# Physical quantity: Wikis

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

# Encyclopedia

Physical quantity is the numerical value of a measurable property that describes a physical system's state at a moment in time. For that reason, the changes in the physical quantities of a system describe its transformation (or evolution between its momentary states).

For example, the values of 'temperature', 'volume', 'pressure', 'molecular mass' and 'internal energy' are physical quantities describing the state of any confined gas; 'current intensity', 'number of turns' and 'magnetic permitivity' are physical quantities completely describing the 'magnetic field intensity' at the center of a very long, evenly wound coil.

The relationship between different physical quantities is described by quantity calculus.

## Examples

Since low density gases (at normal atmospheric pressure) expand their volume proportionally with their temperature, they can be used as thermometers. Such a gas may be placed in a capped glass bowl that extends into the air (through its cap) a capillary tube inside which a drop of mercury will confine the gas from escaping.

Now we can define the Celsius degree and the Celsius scale !

• Mark on the capillary the level of the mercury drop after the glass bowl has sat 'long enough' in ice-water.
• Mark the mercury drop level after the glass bowl has sat 'long enough' in boiling water. This mark will be above the previous.
• Divide the interval between the 2 markings on the capillary tube in 100 equally distanced intervals or divisions.

Now one 'Celsius degree' or 'degree Celsius' or '1°C' is the change in temperature of the bowl-confined gas that will make that mercury-drop rise by just one division ! We write [T]='1°C' as short for 'the international unit for temperature is the Celsius degree'. If the mercury drop rises by 30 divisions, the temperature has increased by 30 × 1°C !

By this example a physical quantity 'Q' is expressed as the product between a numerical value {Q} and a unit of measurement [Q].

Q = {Q} × [Q]

This becomes obvious when expressing a physical quantity (equivalently) in multiples or submultiples of its units — for example length is measured by the meter or [L]=1 m, and the kilometer (km) is a meter multiple, while the 'millimeter' (mm) is a submultiple, such that 1 m = 0.001 km = 1,000 mm.

• So if the diameter of a soccer ball is, say, 0.3 m = 0.3 × 1,000 mm = 300 mm which is the same quantity but expressed in different units.
• Similarly if the 'Eiffel Tower' is 324 m high then 324 m = 324 × 0.001 km = 0.324 km tall !

## Symbols for physical quantities

Usually, the symbols for physical quantities are chosen to be a single letter of the Latin or Greek alphabet written in italic type. Often, the symbols are modified by subscripts and superscripts, in order to specify what they pertain to — for instance Ek is usually used to denote kinetic energy and cp heat capacity at constant pressure. (Note the difference in the style of the subscripts: “k” is the abbreviation of the word “kinetic”, whereas “p” is the symbol of the physical quantity “pressure” rather than the abbreviation of the word “pressure”.)

Symbols for quantities should be chosen according to the international recommendations from ISO 31, the IUPAP red book and the IUPAC green book. For example, the recommended symbol for the physical quantity 'mass' is m, and the recommended symbol for the quantity 'charge' is Q.

Symbols for physical quantities that are vectors are bold italic type. If, e.g., u is the speed of a particle, then the straightforward notation for its velocity is u.

Note that concrete numbers, even those denoted by letters, are always roman (upright) type, e.g.: 1, 2, e (for the base of natural logarithm), i (for the imaginary unit) or π (for 3.14...). Symbols of concrete functions such as sin α must be roman type too. Although not followed by Wikipedia, operators like d in dx should also be roman type.

## 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). SI units are usually preferred today.

## Base quantities, derived quantities and dimensions

The notion of physical dimension of a physical quantity was introduced by Fourier in 1822.[1] By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension. The seven base quantities of the International System of Quantities (ISQ) and their corresponding SI units are listed in the following table. Other conventions may have a different number of fundamental units (e.g. the CGS and MKS systems of units).

International System of Units base quantities
Name Symbol for quantity Symbol for dimension SI base unit Symbol for unit
Length l, x, r, etc. L meter m
Time t T second s
Mass m M kilogram kg
Electric current I, i I ampere A
Thermodynamic temperature T θ kelvin K
Amount of substance n N mole mol
Luminous intensity Iv J candela cd

All other quantities are derived quantities since their dimensions are derived from those of base quantities by multiplication and division. 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.

## Extensive and intensive quantities

A quantity is called:

• extensive when its magnitude is additive for subsystems (volume, mass, etc.)
• intensive when the magnitude is independent of the extent of the system (temperature, pressure, etc.)

Some physical quantities are prefixed in order to further qualify their meaning:

• specific is added to refer to a quantity which is expressed per unit mass (such as specific heat capacity)
• molar is added to refer to a quantity which is expressed per unit 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.

## 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.[2]

## Notes

1. ^ 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.)
2. ^ Tarantola, Albert. Elements for physics - Quantities, qualities and intrinsic theories, Springer, 2006. ISBN 3-540-25302-5. [1]

## References

• Cook, Alan H. The observational foundations of physics, Cambridge, 1994. ISBN 0-521-45597-

# Simple English

A physical quantity is a quantity in physics that can be measured.Or a physical quantity is a physical property that can be quantified. Examples of physical quantities are mass, volume, length, time, temperature,electric current.