of a clockwise rotation of log [q] vs. log M(v) curve (Figure 12) which occurs when the dead volume correction is applied in quantitative analysis. The effect on the molecular weight statistics, however, appeared to...

Figure 5.4A and B compares the uncorrected elution volumes, the elution volumes corrected by simple addition of and the elution volumes calculated using Equation 5.21 in RP gradient elution on a conventional and on a micro-bore C18 column. The effect of the gradient dwell volume is more important for separations on short columns and especially on narrow-bore columns with i.d. 2 mm. 

Figure 6 demonstrates that the effect of the dead volume correction is to rotate the [n] vs. M plot about a point [inKM] which is independent of dead volume. Undercorrecting for dead volume results in values of K which are less than the true value and values of a which are larger than the true value of a. Overcorrecting for dead volume results in values of K larger than the true value of K and values of a less than the true value a. 

Because fuel and oil weights vary per standard volume, they should always be handled and sold on a weight basis, not volume basis. If sold on a volume basis, the volume should always be corrected to 60°F (15.5°C) by utilizing API volume reduction tables. These tables are used to standardize all volumes of petroleum products to a 60°F (15.5°C) volume. Standard API volume correction tables for petroleum products are contained in APPENDIX 3. 

The errors in the vacuum volumetric method arise principally from two sources. The error in measured doses is cumulative, requiring very accurate calibration. Also, the void-volume correction becomes more significant at higher pressures when measuring low surface areas because more molecules are retained in the void volume than are adsorbed. 

To properly fluidize and mix the material in the container, a correct choice of the container and air distributor must be made. The container volume should be chosen such that the bowl is filled to at least 35 0% of its total volume and no more than 90% of its total volume. Correct choice of the air distributor is important. These distributors are made of stainless steel and are available with a 2-30% open area. Typically, the distributor should be chosen so that the pressure drop across the product bed and air... 

Figure 6 7. Value and 95% confidence interval on the volume delivered by a nominal 10.0000-mL pipette, with different corrections applied. Cal. volume calibrated by 10 fill-and-weigh experiments. Temp volume corrected for temperature measured in the laboratory.

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