Other Measured Quantities

As will be discussed in the following chapter, most combustion systems entail oxidation mechanisms with numerous individual reaction steps. Under certain circumstances a group of reactions will proceed rapidly and reach a quasi-equilibrium state. Concurrently, one or more reactions may proceed slowly. If the rate or rate constant of this slow reaction is to be determined and if the reaction contains a species difficult to measure, it is possible through a partial equilibrium assumption to express the unknown concentrations in terms of other measurable quantities. Thus, the partial equilibrium assumption is very much like the steady-state approximation discussed earlier. The difference is that in the steady-state approximation one is concerned with a particular species and in the partial equilibrium assumption one is concerned with particular reactions. Essentially then, partial equilibrium comes about when forward and backward rates are very large and the contribution that a particular species makes to a given slow reaction of concern can be compensated for by very small differences in the forward and backward rates of those reactions in partial equilibrium. 

The "observed" rate constants are, in fact, derived from other measurable quantities, and according to chemists the assumption of constant relative... 

The Bashforth-Adams tables provide an alternate way of evaluating 7 by observing the profile of a sessile drop of the liquid under investigation. If, after all, the drop profiles of Figure 6.15 can be drawn using 0 as a parameter, then it should also be possible to match an experimental drop profile with the (3 value that characterizes it. Equation (85) then relates 7 to 0 and other measurable quantities. This method is claimed to have an error of only 0.1%, but it is slow and tedious and hence not often the method of choice in practice. 

In this section we have examined the three major contributions to what is generally called the van der Waals attraction between molecules. All three originate in dipole-dipole interactions of one sort or another. There are two consequences of this (a) all show the same functional dependence on the intermolecular separation, and (b) all depend on the same family of molecular parameters, especially dipole moment and polarizability, which are fairly readily available for many simple substances. Many of the materials we encounter in colloid science are not simple, however. Hence we must be on the lookout for other measurable quantities that depend on van der Waals interactions. Example 10.2 introduces one such possibility. We see in Section 10.7 that some other difficulties arise with condensed systems that do not apply to gases. 

Method development establishes a procedure for obtaining an acceptable estimate of the measurand. This procedure includes an equation that describes how to calculate a measurement result from other measured quantities, and specifies the conditions under which this equation is expected to hold. 

Dimensions. The fundamental measurables of a unit system in physics—those which are defined through operational definitions. All other measurable quantities in physics are defined through mathematical relations to the fundamental quantities. Therefore any physical measurable may be expressed as a mathematical combination of the dimensions. See operational definitions. 

Scattering and other forms of spectroscopy Rely on the fact that electromagnetic radiation has other interactions with matter beyond that of simple absorption and emission. These interactions generate other measurable quantities such as scattering of polarized light (e.g. circular dichroism), and changes of spectral features of chemical bonds (e.g. Raman spectroscopy). 

The viscosity A coefficient can be related to other measurable quantities through the expression (3,4) ... 

Gaseous diffusion coefficients and temperature Chen and Othmer proposed the following empirical equation to describe gaseous diffusion coefficients in terms of other measurable quantities ... 

Calculations of the effective diffusivity of porous catalysts in terms of other measurable quantities can be made (Wheeler, 1). They rely on certain simplifying assumptions of the geometry of the porous structure. More generally, confidence can be derived from direct measurements of diffusivity, or its indirect determination by way of appropriate catalytic measurements, as will be described. 

It is not a measurable quantity and, consequently, must be related to other measurable quantities (concentrations, pressure, etc.). 

We now replace V and r with two other measurable quantities, V is expressed in terms of the number of reactive molecules. By, that at t=0 are contained and evenly distributed in it ... 

Permeability for a Rock Formation. For natural consolidated porous medium, however, the definitions of the equivalent spherical diameter and the specific surface area per unit volume are not widely used because of its difficulty in determination and relation to other measurable quantities. Just to serve as a comparison, we give the permeability equation based on the previous passage model with the tortuosity given by equation 61 and assuming that the areal porosity equation 54 still holds. The permeability can then be given by... 

How then do we deal with non.spherical panicles The usual approaches arc to assume the particles arc spherical and then to proceed as we would with spheri-cal particles, or we can convert the measureef quantity into that of an equivalent sphere. For example, if we obtain the mass m of a particle, we can convert this into the mass of a sphere because m = (4/3)irr p, where r is the particle radius and p is its density. This allows the particle size to be described by only its diameter (d 2r). This diameter then represents the diameter of a sphere of the same mass as the particle of interest. Similar conversions can be made with other measured quantities, such as surface area or volume. 

Conversion of the instrument signal (counts or count rate) and other measured quantities to an activity concentration, typically expressed in becquerels (Bq) or picocuries (pCi) per unit mass (or per unit volume, area, or time) ... 

There are two approaches to eliminating these errors. The first approach is to use a flow computer supplied with a continuous measurement of calorific value and gravity. The errors are eliminated because all measurements are continuous and instantaneous. No averages are used and the energy flow itself is the only quantity integrated over the measurement period. In the second approach the energy flow is measured directly by the instrument so that the need of calculating it from other measured quantities is eliminated. 

But quantities are often determined indirectly as well, meaning they are found by calculation from other measured quantities. In the field of geodesy, the science of measuring and mapping the Earth s surface, lengths and altitudes have mostly been determined through calculations based on measured angles (Fig. 1.3). When he... 

Born-Haber cycle A thermodynamic cycle based on Hess s law that relates the lattice energy of an ionic substance to its entha y of formation and to other measurable quantities. (Section 8.2)... 

Any system of measurement must decide what to do about the fact that there are literally thousands of physical properties that we measure, each of which is expressed as a measured number of some well-defined unit of measurement. It would be impossible to set up primary standards for the units of each and every one of these thousands of physical quantities, but fortunately there is no need to do so since there are many relationships connecting the measurable quantities to one another. A simple example that is of direct importance to the subject of this book is that of volume as mentioned above, the SI unit of volume (cubic meter) is simply related to the SI unit for length via the physical relationship between the two quantities. So the first question to be settled concerns how many, and which, physical quantities should be defined as SI base quantities (sometimes referred to as dimensions), for which the defined units of measurement can be combined appropriately to give the SI units for all other measurable quantities. 

The International System of Units (Systeme Internationale d Unites, SI) establishes the standards of comparison used by all countries when the measured values of physical and chemical properties are reported. There are seven SI base quantities (dimensions), for which the defined units of measurement can be combined appropriately to give the SI units for aU other measurable quantities (i.e., the SI system is a coherent system of units). 

Just determined (nonredundant) quantities correspond to columns with zero elements in all rows 3 and 4. They are thus represented by columns 6b and 8de other measured quantities are redundant (adjustable). 

Three different formulae were proposed by L Hermite (1955, 1957), each related to other measurable quantities ... 

Are there three significant figures in the denominator, 100 g Al2(S04)3 The 100 is a defined quantity, like 12 inches equal 1 foot. The total percent of anything is defined to be exactly 100. The denominator therefore has an infinite number of significant figures, more than any other measured quantity in the calculation. 

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