Science measuring physical quantities

A physical unit system is implicitly defined by the choice of three underlying base units, which suffice to determine dimensionally consistent units for other measurable physical quantities. (Why three such base units are required is as yet an unanswered physical question.) Although the choice of units may superficially appear arbitrary, it was recognized by Gibbs (in his first scientific communication)1 that one can rationally address the question of the conditions which it is most necessary for these units to fulfil for the convenience both of men of science and of the multitude. ... 

In science, the word error has a very specific meaning it does not mean mistake . All experimental measurements will differ, to some degree, from the accurate or real value of the quantity being measured. The difference between the observed value of a physical quantity and the accurate value is called the error. It is very important to consider all the possible sources of errors in experimental measurements. Every experimental measurement reported should be accompanied by an estimate of the error - scientifically speaking, measurements without accompanying error estimates are worthless. 

Chemistry and physics are experimental sciences, based on measurements. Our characterization of molecules (and of everything else in the universe) rests on observable physical quantities, expressed in units that ideally would be precise, convenient and reproducible. These three requirements have always produced trade-offs. For example, the English unit of length inch was defined to be the length of three barleycorns laid end to end—a convenient and somewhat reproducible standard for an agricultural society. When the metric system was developed in the 1790s, the meter was defined to be... 

Quantity calculus is a system of algebra in which symbols are consistently used to represent physical quantities rather, than their measures, i.e. numerical values in certain units. Thus we always take the values of physical quantities to be the product of a numerical value and a unit (see section 1.1), and we manipulate the symbols for physical quantities, numerical values, and units by the ordinary rules of algebra.1 This system is recommended for general use in science. Quantity calculus has particular advantages in facilitating the problems of converting between different units and different systems of units, as illustrated by the examples below. In all of these examples the numerical values are approximate. 

Characterization, as it applies to catalyst science, is usually used to describe both the performance characteristics (evaluation) and the physical attributes (analyses) of the materials under investigation. Personnel involved in catalyst evaluation utilize custom designed equipment to determine the performance of a catalyst in a particular process. The design of the equipment typically follows that of the process, but on a much smaller laboratory scale. These simulations attempt to "mimic" the process, or parts of the process, and as such the data generated are relative not only to the process but to the test equipment and conditions (see Dartzenburg). Conversion, activity, stability, abrasion resistance, crush strength, etc. are terms often encountered in evaluation. Analysis, on the other hand, describes or measures the physical quantities of size or mat-... 

This useful equation may be used to predict the reaction rate at any temperature once kt and E are known for temperature Tt. This type of calculation is extremely important in pharmaceutical science since it is used to predict shelf-life for medicines. Once a medicine has been manufactured, it is stored under high-stress conditions (e.g. at elevated temperature, high humidity, under strong lighting, etc.), the rates of decomposition are measured and the activation energy is calculated. From these data, the value of k may be predicted and the likely shelf-life for the medicine can be calculated for room temperature (25°C) or refrigerator temperature (4°C). Another useful point to notice is that since k enters into the graphs as In k, and into the equations as a ratio, any physical quantity that is proportional to k, such as the actual reaction rates at fixed concentrations of reactants, may be used in the equation instead of k. 

The establishment of scientific facts and laws is obviously dependent on accurate observations and measurements. Although measurements can be reported as precisely in one system of measurement as another, there has been an effort since the time of the French Revolution in the late l700s to have all scientists embrace the same simple system. The hope was and is to facilitate communication in science. The metric system, which was born of this effort, has two advantages. First, it is easy to convert from one unit to another, since smaller and larger units for the same physical quantity differ only by multiples of ten. Consequently, to change millimeters to meters, the decimal point need only be moved three places to the left... 

SI units are used to express physical quantities in all sciences, including chemistry. Numbers expressed in scientific notation have the form Y X 10", where N is between 1 and 10 and n is a positive or negative integer. Scientific notation helps us handle very large and very small quantities. Most measured quantities are inexact to some extent. The number of significant figures indicates the exactness of the measurement. 

It is interesting to observe the evolution of science in microcosm by following the development of a highly specialized fragment of it, especially one which cuts across several conventional fields, such as the subject of this book. The familiar pattern of alternation between experimental and theoretical advances is apparent. Underlying each advance is a conceptual scheme which is an arbitrary and subjective choice of one investigator or school in this conceptual abstraction, attention is focused on certain aspects of observed behavior that are believed to be particularly important or useful to describe, and other aspects are ignored. The conceptual scheme leads to a set of characteristic physical quantities which can be defined, measured, and correlated by theoretical relationships. 

