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Intensive and extensive properties
 
 
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In the physical science
Physical science

Physical science is an encompassing term for the branches of natural science and science that study non-living systems, in contrast to the biology sciences....
s, an intensive property (also called a bulk property), is a physical property
Physical property

A physical property is any aspect of an object or substance that can be measurement or perception without changing its Identity . Physical properties can be Intensive and extensive properties....
 of a system that does not depend on the system size or the amount of material in the system. By contrast, an extensive property of a system does depend on the system size or the amount of material in the system. (see: examples) Some intensive properties, such as viscosity
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
, are empirical
Empirical

The word empirical denotes information gained by means of observation, experience, or experiment, as opposed to theory. A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or Logical consequence that are observable by the senses....
 macroscopic
Macroscopic

Macroscopic is a word commonly used to describe physics objects that are measurement and observation by the naked eye. When applied to phenomena and abstract objects, it describes existence in the world as we perceive it....
 quantities
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....
  and are not relevant to extremely small systems.

b>intensive quantity (also intensive variable) is a physical quantity
Physical quantity

A physical quantity is a physical property that can be Quantitative. This means it can be measured and/or calculated and expressed in numbers. For example, "weight" is a physical quantity that can be expressed by stating a number of some basic measurement unit such as pound or kilograms, while "beauty" is a property that is difficult to desc...
 whose value does not depend on the amount of the substance for which it is measured.






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In the physical science
Physical science

Physical science is an encompassing term for the branches of natural science and science that study non-living systems, in contrast to the biology sciences....
s, an intensive property (also called a bulk property), is a physical property
Physical property

A physical property is any aspect of an object or substance that can be measurement or perception without changing its Identity . Physical properties can be Intensive and extensive properties....
 of a system that does not depend on the system size or the amount of material in the system. By contrast, an extensive property of a system does depend on the system size or the amount of material in the system. (see: examples) Some intensive properties, such as viscosity
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
, are empirical
Empirical

The word empirical denotes information gained by means of observation, experience, or experiment, as opposed to theory. A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or Logical consequence that are observable by the senses....
 macroscopic
Macroscopic

Macroscopic is a word commonly used to describe physics objects that are measurement and observation by the naked eye. When applied to phenomena and abstract objects, it describes existence in the world as we perceive it....
 quantities
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....
  and are not relevant to extremely small systems.

Intensive quantity

An intensive quantity (also intensive variable) is a physical quantity
Physical quantity

A physical quantity is a physical property that can be Quantitative. This means it can be measured and/or calculated and expressed in numbers. For example, "weight" is a physical quantity that can be expressed by stating a number of some basic measurement unit such as pound or kilograms, while "beauty" is a property that is difficult to desc...
 whose value does not depend on the amount of the substance for which it is measured. It is the counterpart of an extensive quantity. For instance, the mass of an object is an extensive quantity, because it depends on the amount of that substance being measured. Density
Density

The density of a material is defined as its mass per unit volume. The symbol of density is ....
, on the other hand, is an intensive property of the substance.

Combined intensive quantities


At least four functions are needed to describe any thermodynamic system, two intensive ones and two extensive ones.

If a set of parameters, , are intensive quantities and another set, , are extensive quantities, then the function is an intensive quantity if for all ,

It follows, for example, that the ratio
Ratio

A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities, but in theory any number of quantities can be compared....
 of two extensive quantities is an intensive quantity - density (intensive) is equal to mass (extensive) divided by volume (extensive).

Joining systems

Let there be a system or piece of substance a of amount ma and another piece of substance b of amount mb which can be combined without interaction. [For example, lead and tin combine without interaction, but common salt dissolves in water
Water

Water is a common chemical substance that is essential for the survival of all known forms of life. In typical usage, water refers only to its liquid form or States of matter, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam....
 and the properties of the resulting solution
Solution

In chemistry, a solution is a homogeneous mixture composed of two or more substances. In such a mixture, a solute is dissolved in another substance, known as a solvent....
 are not a simple combination of the properties of its constituents.] Let V be an extensive variable. The value of variable V corresponding to the first substance is Va, and the value of V corresponding to the second substance is Vb. If the two pieces a and b are put together, forming a piece of substance "a+b" of amount ma+b = ma+mb, then the value of their extensive variable V is:

which is a weighted mean
Weighted mean

The weighted mean is similar to an arithmetic mean , where instead of each of the data points contributing equally to the final average, some data points contribute more than others....
. Further, if Va = Vb then Va + b = Va = Vb, i.e. the intensive variable is independent of the amount. Note that this property holds only as long as other variables on which the intensive variable depends stay constant.

