Systems of units

There are three classes of SI units base, derived, and supplemental units. A base unit was decreed by the CGPM for each of eight fundamental but dimensionally independent physical quantities. These units are listed in Table 1-2. A derived unit is derived mathematically from two or more base units (Table 1 -3). A supplemental unit is a unit that conforms to the SI but that has not been classified as either base or derived. At present only the radian (for plane angles) and the steradian (for solid angles) are classified this way. 

The CGPM recognizes that some units outside the SI continue to be important and useful in particular applications. An example is the hter as the reference volume in clinical analyses. Liter is the name of the submultiple (cubic decimeter) of the SI unit of volume, the cubic meter. Considering that 1 cubic meter represents some 200 times the blood volume of an adult human, the SI unit of volume is neither a convenient nor a reasonable reference volume in a cHnical context. Nevertheless, the CGPM recommends that such exceptional units as the liter should not be combined with SI units and preferably should be replaced with SI units whenever possible. 

TABLE 1-3 Examples of SI-Dcrived Units Important in Clinical Medicine, Expressed in Terms of Base Units 

Qui ntlty, . Narnp ip 1 Symbol Expression in Terms of Other SI Units Expression inTerrns of SI Base Units o T 

Gpncentr tion of ainquut of LLsubstmice limole per Gubic.met f rnp)/m mol/m  

Lindenmann, J., and Schleuning, W. D., eds. (1999). Interferon The Dawn of Recombinant Protein Drugs. New York Springe r-Verlag. 

The tenth CGPM in 1954 added two more standards when it officially approved both the kelvin for thermodynamic temperature and the candela for luminous intensity. In 1960 the eleventh CGPM renamed its AIKS system of units the International System of Units, and in 1971 the fourteenth CGPM completed the seven-unit system in use today, with the addition of the mole as the unit for the amount of a substance, setting it equal to the gram-molecular weight of a substance. 

SI units fall into two groups basic units and derived units. The basic units are the seven mutually independent units (see Table 1) and include the meter, kilogram, second, ampere, kelvin, mole, and candela. They represent, 

SOURCE Taylor, Bariy N ed.t and National Institute of Standards and Technology (1995). Guide for the Use of the International System of Units (SI). Special Publication 811. Washington, DC U.S. Government Printing Office. 

SI-DERIVED UNITS Derived Quantity Name Symbol 

Currently, the International System of Units (SI) provides standards that are officially used by many countries. 

In this paper, the relevant issues and the proposed redefinitions are reviewed. One of the consequences of these possible redefinitions is that values of many of the fundamental constants, when expressed in the new units, would be exact and many others would have reduced uncertainties. Another possibly surprising result is that the new definitions could be made in such a way that the distinction between base units and derived units, presently specified in the SI, would become unnecessary and could be eliminated. This might be called unit democracy, in which all SI units have equal status. In principle, this scheme could be extended to include an analogous redefinition of the second, but this would have to await improved accuracy in the relevant experiments and theory. Constraints on timing of the proposed redefinitions, which could take effect as early as 2011, will be described. 

The International System of Units is presently defined in terms of seven base units, various coherent derived units, and units that are defined to be in other categories. The seven base units and symbols are  

The derived units are coherent with the base units and each other, which means that relations between equivalent ways of expressing units have unit coefficients. As an example 1 J = 1 kg m s .  

In general, the non-SI units are not coherent with the SI units for example, 1 eV 1.6 X 10 J, where the coefficient is not unity, and in this case depends on measured quantities. 

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The nomenclature used in Volume 1 is based on the recommendations of the lUPAC (International Union of Pure and Applied Chemistry) for the system of units utilized as well as for their symbols. The reference is entitled,... 

One complication is the presence of two systems of units cgs/esu and SI. As in Chapter V, we again present the equations in the cgs/esu system we show alternative forms appropriate to the SI system in Tables VI-2 and VI-3. 

While the Systeme International d Unites (SI) system of units is not particularly relevant to physical chemistry and requires additional and sometimes awkward constants, its broad use deserves attention. The majority of the derivations are made in the cgs/esu (centimeter-gram-second/electrostatic unit) system of units however, both the SI and cgs systems are explained and tables for their interconversion are given in Chapters V and VI. 

Note that these equations do not contain the constants that are typically included in introductory texts, such as the vacuum permitivity constant. Theoreticians, and thus software developers, work with a system of units called atomic units. Within this unit system, many of the fundamental constants are defined as having a value of 1. Atomic units will be used throughout this book unless otherwise specified. 

The authors of this research selected units which could be written with maximum simplification to report their results. We must replace the factors which have canceled out. Assuming that the cgs system of units was used throughout, we note that possible units for H are grams per square centimeter and possible unts for C2 are grams per cubic centimeter, which yield the required units for n/c2 Note that these units of H must be multiplied by the gravitational constant to give H in dynes per square centimeter ... 

It is conventional to use molality—moles of solute per kilogram of solvent (symbol m)—as the concentration unit in electrolyte thermodynamics. Accordingly, we shall represent the concentrations of both the indifferent electrolyte and the polymer in these units in this section m3 and m2, respectively. In the same dilute (with respect to polymer) approximation that we have used elsewhere in this chapter, m2 is related to the mass volume system of units C2 by... 

Coulomb s law. This relationship poses no particular difficulties as a qualitative statement the problem arises when we attempt to calculate something with it, since the proportionality constant depends on the choice of units. In the cgs system of units, the electrostatic unit of charge is defined to produce a force of 1 dyne when two such charges are separated by a distance of 1 cm. In the cgs system the proportionality factor in Coulomb s law is unity and is dimensionless. For charges under vacuum we write... 

