Volume derived base unit

A derived unit is a combination of other units. For example, the SI unit for speed is meters per second (m/s), a derived unit. Notice that this unit is formed from two other SI units— meters and seconds— put together. You are probably more famihar with speed in miles/ hour or kilometers/hour—these are also examples of derived units. Two other common derived units are those for volume (SI base unit is m ) and density (SI base unit is kg/tii ). 

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. 

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. 

The above relationship between 0 and the rate constants is derived based on the conventional formulation of the rate equations. The unit to measure the amount of electrons and holes in the particle is density, the same as in bulk semiconductors. When the particle size is extremely small or the photon density is very low, only a few pairs of electron and hole are photogenerated and recombine with each other in the particle. This means that photon density does not take continuous values as suitably used in the conventional rate equations, but takes some series of values whose unit is the inverse of the particle volume. Taking into account this deviation, we proposed a new model in which particles are assigned by two integers, n and m, which represent the numbers of... 

Look back at the seven fundamental SI units given in Table 1.3 and you ll find that measures for such familiar quantities as area, volume, density, speed, and pressure are missing. All are examples of derived quantities rather than fundamental quantities because they can be expressed using one or more of the seven base units (Table 1.5). 

The prefix multipliers increase or decrease the size of the base unit, so that it more conveniently describes the system being measured. The base units that we will be using are listed in Table 1.1. For the purists, it is not strictly correct to include liters as a base unit, because volume is derived from length, and thus the official SI unit of volume is the cubic meter (m3), which is derived from the length base unit, the meter. Chemists frequently express mass in units of grams, which is derived from the kilogram. There are three other SI base units (the mole, the candela, and the ampere). We will consider moles (amount of material) and amperes (electric current) in subsequent chapters. The candela is a unit of light intensity or luminosity and does not concern us at this point. 

From the nine base units, over 58 further units have been derived and are known as derived units. There are two types of derived units those that have special names (see Table 2.3) and those that have no special names (see Table 2.4). An example of a derived unit with a special name is force, which has the unit newton (the symbol N) and is calculated by the formula N = kg "Vs2. An example of a derived unit that does not have a special name is volume, which has the unit of cubic meter (no special symbol) and is calculated by the formula volume = m3. ... 

This book focuses in on the original base units (length, mass, and temperature), plus one of the derived units (volume), because these measurements are the most commonly used measurements in the lab. Time is included in this section only because it provides an interesting commentary on the metrologists desire to split hairs in their endeavor to achieve accuracy. 

Table 3.2). All other units are derived from these base units such as area (m ), volume (m or 1,000 liters), speed ...

Steric descriptors and/or -> size descriptors representing the volume of a molecule. The volume of a molecule can be derived from experimental observation such as the volume of the unit cell in crystals or the molar volume of a solution or from theoretical calculations. In fact, analytical and numerical approaches have been proposed for the calculation of molecular volume where the measure depends directly on the definition of - molecular surface-, -> van der Waals volume and -> solvent-excluded volume are two volume descriptors based on van der Waals surface and solvent-accessible surface, respectively. 

Use the following terms to complete the concept map volume, derived unit, mass, density, base unit, time, length. 

In addition to base and derived SI units, several units that are not officially sanctioned are used in this book. The first is the liter (abbreviated L), a very convenient size for volume measurements in chemistry a liter is 10 m, or 1 cubic decimeter (dm ) ... 

Some properties, such as time or length, can be expressed in terms of SI base units. Other properties, such as volume or density, are expressed in SI derived units, which are really made by combining the SI base units. Following are some examples of physical properties and the Si-derived units, which can be used to measure them. 

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. 

Many properties cannot be described directly with one of the seven SI base units. For example, chemists often need to measure volume (the amount of space that something occupies), and volume is not on the list of SI base units (Table 1.1). Rather than create a new definition for volume, we derive its units from the base unit for length, the meter. Volume can be defined as length cubed, so cubic meters, m, can be used as a volume unit. Various other units are derived in similar ways. 

SI units consist of seven base units and numerous derived units. Exponential notation and prefixes based on powers of 10 are used to express very small and very large numbers. The SI base unit of length is the meter (m). Length units on the atomic scale are the nanometer (nm) and picometer (pm). Volume units are derived from length units the most important volume units are the cubic meter (m ) and the liter... 

I have deliberately violated this rule in using two different symbols for the volume concentration. The traditional symbol for the volume concentration in units of mol per litre is c. This is a non-SI unit in the sense that it is not derived directly from the base units, but involves a numerical factor as well. It is an SI unit in the sense that it involves legitimate SI units for amount of substance (mol) and volume (dm ). As a laboratory unit of concentration c is going to be with us for a long time. Rather than use this symbol for the SI unit of concentration derived simply from the base units, mol/m, I have introduced the symbol c for the SI base unit concentration. The use of c in the equations avoids both cumbersome numerical factors and confusion with the moles-per-litre concentration. Similarly, I have used A for number of molecules per cubic metre. 

