Measurements of Length, Volume, and Mass

AiM To understand the metric system for measuring iength, voiume, and mass. 

The fundamental SI unit of length is the meter, which is a little longer than a yard (1 meter = 39.37 inches). In the metric system fractions of a 

The meter was originally defined, in the eighteenth century, as one ten-millionth of the distance from the equator to the North Pole and then, in the late nineteenth century, as the distance between two parallel marks on a special metal bar stored in a vault in Paris. More recently, for accuracy and convenience, a definition expressed in terms of light waves has been adopted. 

Other English-metric equivalences are given in Section 2.6. 

Volume is the amount of three-dimensional space occupied by a substance. The fundamental unit of volume in the SI system is based on the volume of a cube that measures 1 meter in each of the three directions. That is, each edge of the cube is 1 meter in length. The volume of this cube is 

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The metric system, or Systeme International d Unites (SI system as it is commonly known), is the predominant system of measurement in the world. In fact, the United States is one of only about three countries that do not commonly use the metric system. The metric system attempts to eliminate odd and often difircult-to-remember conversions for measurements (5,280 feet in a mile, for example). It is a decimal-based system with standard terminology for measurements of length, volume, and mass (weight). It also uses standard prefixes to measure multiples of the standard units. 

Measurements of Length, Volume, and Mass Uncertainty in Measurement Significant Figures Problem Solving and Dimensional Analysis Temperature Conversions ... 

The measures of length, volume, mass, energy, and temperature are used to evaluate our physical and chemical environment. Table 2.2 compares the metric system with the more recently accepted SI system (International System of Units). The laboratory equipment associated with obtaining these measures is also listed. 

Write the names and abbreviations for the metric or SI units used in measurements of length, volume, mass, temperature, and time. 

Scientists measure many different quantities—length, volume, mass (weight), electric current, temperature, pressure, force, magnetic field intensity, radioactivity, and many others. The metric system and its recent extension, Systeme International d Unites (SI), were devised to make measurements and calculations as simple as possible. In this chapter, length, area, volume, and mass will be introduced. Temperature will be introduced in Sec. 2.7 and used extensively in Chap. 11. The quantities to be discussed here are presented in Table 2-1. Their units, abbreviations of the quantities and units, and the legal standards for the quantities are also included. 

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 basic measurement of length or volume is called ddatometry if it is carried out at constant pressure or stress. Details are given in Sect. 4.1. When measuring stress as well as strain, the technique is called thermomechanical analysis, TMA. This technique is described in Sect. 4.5. Measurements can be made at constant or variable stress or strain, including periodic changes as in dynamic mechanical analysis, DMA, also discussed in Sect. 4.5. Finally, the thermal analysis technique to measure mass as a function of temperature and time is thermogravimetry, TGA. The technique is treated in Sect. 4.6. 

The two base quantities that are most important for quantitative chemical analysis are amount of substance (measured in moles, mol) and mass (measured in kilograms, kg), although length (measured in meters, m) is also important via its derived quantity volume in view of the convenience introduced by our common use of volume concentrations for liquid solutions. 

The measured value of an intensive property does not depend on how much matter is being considered. Density, defined as the mass of an object divided by its volume, is an intensive property. So is temperature. Suppose that we have two beakers of water at the same temperature. If we combine them to make a single quantity of water in a larger beaker, the temperature of the larger quantity of water will be the same as it was in the two separate beakers. Unlike mass, length, volume, and energy, temperature and other intensive properties are nonadditive. 

Most calculations in chemistry require that all measurements of the same quantity (mass, length, volume, temperature, and so on) be expressed in the same unit. To change the units of a quantity, you can multiply the quantity by a conversion factor. With SI units, such conversions are easy because units of the same quantity are related by multiples of 10,100,1000, or 1 million. Suppose you want to convert a given amount in milliliters to liters. You can use the relationship 1 L = 1000 mL. From this relationship, you can derive the following conversion factors. 

The mode of distribution is simply the value of the most frequent size present. A distribution exhibiting a single maximum is referred to as a unimodal distribution. When two or more maxima are present, the distribution is caUed bimodal, trimodal, and so on. The mode representing a particle population may have different values depending on whether the measurement is carried out on the basis of particle length, surface area, mass, or volume, or whether the data are represented ia terms of the diameter or log (diameter). 

The definition of N as the total length of mobile disloeation per unit volume takes us from the mieroseale (atoms in a erystal lattiee) to the meso-seale (a sealar quantity N. Equation (7.1) then takes us from the mesoseale to the maeroseale in whieh we aetually make measurement of the rate at whieh materials aeeumulate plastie strain. The quantity may also have its own evolutionary law involving yet another mesoseale variable. When the number of evolutionary equations (ealled the material eonstitutive deserip-tion) equals the number of variables, we ean perform a ealeulation of expeeted material response by eombination of the evolutionary law with equations of mass, momentum, and energy eonservation. 

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