Derived unit of measurement

Area and volume are examples of derived units of measurement they are obtained or derived from the basic unit of length ... 

SI units of measurement, used by scientists around the world, derive their name from the French Systeme International d Unites. Fundamental units (base units) from which all others are derived are defined in Table 1-1. Standards of length, mass, and time are the meter (m). kilogram (kg), and second (s), respectively. Temperature is measured in kelvins (K), amount of substance in moles (mol), and electric current in amperes (A). 

Whereas the types of measurements in physics and engineering do not exceed the numbers of base and derived units of the SI, chemical measurements are virtually infinite, equal to the number of chemical ele-... 

For gases and liquids the liter is a much more practical measure of volume, especially in concentration expressions, than the derived unit of cubic meter, m3. Usage therefore has established the liter (L) as an accepted named unit, even though cubic decimeter (dm3) is the correct SI designation. The only prefix to be used with liter is milli, that is milliliter (ml). The symbol L is used for liter to prevent confusion with the letter I and the number 1. 

As a matter of interest, wafer uniformity is also plotted. The unit of measure is the slope, which derives from a manipulation of the standard 13 point measurement. A center point is measured, followed by three sets of four points, each set at a single radius. A regression consisting of the center point and the averages of the subsequent three rings of four points provides a measure of the concentric nonuniformity. Note that the wafer begins extremely edge fast, then falls to a somewhat center fast condition. 

Many quantities you can measure need units other than the seven basic SI units. These units are derived by multiplying or dividing the base units. For example, speed is distance divided by time. The derived unit of speed is meters per second (m/s). A rectangle s area is found by multiplying its length (in meters) by its width (also in meters), so its unit is square meters (m ). 

Laboratories around the world use the same standardized units of measurements, called the International System of Units, or SI. The SI system has seven base units from which all the others are derived. The base units of this system include a unit of length, meters, and a unit of mass, kilograms. Volume is derived unit and is measured in cubic meters. These units can be described in various sizes. Common divisions of these units are given in Table 1.3. Thus we can measure distance in meters, centimeters or millimeters we can measure weight in kilograms, or micrograms we can measure volume in cubic meters, cubic centimeters, and so on. 

The metric system is a system of measurement using units based on the decimal system. Today, in English, it is formally called the International System, abbreviated SI from the original French, Systtme International. The base units of the modern metric system used in general chemistry are given in the following table. From these, you can derive all other units of measure. 

For many years scientists recorded measurements in metric units, which are related decimally, that is, by powers of 10. In 1960, however, the General Conference of Weights and Measures, the international authority on units, proposed a revised metric system called the International System of Units (abbreviated SI, from the French 5ysteme /ntemationale d Unites). Table 1.2 shows the seven SI base units. All other units of measurement can be derived from these base units. Like metric units, SI units are modified in decimal fashion by a series of prefixes, as shown in Table 1.3. We will use both metric and SI units in this book. 

Pressure is one of the most readily measurable properties of a gas. In order to understand how we measure the pressure of a gas, it is helpful to know how the units of measurement are derived. We begin with velocity and acceleration. 

Let us consider a rotating or synodic reference frame centered at the barycenter of P and P2 assume that the units of measure are such that the relative angular velocity of P and P2 is unity. Then, the coordinates of Pi and P2 are, respectively, Pi( 2>0) and P2(—Mi,0). Let (qi,q2) be the coordinates of S in the synodic frame (see Figure 4). In order to derive the synodic Hamiltonian, we consider the generating function... 

The following table gives conversion factors from various units of measure to SI units. It is reproduced from NIST Special Publication 811, Guide for the Use of the International System of Units (SI). The table gives the factor by which a quantity expressed in a non-SI unit should be multiplied in order to calculate its value in the SI. The SI values are expressed in terms of the base, supplementary, and derived units of SI in order to provide a coherent presentation of the conversion factors and facilitate computations (see the table International System of Units in this section). If desired, powers of ten can be avoided by using SI prefixes and shifting the decimal point if necessary. 

UNITS OF MEASUREMENT (SECTION 1.4) Measurements in chemistry are made using the metric system. Special emphasis is placed on SI units, which are based on the meter, the kilogram, and the second as the basic units of length, mass, and time, respectively. SI units use prefixes to indicate fractions or multiples of base units. The SI temperature scale is the Kelvin scale, although the Celsius scale is frequently used as well. Absolute zero is the lowest temperature attainable. It has the value 0 K. A derived unit is obtained by multiplication or division of SI base units. Derived units are needed for defined quantities such as speed or volume. Density is an important defined quantity that equals mass divided by volume. 

Analytical chemistry uses many specialized terms that may be new to you. The definitions of the terms, usually shown in boldface, must be learned. The units used in this text are, for the most part, the units of the Systdme International d Unitds (SI system). The SI system is used around the world by scientists and engineers. The tables inside the textbook covers give the primary units of measurement in the SI system. A comprehensive list of SI units, Sl-derived units and definitions, as well as non-SI units may be found at the US National Institute of Standards and Technology (NIST) website at http //physics.nist.gov. 

All other units of measurement can be derived from these seven base units. SI units are modified in decimal fashion by a series of prefixes, as shown in Table ALL Table A1.2 lists the definitions of a number of common units derived from the SI system. 

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