Units of physical quantities

In Chapter 1, the rales of nomenclature are reviewed— units of physical quantities, abbreviations, conversion between SI and British Units— and the various national and international standards bureaus are mentioned. Chapter 2 introduces significant figures and concepts of accuracy, precision and error analysis. Experimental planning is discussed in some detail in Chapter 3. This subject is enormous and we try to distil the essential elements to be able to use the techniques. Chapters 4 and 5 cover many aspects of measuring pressure and temperature. The industrial context is often cited to provide the student with a picture of the importance of these measurements and some of the issues with making adequate measurements. Flow measurement instrumentation is the subject of Chapter 6. A detailed list of the pros and cons of most commercial... 

The principles of action in classical and quantum mechanics perspective - short history. Basic concepts of force, motion, mass and units of physical quantities used in laws of motion. Quick survey of laws of motion. The Lagiangian function and its main role in the principle of least action. The motion by Euler-Lagrange equation. Newton equation and the second principle of classical mechanics. Correspondence with quantum mechanics. 

Chemical species and units of physical quantities are denoted by Roman type characters, whereas physical quantities that can be expressed by numerical values are denoted by Greek or italic characters. Mathematical symbols have their usual meaning and are not listed here. The same symbol is used for an extensive property of a system and for the molar quantity of a constituent of the system. The SI system of physical units is used throughout, but some extra SI units commonly used in the physicochemical literature are also included where they simplify the notation. These include the symbols °C for centigrade temperatures (T/K-273.15), M for mol-dm , and m for mol (kg solvent)". ... 

Appendix Units of physical quantities, multiples and submultiples of units... 

Table I.l. Units of physical quantities relevant to the physics of solids.

The second is one of seven base units in the International System of Units (SI). The base units are used to derive other units of physical quantities. Use of the SI means that physical quantitie s such as the second and hertz are defined and measured in the same way throughout the world. 

Table 1 shows some symbols and abbreviations commonly used in analytical chemistry Table 2 shows some of the alternative methods for expressing the values of physical quantities and the relationship to the value in SI units. 

A related concept to dimensional analysis is quantity calculus, a method we find particularly useful when it comes to setting out table header rows and graph axes. Quantity calculus is the handling of physical quantities and their units using the normal rules of algebra. A physical quantity is defined by a numerical value and a unit ... 

The authoritative values for physical constants and conversion factors used in thermodynamic calculations are assembled in Table 2.3. Furthermore, information about the proper use of physical quantities, units, and symbols can be found in several additional sources [5]. 

A substantial number of definitions in the terminology section are either of physical quantities or are expressed mathematically. In such cases, there are recommended symbols for the quantities and, when appropriate, corresponding SI units. Other terms have eommon abbreviations. The following format is used to indicate these essential eharaeteristics name of term (abbreviation), symbol, SI unit unit. Typical examples are tensile stress, interpenetrating polymer network (IPN). If there are any, alternative names or synonyms follow on the next line, and the definition on the sueeeeding lines. 

IAMAP, Terminology and Units of Radiation Quantities and Measurements, Radiation Commission of the International Association of Meteorology and Atmospheric Physics, Boulder, CO, 1978. 

Reduction of the number of parameters required to define the problem. The n theorem states that a physical problem can always be described in dimensionless terms. This has the advantage that the number of dimensionless groups, which fully describe it, is much smaller than the number of dimensional physical quantities. It is generally equal to the number of physical quantities minus the number of basic units contained in them. 

A group of physical quantities with each quantity raised to a power such that all the units associated with the physical quantities cancel, i.e. dimensionless. 

It is a common, but illogical, practice to refer to this unit as a wave number correctly used, the term wave number refers to the physical quantity 1/Avac, and not to the unit of this quantity. 

The importance of using common reference scales has been recognised for centuries. For example, in England, King John introduced consistent measures throughout the land in 1215. Other countries also had their own measurements scales standards. Many city museums show the standard measures used for trade within the city or local state. As trade widened so did the need for comparability of measurement results and the use of common units widened. The many different measurements scales were harmonised with the introduction of the metric system and the SI units under the Convention of the Metre signed in 1875. An excellent summary of the historical development of units of measurement is given in the NBS Special Publication 420 [1], Under the Convention of the Metre a hierarchical chain of national and international measurement standards has been developed for the measurement of most of physical quantities. 

