Physical quantities and their units

A property can usually be expressed numerically by a physical quantity or by a combination or a function of physical quantities. The concept physical quantity was created by Maxwell (1873). Since then it has obtained a central position in the mathematical formalism of science and technology. In general one may write (Maxwell, 1873)  

The unit of a physical quantity is in essence a reference quantity in which other quantities of the same kind can be expressed. 

A well-organised system of units forms an essential part of the whole system of physical quantities and the equations by which they are interrelated. Many different unit systems have been in use, which has given rise to much confusion and trouble. Here we confine ourselves to two of these units systems. 

Nowadays the so-called practical unit system is in general used. It is a really coherent system, which means that no multiplication factors are introduced in the definition of derived units as soon as the base units have been defined. In 1969 this coherent system was recommended by the International Organisation for Standardisation as International System of Units (SI = Systeme International d Unites) and in 1973 it was accepted as such, according to International Standard ISO 1000. 

The International System of Units is founded on seven base quantities (Table 3.1) that cover the whole field of natural science. Again, the system of quantities and equations of mechanics rests on the three base quantities length, mass and time, for which the units meter, kilogram and second are now internationally accepted. The derived unit of force is the Newton (N), being the force that gives the unit mass (kg) a unit acceleration (1 m s-2). The derived unit of energy is the Newton meter (N m). 

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A related concept to dimensional analysis is quantity calculus, a method we find particularly useful when it comes to setting out table header rows and graph axes. Quantity calculus is the handling of physical quantities and their units using the normal rules of algebra. A physical quantity is defined by a numerical value and a unit ... 

Table 1.1 summarizes the seven base (or fundamental ) SI physical quantities and their units. The last unit, luminous intensity, will not require our attention any further. 

Table 1.1 The seven fundamental SI physical quantities and their units...

The method described here for handling physical quantities and their units is known as quantity calculus. It is recommended for use throughout science and technology. The use of quantity calculus does not imply any particular choice of units indeed one of the advantages of quantity calculus is that it makes changes between units particularly easy to follow. Further examples of the use of quantity calculus are given in chapter 7, which is concerned with the problems of transforming from one set of units to another. 

In handling physical quantities and their units we have used the method of quantity calculus [3] (also called dimensional analysis). The value of a physical quantity is expressed as the product of a numerical value and a unit... 

Dimensional formulae - f6r-myo-b n. If mass, length, and time are considered fundamental quantities, the relation of other physical quantities and their units to these three may be expressed by a formula involving the symbols L, M, and T, respectively, with appropriate exponents. For example the dimensional formula for volume would be expressed [L j velocity [LT j force [MLT j. Other fundamental quantities used in dimensional formulae may be indicated as follows 0, temperature 8, the dielectric constant of a vacuum /i, the magnetic permeability of a vacuum. 

Dimensional Formulae n - f6r-my9-b If mass, length, and time are considered fundamental quantities, the relation of other physical quantities and their units to... 

A physical unit system is essentially defined by three chosen base quantities and corresponding base units, which suffice to determine dimensionally consistent units for other measurable physical quantities. In the Systeme International d Unites (SI) framework, the three base quantities and their units are as follows ... 

TABLE 1.1 METRIC UNITS FOR I PHYSICAL QUANTITIES AND THEIR USCS ... 

The first step in generating the dimensionless variables is to set-up a dimensional matrix with the physical quantities and their respective units,... 

Table 1 shows some symbols and abbreviations commonly used in analytical chemistry, while Table 2 shows some of the alternative methods for expressing the values of physical quantities and their relationship to the values in SI units. In addition. Table 3 lists prefixes for SI units and Table 4 shows the recommended values of a selection of physical constants. 

Dimensional analysis is commonly applied to complex materials and processes to assess the significance of some phenomenon or property regime. It enables analysis of situations that cannot be described by an equation however, there is no a priori guarantee that a dimensionless analysis will be physically meaningful. Dimensionless quantities are combinations of variables that lack units (i.e., pure numbers), used to categorize the relationship of physical quantities and their interdependence in order to anticipate the behavior. Several dimensionless quantities relevant to polymer rheology and processing are... 

The International System of Units (SI), Physical Quantities, and Their Dimensions... 

Physical quantities are tools which allow us to specify and quantify the properties of physical objects and to model the events, phenomena, and patterns of behavior of objects in nature and in technology. The system of physical quantities used with the SI units is dealt by Technical Committee 12 of the International Organization for Standardization (ISO/TC 12). Since 1955, ISO/TC 12 has published a series of international standards on quantities and their units, in which the use of SI units is strongly recommended. 

TABLE 1.1 Atomic units for common physical quantities, and their SI equivalents. 

Each physical quantity is given a symbol that is either italic or Greek. Table 1 lists most of the symbols used in this text and their units (see also... 

We exceptionally break our rule that S3mibols denote physical quantities, not their measure in chosen imits. When we have a long or complicated expression involving only the temperature we shall sometimes vrite T instead of T/deg because we always measure T in the same units. For example the relation between the vapour pressure p of benzene and the temperature may be written... 

TABLE A.8.3 Custom Physical Quantities with Their Common Symbols, Measured Values (Relative Errors in Parenthesis) and Units Within the International System Framework... 

Units (1.4) Labels designating the type of quantity measured and the particular scale on which the measurement was made. Most measurements have no physical meaning if their units are omitted. 

The PDF (Portable Document Format) display presents the numerical data in a more traditional tabular and graphical form. The property type, including the physical quantities with their SI units, the state of the chemical system, and the method used to obtain the data, the molecular formulas, primary names and CAS Registry Numbers of the components are given. Alternate names (synonyms) are listed in the Name Index of Substances (Chap. 4.2). The full reference to the original source of data is given with the author(s) and the title of the publication. 

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