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2.1: International System of Units

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  • Table \(\PageIndex{1}\): S.I. Basic Units

    Quantity Name Symbol Definition
    length meter m The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.
    mass kilogram kg The kilogram is the unit of mass equal to the international prototype of the kilogram.
    time second s The second is the duration of 9 192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
    electric current ampere A The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to \(2\times 10^{-7}\) newton per meter of length.
    temperature kelvin K The Kelvin, unit of thermodynamic temperature, is the fraction of 1/273.16 of the thermodynamic temperature of the triple point of water.
    elemental entities mole mol The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12.
    luminous intensity candela cd The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency \(540\times 10^{12}\) hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

    In 1960 a conference was held in Paris to find agreement on a set of standards. From that conference there arose what are called the SI (Système International) system of basic units3 which are listed in Table \(\PageIndex{1}\). Note that the SI system does not use the electric charge as a standard, but rather the electric charge per unit time or the electric current. In addition, the SI system of basic units includes three additional units, the thermodynamic temperature, the mole, and the luminous intensity. These three additional units are not necessary to assign numerical values to any observable, thus their role is somewhat different than the four fundamental standards identified by Hurley and Garrod. For example, a mole consists of \(6.02209...\times 10^{23}\) entities such as atoms, molecules, photons, etc., and the basic unit associated with counting entities is one. Feynman et al4 emphasize this point with the statement, “We use 1 as a unit, and the chemists use \(6\times 10^{23}\) as a unit!” Nevertheless, a mole is a convenient unit for engineering calculations because one of them is significant, and we will use moles to count atoms and molecules throughout this text5.

    2.1.1 Molecular mass

    Here we follow the SI convention concerning the definition of molecular mass which is


    \[\text{molecular mass}=\frac{\text{mass of the substance}}{\text{amount of the substance}} \label{1}\]

    Continuing with the SI system, we represent the mass of the substance in kilograms and the amount of the substance in moles. For the case of carbon-12 identified in Table \(\PageIndex{1}\), this leads to

    \[\text{ molecular mass of carbon-12}=\frac{ 0.012 \text{ kilogram}}{ \text{mole}} \label{2}\]

    Using the compact notation indicated in Table \(\PageIndex{1}\), we express this result as

    \[MW_{ C^{ 12} } =\frac{ 0.012 \ kg }{ mol } \label{ZEqnNum275044}\]

    in which the symbol \(MW\) is based on the historical use of molecular weight to describe the molecular mass. The molecular mass of carbon-12 can also be expressed in terms of grams leading to

    \[MW_{ C^{12} } =\frac{ 12 \ g}{ mol} \label{ZEqnNum446546}\]

    While Equation \ref{ZEqnNum275044} represents the molecular mass in the preferred SI system of units, the form given by Equation \ref{ZEqnNum446546} is extremely common, and we have used this form to list atomic masses and molecular masses in Tables \(A1\) and \(A2\) of Appendix \(A\).

    Energy can be described in units of \(kg\) \(m^2/s^2\); however, the thermodynamic temperature represents an extremely convenient unit for the description energy and many engineering calculations would be quite cumbersome without it. The same comment applies to the luminous intensity which is an observable that can be assigned a numerical value in terms of the four fundamental standards of length, mass, time and electric charge. One of the attractive features of the SI system is that alternate units are created as multiples and submultiples of powers of 10, and these are indicated by prefixes such as giga for \(10^{9}\), centi for \(10^{-2}\), nano for \(10^{-9}\), etc. Some of these alternate units are listed in Table \(\PageIndex{2}\) for the meter6. In other systems of units, multiples of 10 are not necessarily used in the creation of alternate units, and this leads to complications which in turn lead to errors.

    Table \(\PageIndex{2}\): Alternate Units of Length

    1 kilometer (km) = \(10^3\) meter (m)
    1 decimeter (dm) = \(10^{-1}\) m
    1 centimeter (cm) = \(10^{-2}\) m
    1 millimeter (mm) = \(10^{-3}\) m
    1 micrometer (\(\mu\)m) = \(10^{-6}\) m
    1 nanometer (nm) = \(10^{-9}\) m

    2.1.2 Systems of units

    If we focus our attention on the fundamental standards and ignore the electric charge, we can think of the SI (Système International) system as dealing with length, mass and time in terms of meters, kilograms and seconds. At one time this was known as the MKS-system to distinguish it from the CGS-system in which the fundamental units were expressed as centimeters, grams and seconds. Another well-known system of units is referred to as the British (or English) system in which the fundamental units are expressed in terms of feet, pounds-mass, and seconds. Even though there was general agreement in 1960 that the SI system was preferred, and is now required in most scientific and technological applications, one must be prepared to work with the CGS and the British system, in addition to other systems of units that are associated with specific technologies.

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