A well-organised system of units forms an essential part of the whole system of physical quantities and the equations by which they are interrelated. Many different unit systems have been in use, which has given rise to much confusion and trouble. Here we confine ourselves to two of these units systems. 

SI units are recommended for use throughout science and technology. However, some non-SI units are in use, and in a few cases they are likely to remain so for many years. Moreover, the published literature of science makes widespread use of non-SI units. It is thus often necessary to convert the values of physical quantities between SI and other units. This chapter is concerned with facilitating this process. 

Section 7.1 gives examples illustrating the use of quantity calculus for converting the values of physical quantities between different units. The table in section 7.2 lists a variety of non-SI units used in chemistry, with the conversion factors to the corresponding SI units. Conversion factors for energy and energy-related units (wavenumber, frequency, temperature and molar energy), and for pressure units, are also presented in tables inside the back cover. 

Quantity calculus is a system of algebra in which symbols are consistently used to represent physical quantities rather, than their measures, i.e. numerical values in certain units. Thus we always take the values of physical quantities to be the product of a numerical value and a unit (see section 1.1), and we manipulate the symbols for physical quantities, numerical values, and units by the ordinary rules of algebra.1 This system is recommended for general use in science. Quantity calculus has particular advantages in facilitating the problems of converting between different units and different systems of units, as illustrated by the examples below. In all of these examples the numerical values are approximate. 

However, in this form the symbols do not represent physical quantities, but the numerical values of physical quantities in certain units. Specifically, the last equation is true only if A is the molar conductivity in S mol"1 cm2, k is the conductivity in Scm"1, and c is the concentration in mol dm"3. This form does not follow the rules of quantity calculus, and should be avoided. The equation A = k/c, in which the symbols represent physical quantities, is true in any units. If it is desired to write the relationship between numerical values it should be written in the form... 

The importance of atomic units lies in the fact that ab initio calculations in theoretical chemistry necessarily give results in atomic units (i.e. as multiples of me, e, ft, Eh and a0). They are sometimes described as the natural units of electronic calculations in theoretical chemistry. Indeed the results of such calculations can only be converted to other units (such as the SI) by using the current best estimates of the physical constants me, e, ft, etc., themselves expressed in SI units. It is thus appropriate for theoretical chemists to express their results in atomic units, and for the reader to convert to other units as and when necessary. This is also the reason why atomic units are written in italic (sloping) type rather than in the roman (upright) type usually used for units the atomic units are physical quantities chosen from the fundamental physical constants of electronic structure calculations. There is, however, no authority from CGPM for designating these quantities as units , despite the fact that they are treated as units and called atomic units by workers in the field. 

The objective of this manual is to improve the international exchange of scientific information. The recommendations made to achieve this end come under three general headings. The first is the use of quantity calculus for handling physical quantities, and the general rules for the symbolism of quantities and units, described in chapter 1. The second is the use of internationally agreed symbols for the most frequently used quantities, described in chapter 2. The third is the use of SI units wherever possible for the expression of the values of physical quantities the SI units are described in chapter 3. 

In tabulating the numerical values of physical quantities, or labelling the axes of graphs, it is particularly convenient to use the quotient of a physical quantity and a unit in such a form that the values to be tabulated are pure numbers, as in equations (3) and (4). 

Units are one of the most important, yet freqnently forgotten, elements of physical quantities. Typically in physical chemistry we are concerned with measurement we might talk about a mass of 5.72 g, a concentration of 0.15 mol dm, or a wavelength of 560 nm. These quantities are very different from a mass of 5.72 kg, a concentration of 0.15 mmol dm, or a wavelength of 560 pm, even though the same number is involved. 

When describing a measurement, you normally state both a number and a unit (e.g. the length is 1.85 metres ). The number expresses the ratio of the measured quantity to a fixed standard, while the unit identifies that standard measure or dimension. Clearly, a single unified system of units is essential for efficient communication of such data within the scientific community. The Systeme International d Unites (SI) is the internationally ratified form of the metre-kilogram-second system of measurement and represents the accepted scientific convention for measurements of physical quantities. 

A coherent system of units is such that equations between numerical values of physical quantities can be written exactly as the corresponding equations between the physical quantities themselves. This coherent system therefore avoids numerical factors between units and is especially useful for so-called dimensional checking. The SI is such a coherent system of units. The coherence is lost, however, when prefixes are used. 

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