The International Standards Association has in the series ISO 31 published a number of standard sheets specifying physical quantities, measurement units and symbols used within the essential areas of science and technology. The ISO 31 series describes the international stem of units SI, which is short for Systeme international d Unite . The following overview comprises a range of SI units, symbols and terms that are frequently used to describe systems of substance. 

As pointed out above the comparison between both sets of results relies upon the physical equivalence of the two measureable quantities work function (surface science) and electrode potential (electrochemistry) 111. This equivalence has been realized in electrochemistry some time ago and has been exploited to analyze measured values of the potential of zero charge 111 and of work function changes upon emersion of electrodes at fixed potential 181. In the simulation experiments the approach is quite similar in that one prepares a well-defined composition of the synthetic electrochemical adsorbate layer and then obtains the electrostatic potential drop across it by a work function measurement. 

The first part of the growth of a physical science consists in the discovery of a system of quantities on which its phenomena may be conceived to depend. The next stage is the discovery of the mathematical form of the relations between these quantities. After this, the science may he treated as a mathematical science, and the verification of the laws is effected by a theoretical investigation of the conditions under which certain quantities can he most accurately measured, followed by an experimental realization of these conditions, and actual measurement of the quantities. 

Table 1.6 also lists the radius of gyration. This is an average dimension often used in colloid science to characterize the spatial extension of a particle. We shall see that this quantity can be measured for polydisperse systems by viscosity (Chapter 4) and light scattering (Chapter 5). It is therefore an experimental quantity that quantifies the dimensions of a disperse system and deserves to be included in Table 1.6. Since the typical student of chemistry has probably not heard much about the radius of gyration since general physics, a short review seems in order.

Measurement is the key to quantitative physical science. The results of every measurement must include both a numeric value and a unit (or set of units). Be sure to use standard abbreviations for all units. The factor label method is used to convert a quantity from one set of units to another without changing its value. The original quantity is multiplied by a factor equal to 1. (The numerator and denominator of the factor are equal to each other in value but different in form.) To use the factor label method (1) write down the quantity given, (2) multiply by a factor that will yield the desired units, (3) cancel the units, (4) multiply all numbers in the numerators and divide by the number(s) in the denominator(s). Sometimes, it is necessary to multiply by more than one factor. We may solve for the intermediate answers, but we do not have to. (Section 2.1)... 

Available Instrumentation One of the most obvious constraints on chamber design and experimental programme is the availability of instrumentation to probe the quantities of interest. As outlined above, it is frequently necessary to simultaneously monitor aerosol physical and chemical properties in addition to gas phase ehemical composition. A wide range of instruments are available for deployment in ground and aircraft-based field measurement within the Atmospheric Sciences Group at the University of Manchester. These will be available for deployment in the ehamber in scheduled campaign mode and otherwise periodically when not in field use. In addition, there are a range of core instruments available for all experiments. The instrumentation suite is broadly classified as follows ... 

Any device or system that has one or more physical properties (e.g., electrical resistance, electrical potential, length, pressure at constant volume, or volume at constant pressure) that vary monotonically and repro-ducibly with temperature may be used to measure temperature. The science of the measurement of temperature is called thermometry. In the past, the measurement of high temperature was known as pyrometry but now that term usually refers to radiation thermometry at any temperature. Although the accuracy of a measurement refers to the difference between the measured value and the true value of the quantity being measured, and the precision of measurement refers to the degree of agreement among repeated measurements of the same quantity, it follows that a set of measurements of the same quantity, it follows that a set of measurements may be very precise but terribly inaccurate. Since in many instances the word accuracy is used when inaccuracy is meant and the word precision is used when imprecision is meant, perhaps it would be better always to refer to uncertainties of measurement, statistical and systematic, rather than to accuracy and precision. 

The problems related to the water cycle will also not be considered in spite of the fact that, taking into account its quantity and atmospheric effects, water is one of the most important trace materials. This omission is explained by a historical precedent. The study of the atmospheric cycle of the water as well as the measurement of its concentration were included in the past in the program of other branches of atmospheric science. Thus, the formation of clouds and precipitation, the subject of the cloud physics (e.g. Mason, 1957, Fletcher, 1962), will only be discussed in relation with the wet removal of aerosol particles and water-soluble gases. 

The dramatic story of the discovery of Ceo and of a way of manufacturing this new molecule in gram quantities is now well known to professionals and amateurs of science alike. " Cgo and its companion C70 have become the prototypes of a whole new class of molecules—the fullerenes—and the chemistry, physics, and materials science literature since 1985 and especially since 1990 has been flooded with reports of measurements, calculations, and speculations on their properties. For the theoretical chemist, one of the prime motivations for studying the fullerenes is that they show a clear link between geometrical/topological and electronic structure. This link will be reviewed here. 

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