Compare a base unit and a derived unit, and list the derived units used for density and volume. 

The international system of units (usually known as SI units, from the French Sys-ttme International) consists of several base units from which all other units (such as those of volume or energy) are derived. Some of the base units are shown in Table 1.1. 

In another approach, He et al. (He et al., 2013) proposed a 2-site per nucleotide (NARES-2P, nucleic acid united residue 2-point model) CG model where chain connectivity, excluded volume and base dipole interactions are sufficient to form helical DNA and RNA structures. This model was parametrized using a bottom-up strategy by employing a set of statistical potentials, derived from DNA and RNA structures from the Protein Data Bank, and the Boltzmann inversion method to reproduce the structural features. The base-base interactions were parametrized by fitting the potential of mean force to detailed all-atoms MD simulations using also the Boltzmann inversion approach. The respective potentials do not explicitly define the nucleic-acid structure, dynamics and thermod3mamics, but are derived as potentials of mean force. By detailed analysis of the different contribution to the Hamiltonian, the authors determined that the multipole-multipole interactions are the principal factor responsible for the formation of regular structures, such as the double helical structures. 

The SI base units are used to obtain derived units. To do so, we use the defining equation for the quantity, substituting the appropriate base units. For example, speed is defined as the ratio of distance traveled to elapsed time. Thus, the SI unit for speed—m/s, read meters per second —is a derived unit, the SI unit for distance (length), m, divided by the SI unit for time, s. Two common derived units in chemistry are those for volume and density. 

In the International System of Units, all physical quantities are represented by appropriate combinations of the base units listed in Table G.l. The result is a derived unit for each kind of measured quantity. The most common derived units are listed in Table G.3. It is easy to see that the derived unit for area is length X length = meter X meter = square meter (m ) or that the derived unit for volume is length X length X length = meter X meter X meter = cubic meter (m ). The more complex derivations are arrived at by the same kind of combination of units. Units such as... 

The slip flow near the boundary surface can be analyzed based on the type of fluids, i.e., gas and Newtonian and non-Newtonian liquids. The sUp flow in gases has been derived based on Maxwell s kinetic theory. In gases, the concept of mean free path is well defined. Slip flow is observed when characteristic flow length scale is of the order of the mean free path of the gas molecules. An estimate of the mean free path of ideal gas is /m 1/(Vlna p) where p is the gas density (here taken as the number of molecules per unit volume) and a is the molecular diameter. The mean free path / , depends strongly on pressure and temperature due to density variation. Knudsen number is defined as the ratio of the mean free path to the characteristic length scale... 

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. 

The low polarizability provided by the aUcychc Epiclon moieties leads to Pis with low refractive index. The ellipsometricaly measured values listed in Table 2 show that refractive indices of this type of Pis measured at 632.8 nm correspond to transparent materials, i.e. 1.6-1.7, and are in good agreement with theoretical estimations based on molar refraction and molar volume derived from group contributions theory [29,36]. This approach is based on the assumption that the molar volume, Vu, and the molar refraction, Ru, of the chain repeating unit are additive functions of composition ... 

The SI unit of speed is meters per second (that is, meters divided by seconds). The unit is symbohzed m/s or m s The unit of speed is an example of an SI derived unit, which is a unit derived by combining SI base units. Table 1.4 defines a number of derived units. Volume and density are discussed in this section pressure and energy are discussed later (in Sections 5.1 and 6.1, respectively). 

A quantitative science requires the making of measurements. Any measurement has limited precision, which you convey by writing the measured number to a certain number of significant figures. There are many different systems of measurement, but scientists generally use the metric system. The International System (SI) uses a particular selection of metric units. It employs seven base units combined with prefixes to obtain units of various size. Units for other quantities are derived from these. To obtain a derived unit in SI for a quantity such as the volume or density, you merely substitute base units into a defining equation for the quantity. 

Of the derived units, it may be noted that the unit for force is the newton (N), which, expressed in terms of SI base units, is mkgs the unit for density or mass density is kilogram per cubic metre (kgm ) the unit for concentration (of amount of substance) is mole per cubic metre (mol m ) the unit for specific volume is cubic metre per kilogram (m kg ). Some other derived units have special names for example, the name for the unit of energy, work, or quantity of heat is the joule (J), equal to the newton metre (N m). The imit of power is the watt (W), equal to J s. The unit for heat capacity and entropy is the joule per kelvin (JK ) the unit for molar energy is joule per mole (J mol" ) and for molar entropy and molar heat capacity is joule per kelvin mole (J mol" ). 

The SI system descrihes seven base units. This chapter describes three of these—mass, length, and temperature. We also refer to time, another base unit. Other quantities are made up of combined base units these are called derived units. Two of these, volume and density, appear in this chapter. 

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