Unit, derived

Each predefined unit is related to its adjacency matrix representation. Finally, the derived units are assembled thus, the structural information is derived from the compound name. 

These units are formed by combining base units, supplementary units, and other derived units (2—4). Those derived units having special names and symbols are marked with an asterisk in the Hst below. 

Most by-product acetylene from ethylene production is hydrogenated to ethylene in the course of separation and purification of ethylene. In this process, however, acetylene can be recovered economically by solvent absorption instead of hydrogenation. Commercial recovery processes based on acetone, dimetbylform amide, or /V-metby1pyrro1idinone have a long history of successfiil operation. The difficulty in using this relatively low cost acetylene is that each 450, 000 t/yr world-scale ethylene plant only produces from 7000 9000 t/yr of acetylene. This is a small volume for an economically scaled derivatives unit. 

In 1995 the 20th CGPM approved eliminating the class of supplementary units as a separate class in SI. Thus the new SI consists of only two classes of units base units and derived units, with the radian and steradian subsumed into the class of derived units of the SI. 

Each physical quantity is expressed in one and only one unit, eg, the meter for length, the kilogram for mass, and the second for time. Derived units are defined by simple equations relating two or more base units. Some are given special names, such as newton for force and joule for work and energy. 

The system is coherent. There is no dupHcation of units for a quantity, and all derived units are obtained by a direct one-to-one relation of base units or derived units eg, one newton is the force required to accelerate one kilogram at the rate of one meter per second squared one joule is the energy... 

SI rests on seven base units and a number of derived units, some of which have special names. A Hst of these units is given in the introduction to this volume. 

Table 1. SI Derived Units with Special Names...

Table 1-2 7 Derived Units of SI that Have Special Names. 1-3...

Two systems of units are in common usage in mechanics. The first, the SI system, is an absolute system based on the fundamental quantities of space, time, and mass. All other quantities, including force, are derived. In the SI system the basic unit of mass is the kilogram (kg), the basic unit of length (space) is the meter (m), and the basic unit of time is tbe second (s). The derived unit of force is the Newton (N), which is defined as the force required to accelerate a mass of 1 kg at a rate of 1 m/s-. 

Table 1 lists the SI base and derived units for quantities commonly referred to in general chemistry. Perhaps the least familiar of these units to the beginning chemistry student are the ones used to represent force, pressure, and energy. 

This method of fixing the derived unit by making the arbitrary constant equal to unity was largely extended by Gauss and Weber. 

If, however, some other physical law were to be introduced so that, for instance, the attractive force between two bodies would be proportional to the product of their masses, then this relation between F and M would no longer hold. It should be noted that mass has essentially two connotations. First, it is a measure of the amount of material and appears in this role when the density of a fluid or solid is considered. Second, it is a measure of the inertia of the material when used, for example, in equations 1.1-1.3. Although mass is taken normally taken as the third fundamental quantity, as already mentioned, in some engineering systems force is used in place of mass which then becomes a derived unit. 

Units may be combined together into derived units to express a property more complicated than mass, length, or time. For example, volume, V, the amount of space occupied by a substance, is the product of three lengths therefore, the derived unit of volume is (meter)3, denoted m3. Similarly, density, the mass of a sample divided by its volume, is expressed in terms of the base unit for mass divided by the derived unit for volume—namely, kilogram/(meter)3, denoted kg/m3 or, equivalently, kg-m-3. The SI convention is that a power, such as the 3 in cm3, refers to the unit and its multiple. That is, cm3 should be interpreted as (cm)3 or 10-6 m3 not as c(m3), or 10 2 m3. Many of the more common derived units have names and abbreviations of their own. 

A note on good practice Notice that to manipulate the units we have expressed derived units (J in this case) in terms of base units. Notice too that we are using the more precise values of the fundamental constants given inside the hack cover (rather than the less precise values quoted in the text) to ensure reliable results. 

Derived units are combinations of the base units (Sec- with a lowercase letter but their abbreviations are upper-tion A). Table 4 lists some derived units. Note that the case, names of units derived from the names of people all begin... 

When we consider the mechanical properties of polymeric materials, and in particular when we design methods of testing them, the parameters most generally considered are stress, strain, and Young s modulus. Stress is defined as the force applied per unit cross sectional area, and has the basic dimensions of N m in SI units. These units are alternatively combined into the derived unit of Pascals (abbreviated Pa). In practice they are extremely small, so that real materials need to be tested with a very large number of Pa... 

A unit equality may link SI units and non-SI units (1 quart = 0.946353 L), decimally related units (10 c = 1 m ), or base units and derived units (1 L = 10 m ). Some of the more common unit equalities are given on the inside back cover of this text. Examples and treat unit conversions. 

The Systeme International d Unites (International System of Units) has the abbreviation SI. It includes base units, supplementary and derived units which together form a coherent system of units. Prefixes are used to form decimal multiples and sub-multiples of the SI units. 

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