In a medium where the relative dielectric constant is e, the force between fixed chages at a definite separation is decreased by the dimensionless factor e. This is true regardless of the system of units and is incorporated into Eqs. (10.101) and (10.102) by dividing the right-hand side of each by e. ... 

Basic Standards for Chemical Technology. There are many numerical values that are standards ia chemical technology. A brief review of a few basic and general ones is given hereia. Numerical data and definitions quoted are taken from References 16—19 (see Units and conversion factors) and are expressed ia the International System of Units (SI). A comprehensive guide for the appHcation of SI has been pubUshed by ASTM (20). 

Time. The unit of time in the International System of units is the second "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental state of the atom of cesium-133" (25). This definition is experimentally indistinguishable from the ephemetis-second which is based on the earth s motion. 

Units. The SI system of units and conversion factors (qv) has been formally adopted worldwide, with the exception of Bmnei, Burma, Yemen, and the United States. The participation of the United States in the metrication movement is evident by the passage of the Metric Acts of 1866 and 1975 and the subsequent estabUshment of the American National Metric Council (private) and the U.S. Metric Board (pubHc) to plan, coordinate, monitor, and encourage the conversion process. 

Pressure is defined as force per unit of area. The International System of Units (SI) pressure unit is the pascal (Pa), defined as 1.0 N /m. Conversion factors from non-SI units to pascal are given in Table 1 (see also Units and conversion factors front matter). An asterisk after the sixth decimal place indicates that the conversion factor is exact and all subsequent digits are 2ero. Relationships that are not followed by an asterisk are either the results of physical measurements or are only approximate. The factors are written as numbers greater than 1 and less than 10, with 6 or fewer decimal places (1). 

In 1954, the 10th CGPM added the degree Kelvin as the unit of temperature and the candela as the unit of luminous intensity. At the time of the 11th CGPM in 1960, this new system with six base units was formalized with the tide International System of Units. Its abbreviation in all languages is SI, from the French l e Sjstume International d Unitus. 

The same simplified system of units can be used by the research scientist, the technician, the practicing engineer, and by members of the lay pubHc. 

As indicated earlier, the vaUdity of the method of dimensional analysis is based on the premise that any equation that correcdy describes a physical phenomenon must be dimensionally homogeneous. An equation is said to be dimensionally homogeneous if each term has the same exponents of dimensions. Such an equation is of course independent of the systems of units employed provided the units are compatible with the dimensional system of the equation. It is convenient to represent the exponents of dimensions of a variable by a column vector called dimensional vector represented by the column corresponding to the variable in the dimensional matrix. In equation 3, the dimensional vector of force F is [1,1, —2] where the prime denotes the matrix transpose. 

NOTE Copyright SPE-AIME, The SI Metric System of Units and SFE s Tentative Mehic Standai d, Society of Petroleum Engineers, Dallas, 1977. 

Considerations of reader interest, space availability, the system or systems of units employed, copyright considerations, etc., have all influenced the revision of material in previous editions for the present edition. Reference is made at numerous places to various specialized works and also, when appropriate, to more general works. A listing of general works may he useful to readers in need of further information. 

Density is defined as the mass of a substance contained in a unit volume. In the SI system of units, the ratio of the density of a substance to the density of water at I5°C is known as its relative density, while the older term specific gravity is the ratio relative to water at 60°F. Various units of density, such as kg/m, Ib-mass/fF, and g/cm, are commonly used. In addition, molar densities, or the density divided by the molecular weight, is often specified. This section briefly discusses methods of correlation of density as a function of temperature and presents the most common accurate methods for prediction of vapor, liquid, and solid density. 

Except where otherwise noted here or in the text, either consistent system of units (SI or U.S. customary) may he used. Only SI units may he used for electrical quantities, since no comparable electrical units exist in the U.S. customary system. When special units are used, they are noted at the point of use. 

From Eq. (6-1) it is evident that A has the units of k and that E has the units energy per mole. For many decades the usual units of E were kilocalories per mole, but in the International System of Units (SI) E should be expressed in kilojoules per mole (1 kJ = 4.184 kcal). In order to interpret the extant and future kinetic literature, it is essential to be able to use both of these forms. 

Most of the units used in tliis book are consistent with those adopted by the engineering profession in tlie United States. For engineering work, International SySterne (SI) and English units are most often employed in the United States, tlie English engineering units are generally used. Tliese systems of units are shown in Table 4.2.1. ... 

It is usual these days to express all physical quantities in the system of units referred to as the Systeme International, SI for short. The International Unions of Pure and Applied Physics, and of Pure and Applied Chemistry both recommend SI units. The units are based on the metre, kilogram, second and the ampere as the fundamental units of length, mass, time and electric current. (There are three other fundamental units in SI, the kelvin, mole and candela which are the units of thermodynamic temperature, amount of substance and luminous intensity, respectively.)... 

Even worse is the confusion regarding the wavefunction itself. The Born interpretation of quantum mechanics tells us that i/f (r)i/f(r) dr represents the probability of finding the particle with spatial coordinates r, described by the wavefunction V (r), in volume element dr. Probabilities are real numbers, and so the dimensions of i/f(r) must be of (length)" /. In the atomic system of units, we take the unit of wavefunction to be... 

In the atomic system of units, the energy of a ground-state hydrogen atom is... 

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