A physical quantity is a physical property that can be quantified. Quantity is a kind of property which exists as magnitude or multitude A physical property is any aspect of an object or substance that can be measured or perceived without changing its identity. This means it can be measured and/or calculated. The value of a physical quantity Q is expressed as the product of a numerical value {Q} and a physical unit [Q]. In Mathematics, a product is the Result of multiplying, or an expression that identifies factors to be multiplied A number is an Abstract object, tokens of which are Symbols used in Counting and measuring.

Q = {Q} x [Q]

(SI units are usually preferred today). The notion of physical dimension of a physical quantity was introduced by Fourier (1822).

Example

If a certain value of power is written as

P = 42. In Physics, power (symbol P) is the rate at which work is performed or energy is transmitted or the amount of energy required or expended for 3 x 103 W = 42. 3 kW,

then

P represents the physical quantity of power
42. 3 x 103 is the numerical value {P}
k is the SI prefix kilo, representing 103
W is the symbol for the unit of power [P], the watt

Symbols for physical quantities

Symbols for quantities should be chosen according to the international recommendations from ISO 31, the IUPAP red book and the IUPAC green book. International Standard ISO 31 ( Quantities and units International Organization for Standardization, 1992 is the most widely respected style guide for the The International Union of Pure and Applied Physics ( IUPAP) is an international Non-governmental organization devoted to the advancement of Physics. Quantities Units and Symbols in Physical Chemistry Third Edition (ISBN 978-0-85404-433-7 also known as the Green Book, Prepared for publication by E For example, the recommended symbol for a physical quantity of mass is m, and the recommended symbol for a quantity of charge is Q.

Units of physical quantities

Most physical quantities Q include a unit [Q] (where [Q] means "unit of Q"). Neither the name of a physical quantity, nor the symbol used to denote it, implies a particular choice of unit. For example, a quantity of mass might be represented by the symbol m, and could be expressed in the units kilograms (kg), pounds (lb), or daltons (Da).

Base quantities, derived quantities and dimensions

By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension. In the SI system of units, there are seven base units, but other conventions may have a different number of fundamental units. A set of fundamental units is a set of units for physical quantities from which every other unit can be generated The base quantities according to the International System of Quantities (ISQ) and their dimensions are listed in the following table:

ISQ base quantities
NameSymbol for quantitySymbol for dimensionSI base unit
LengthlLmeter
TimetTsecond
MassmMkilogram
Electrical currentIIampere
Thermodynamic temperatureTθkelvin
Amount of substancenNmole
Luminous intensityIvJcandela

All other quantities are derived quantities since their dimensions are derived from those of base quantities by multiplication and division. Length is the long Dimension of any object The length of a thing is the distance between its ends its linear extent as measured from end to end The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic Matter is commonly defined as being anything that has mass and that takes up space. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a Light source in a particular direction per unit Solid The candela (kanˈdɛlə /-ˈdiːlə/ symbol cd) is the SI base unit of Luminous intensity; that is power emitted by a light source in a particular For example, the physical quantity velocity is derived from base quantities length and time and has dimension L/T. Some derived physical quantities have dimension 1 and are said to be dimensionless quantities. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units

Further information: dimensional analysis

Extensive and intensive quantities

A quantity is called:

• extensive when its magnitude is additive for subsystems (volume, mass, etc. Dimensional analysis is a conceptual tool often applied in Physics, Chemistry, Engineering, Mathematics and Statistics to understand In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the )
• intensive when the magnitude is independent of the extent of the system (temperature, pressure, etc. In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the )

Some extensive physical quantities may be prefixed in order to further qualify their meaning:

• specific is added to refer to the quantity divided by its mass (such as specific volume)
• molar is added to refer to the quantity divided by the amount of substance (such as molar volume)

There are also physical quantities that can be classified as neither extensive nor intensive, for example angular momentum, area, force, length, and time. Specific volume (v is the volume occupied by a unit of mass of a material The molar volume, symbol V m is the Volume occupied by one mole of a substance ( Chemical element or Chemical compound) In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position Area is a Quantity expressing the two- Dimensional size of a defined part of a Surface, typically a region bounded by a closed Curve. In Physics, a force is whatever can cause an object with Mass to Accelerate. Length is the long Dimension of any object The length of a thing is the distance between its ends its linear extent as measured from end to end For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of

Physical quantities as coordinates over spaces of physical qualities

The meaning of the term physical quantity is generally well understood (everyone understands what is meant by the frequency of a periodic phenomenon, or the resistance of an electric wire). It is clear that behind a set of quantities like temperature − inverse temperature − logarithmic temperature, there is a qualitative notion: the cold−hot quality. Over this one-dimensional quality space, we may choose different coordinates: the temperature, the inverse temperature, etc. Other quality spaces are multidimensional. For instance, to represent the properties of an ideal elastic medium we need 21 coefficients, that can be the 21 components of the elastic stiffness tensor cijkl , or the 21 components of the elastic compliance tensor (inverse of the stiffness tensor), or the proper elements (six eigenvalues and 15 angles) of any of the two tensors, etc. Again, we are selecting coordinates over a 21-dimensional quality space. On this space, each point represents a particular elastic medium.

It is always possible to define the distance between two points of any quality space, and this distance is —inside a given theoretical context— uniquely defined. For instance, two periodic phenomena can be characterized by their periods, T1 and T2, or by their frequencies, ν1 and ν2 . The only definition of distance that respects some clearly defined invariances is D = | log(T2 / T1) | = | log2 / ν1) | .

These notions have implications in physics. As soon as we accept that behind the usual physical quantities there are quality spaces, that usual quantities are only special coordinates over these quality spaces, and that there is a metric in each space, the following question arises: Can we do physics intrinsically, i. e. , can we develop physics using directly the notion of physical quality, and of metric, and without using particular coordinates (i. e. , without any particular choice of physical quantities)? In fact, physics can (and must?) be developed independently of any particular choice of coordinates over the quality spaces, i. e. , independently of any particular choice of physical quantities to represent the measurable physical qualities. This point of view has recently been developed (Tarantola, 2006 [1] ).

Books

• Cook, Alan H. The observational foundations of physics, Cambridge, 1994. ISBN 0-521-45597-9.
• Fourier, Joseph. Théorie analytique de la chaleur, Firmin Didot, Paris, 1822. (In this book, Fourier introduces the concept of physical dimensions for the physical quantities. )
• Tarantola, Albert. Elements for physics - Quantities, qualities and intrinsic theories, Springer, 2006. ISBN 3-540-25302-5. [2]