1 PHYSICAL QUANTITIES AND UNITS: Difference between revisions
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==1.1 PHYSICAL QUANTITIES AND QUANTITY CALCULUS== | |||
The value of a physical quantity Q can be expressed as the product of a numerical value {Q} and a unit [Q] | The value of a physical quantity Q can be expressed as the product of a numerical value {Q} and a unit [Q] | ||
$Q = \{Q\}[Q] \quad (1)$ | |||
Neither the name of the physical quantity, nor the symbol used to denote it, implies a particular choice of unit. | Neither the name of the physical quantity, nor the symbol used to denote it, implies a particular choice of unit. | ||
Physical quantities, numerical values, and units may all be manipulated by the ordinary rules of algebra. Thus we may write, for example, for the wavelength of one of the yellow sodium lines | Physical quantities, numerical values, and units may all be manipulated by the ordinary rules of algebra. Thus we may write, for example, for the wavelength of one of the yellow sodium lines | ||
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where m is the symbol for the unit of length called the metre (see Section 2.2, p. 11), nm is the symbol for the nanometre, and the units metre and nanometre are related by | where m is the symbol for the unit of length called the metre (see Section 2.2, p. 11), nm is the symbol for the nanometre, and the units metre and nanometre are related by | ||
$1\ \rm{nm} = 10^{−9}\ \rm{m}\ \rm{or}\ \rm{nm} = 10^{−9}\ \rm{m} \quad (3)$ | $1\ \rm{nm} = 10^{−9}\ \rm{m}\ \rm{or}\ \rm{nm} = 10^{−9}\ \rm{m} \quad (3)$ | ||
The equivalence of the two expressions for | The equivalence of the two expressions for $\lambda$ in Equation (2) follows at once when we treat the units by the rules of algebra and recognize the identity of 1 nm and $10^{−9}\ \rm{m}$ in Equation (3). The wavelength may equally well be expressed in the form | ||
$\lambda/\rm{m} = 5.896\ \times 10^{−7}\ \rm{or}\ \lambda/\rm{nm} = 589.6 \quad (4)$ | $\lambda/\rm{m} = 5.896\ \times 10^{−7}\ \rm{or}\ \lambda/\rm{nm} = 589.6 \quad (4)$ | ||
It can be useful to work with variables that are defined by dividing the quantity by a particular unit. For instance, in tabulating the numerical values of physical quantities or labeling 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 numerical values, as in Equations (4). | It can be useful to work with variables that are defined by dividing the quantity by a particular unit. For instance, in tabulating the numerical values of physical quantities or labeling 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 numerical values, as in Equations (4). | ||
Algebraically equivalent forms may be used in place of $10^3\ \rm{K/T}$ , such as $\rm{kK}/T$ or $10^3\ (T/\rm{K})^{−1}$. Equations between numerical values depend on the choice of units, whereas equations between quantities have the advantage of being independent of this choice. The method described here for handling physical quantities and their units is known as quantity calculus (see ISO [5.a] and [11–14]). It is recommended for use throughout science and technology. The use of quantity calculus does not imply any particular choice of units (see Section 3.1, p. 15 for quantity calculus). | |||
==1.2 BASE QUANTITIES AND DERIVED QUANTITIES== | |||
Revision as of 09:49, 15 May 2024
1.1 PHYSICAL QUANTITIES AND QUANTITY CALCULUS
The value of a physical quantity Q can be expressed as the product of a numerical value {Q} and a unit [Q] $Q = \{Q\}[Q] \quad (1)$ Neither the name of the physical quantity, nor the symbol used to denote it, implies a particular choice of unit. Physical quantities, numerical values, and units may all be manipulated by the ordinary rules of algebra. Thus we may write, for example, for the wavelength of one of the yellow sodium lines $\lambda = 5.896\ \times 10^{−7}\ \rm{m} = 589.6\ \rm{nm} \quad (2)$ where m is the symbol for the unit of length called the metre (see Section 2.2, p. 11), nm is the symbol for the nanometre, and the units metre and nanometre are related by $1\ \rm{nm} = 10^{−9}\ \rm{m}\ \rm{or}\ \rm{nm} = 10^{−9}\ \rm{m} \quad (3)$ The equivalence of the two expressions for $\lambda$ in Equation (2) follows at once when we treat the units by the rules of algebra and recognize the identity of 1 nm and $10^{−9}\ \rm{m}$ in Equation (3). The wavelength may equally well be expressed in the form $\lambda/\rm{m} = 5.896\ \times 10^{−7}\ \rm{or}\ \lambda/\rm{nm} = 589.6 \quad (4)$ It can be useful to work with variables that are defined by dividing the quantity by a particular unit. For instance, in tabulating the numerical values of physical quantities or labeling 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 numerical values, as in Equations (4).
Algebraically equivalent forms may be used in place of $10^3\ \rm{K/T}$ , such as $\rm{kK}/T$ or $10^3\ (T/\rm{K})^{−1}$. Equations between numerical values depend on the choice of units, whereas equations between quantities have the advantage of being independent of this choice. The method described here for handling physical quantities and their units is known as quantity calculus (see ISO [5.a] and [11–14]). It is recommended for use throughout science and technology. The use of quantity calculus does not imply any particular choice of units (see Section 3.1, p. 15 for quantity calculus).