Informally, a physical quantity Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity. Being a fundamental term, quantity is used to refer to any type of quantitative properties or attributes of things is a physical property A physical property is any aspect of an object or substance that can be measured or perceived without changing its identity. Physical properties can be intensive or extensive. An intensive property does not depend on the size or amount of matter in the object, while an extensive property does. In addition to extensiveness, properties can also be that can be quantified A quantitative attribute is one that exists in a range of magnitudes, and can therefore be measured. Measurements of any particular quantitative property are expressed as a specific quantity, referred to as a unit, multiplied by a number. Examples of physical quantities are distance, mass, and time. Many attributes in the social sciences,. This means it can be measured and/or calculated and expressed in numbers. For example, "weight In the physical sciences, the weight of an object is the magnitude, W, of the force that must be applied to an object in order to support it in a gravitational field. The weight of an object equals the magnitude of the gravitational force acting on the object, less the effect of its buoyancy in any fluid in which it might be immersed. Near the" is a physical quantity that can be expressed by stating a number of some basic measurement unit such as pounds The pound-force or simply pound is a unit of force or newton The newton is the SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics, while "beauty Beauty is a characteristic of a person, animal, place, object, or idea that provides a perceptual experience of pleasure, meaning, or satisfaction. Beauty is studied as part of aesthetics, sociology, social psychology, and culture. As a cultural creation, beauty has been extremely commercialized. An "ideal beauty" is an entity which is" is a property that is difficult to describe with a number.
Formally, the International Vocabulary of Metrology (VIM) [1] defines quantity as 'an attribute of a phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively'.
The value of a physical quantity Q is expressed as the product In the a mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. The order in real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication. When matrices or members of various other associative algebras are multiplied the product of a numerical value A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels , {Q} and a physical unit The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Disparate systems of measurement used to be very common. Now there is a global standard, the International System of units, the modern form of the metric system. The SI has been or is in the process of [Q].
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- Q = {Q} x [Q]
The relationship between different physical quantities are described by quantity calculus Quantity calculus is the formal method for describing the mathematical relations between abstract physical quantities. Despite the name, it is more analogous to a system of algebra than calculus in the mathemtaical sense of the term. However, units refer to actual quantities, such as the cm, and are not algebraic symbols. SI The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science units The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Disparate systems of measurement used to be very common. Now there is a global standard, the International System of units, the modern form of the metric system. The SI has been or is in the process of are usually preferred today. The notion of physical dimension In mathematics and science, dimensional analysis is a tool to understand the properties of physical quantities independent of the units used to measure them. Every physical quantity is some combination of mass, length, time, electric charge, and temperature, . For example, velocity, which may be measured in meters per second (m/s), miles per hour ( of a physical quantity was introduced by Fourier (1822).
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Examples
If a person weighs 120 pounds The pound-force or simply pound is a unit of force, then "120" is the numerical value and "pound" is the unit. This physical quantity would be written as "120 lbs."
If the temperature outside is 30 degrees Celsius Celsius is a temperature scale that is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale two years before his death. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale as well as serve as a unit increment to indicate a temperature interval (a difference between, then "30" is the numerical value and "degree Celsius" is the unit. This quantity would be written as "30 °C".
In equation form, a measurement of power In physics, power is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time. As a rate of change of work done or the energy of a subsystem, power is, employing SI The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science units and scientific notation Scientific notation, also known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is often favored by scientists, mathematicians and engineers, who work with such for the number, might be written as
- P = 42.3 x 103 W,
Here, P represents the physical quantity 'power', 42.3 x 103 is the numerical value {P}, and W is the symbol for the unit SI derived units are part of the SI system of measurement units and are derived from the seven SI base units of power [P], the watt The watt is a derived unit of power in the International System of Units (SI). It measures rate of energy conversion. One watt is equivalent to 1 joule (J) of energy per second
Symbols for physical quantities
Usually, the symbols A symbol is something such as an object, picture, written word, sound, or particular mark that represents something else by association, resemblance, or convention. For example, a red octagon may stand for "STOP". On maps, crossed sabres may indicate a battlefield. Numerals are symbols for numbers for physical quantities are chosen to be a single letter of the Latin The Latin alphabet, also called the Roman alphabet, is the most widely used alphabetic writing system in the world today. It evolved from the western variety of the Greek alphabet called the Cumaean alphabet, and was initially developed by the ancient Romans to write the Latin language or Greek alphabet The Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th or early 8th century BCE. It is the first and oldest alphabet in the narrow sense that it notes each vowel and consonant with a separate symbol. It is as such in continuous use to this day. The letters were also used to represent written in italic type. Often, the symbols are modified by subscripts A subscript or superscript is a number, figure, symbol, or indicator that appears smaller than the normal line of type and is set slightly below or above it – subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are perhaps best known for their use in formulas, mathematical expressions, and and superscripts A subscript or superscript is a number, figure, symbol, or indicator that appears smaller than the normal line of type and is set slightly below or above it – subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are perhaps best known for their use in formulas, mathematical expressions, and, in order to specify what they pertain to — for instance Ep is usually used to denote potential energy Potential energy can be thought of as energy stored within a physical system. It is called potential energy because it has the potential to be converted into other forms of energy, such as kinetic energy, and to do work in the process. The standard unit of measure for potential energy is the joule, the same as for work or energy in general and cp heat capacity Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the temperature of a unit quantity of a substance by a certain temperature interval. The term originated primarily through the work of 18th-century physicist Joseph Black who conducted various heat measurements and used the phrase & at constant pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
Symbols for quantities should be chosen according to the international recommendations from ISO 31 International Standard ISO 31 is the most widely respected style guide for the use of physical quantities and units of measurement, and formulas involving them, in scientific and educational documents worldwide[citation needed]. In most countries, the notations used in mathematics and science textbooks at schools and universities follow closely, the IUPAP red book The International Union of Pure and Applied Physics is an international non-governmental organization devoted to the advancement of physics. It was established in 1922 and the first General Assembly was held in 1923 in Paris 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.
Units of physical quantities
Most physical quantities Q include a unit The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Disparate systems of measurement used to be very common. Now there is a global standard, the International System of units, the modern form of the metric system. The SI has been or is in the process of [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 The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science 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 The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science (ISQ) and their dimensions are listed in the following table:
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.
Further information: dimensional analysisExtensive 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 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.
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) | = | log(ν2 / 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]
See also
References
- ^ JCGM.2008.International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM) 3rd Ed.
External links
- Complex Converter Expression Evaluator (with examples) that handles units in any proper combination
Categories: Physical quantities | Introductory physics
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