As an example, 60 kg of lead
Lead

Lead is a main-group Chemical element with symbol Pb and atomic number 82. Lead is a soft, malleable poor metal, also considered to be one of the heavy metal ....
, of density
Density

The density of a material is defined as its mass per unit volume. The symbol of density is ....
 11.34 ?g·cm-3 and 40 kg of tin
Tin

Tin is a chemical element with the symbol Sn and atomic number 50. Tin is obtained chiefly from the mineral cassiterite, where it occurs as an oxide, SnO2....
, of density 6.99 ?g·cm-3 will combine to form 60 + 40 = 100 kg of 60/40 solder
Solder

A solder is a fusible alloy metal alloy with a melting point or melting range of 90 to 450 ?Celsius , used in a process called soldering where it is melted to join metallic surfaces....
 of density = 9.60 g·cm-3

In a thermodynamic system
Thermodynamic system

In thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration....
 composed of two monatomic
Monatomic

In physics and chemistry, monatomic is a combination of the words "mono" and "atomic," and means "single atom." It is usually applied to gases: a monatomic gas is one in which atoms are not bound to each other....
 ideal gas
Ideal gas

The ideal gas model is a model of matter in which the molecules are treated as non-interacting point particles which are engaged in a random motion that obeys conservation of energy....
es, a and b, if the two gases are mixed, the final temperature T is

a weighted mean where is the number of particles in gas i, and is the corresponding temperature.

Examples

Examples of intensive properties include:
  • temperature
    Temperature

    In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
  • chemical potential
    Chemical potential

    In thermodynamics, physics and chemistry, chemical potential, symbolized by ?, is a term introduced by the American engineer, chemist and mathematical physicist Willard Gibbs, which he defined as follows:...
  • density
    Density

    The density of a material is defined as its mass per unit volume. The symbol of density is ....
  • viscosity
    Viscosity

    Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
  • velocity
    Velocity

    In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
  • electrical resistivity
  • spectral absorption maxima (in solution
    Solution

    In chemistry, a solution is a homogeneous mixture composed of two or more substances. In such a mixture, a solute is dissolved in another substance, known as a solvent....
    )
  • specific energy
    Specific energy

    Specific energy is defined as the energy per unit mass: J/kg or, in basic SI units: m2/s2. It is an intensive property. Contrast this with energy, which is an extensive property....
  • specific heat capacity
    Specific heat capacity

    Specific heat capacity, also known simply as specific heat, is the measure of the energy required to increase the temperature of a of a substance by a certain Celsius#Temperatures_and_intervals....
  • lustre
    Lustre (mineralogy)

    Lustre is a description of the way light interacts with the surface of a crystal, rock , or mineral. For example, a diamond is said to have an adamantine lustre and pyrite is said to have a metallic lustre....
  • hardness
  • melting point
    Melting point

    The melting point of a solid is the temperature range at which it changes states of matter from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium....
     and boiling point
    Boiling point

    The boiling point of a liquid is the temperature at which the vapor pressure of the liquid equals the environmental pressure surrounding the liquid....
  • pressure
    Pressure

    Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
  • buoyancy
    Buoyancy

    In physics, buoyancy is the upward force that keeps things afloat. The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body....
  • ductility
    Ductility

    Ductility is a mechanical property used to describe the extent to which materials can be deformed deformation without fracture.In material science, ductility specifically refers to a material's ability to deform under tensile stress; this is often characterized by the material's ability to be stretched into a wire....
  • elasticity
    Elasticity

    Elasticity may refer to:*Elasticity , continuum mechanics of bodies which deform reversibly under stressVarious uses are derived from this physical sense of the term, especially in economics:...
  • malleability
  • magnetism
    Magnetism

    In physics, magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well-known materials that exhibit easily detectable magnetic properties are nickel, iron, cobalt, and their alloys; however, all materials are influenced to greater or lesser degree by the presence of a magnetic fiel...
  • odor
    Odor

    An odor or odour is a volatilized chemical compound, generally at a very low concentration, that humans or other animals perceive by the sense of olfaction....
  • state
    State

    A state is a political Social contract with effective sovereignty over a geographic area and representing a population. These may be nation states, State or multinational states....
  • concentration
    Concentration

    In chemistry, concentration is the measure of how much of a given chemical substance there is mixed with another substance. This can apply to any sort of chemical mixture, but most frequently the concept is limited to homogeneous solutions, where it refers to the amount of solute in the solvent....


Extensive quantity

An extensive quantity (also extensive variable or extensive parameter) is a physical quantity, whose value is proportional to the size of the system
System

System is a set of interacting or interdependent entities, real or abstract, forming an integrated whole.The concept of an "integrated whole" can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and from relationships between an element of the se...
 it describes. Such a property can be expressed as the sum of the quantities for the separate subsystems that compose the entire system.

Extensive quantities are the counterparts of intensive quantities, which are intrinsic to a particular subsystem and remain constant regardless of size. Dividing one type of extensive quantity by a different type of extensive quantity will in general give an intensive quantity. For example, mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 (extensive) divided by volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 (extensive) gives density
Density

The density of a material is defined as its mass per unit volume. The symbol of density is ....
 (intensive).

Combined extensive quantities


If a set of parameters are intensive quantities and another set are extensive quantities, then the function is an extensive quantity if for all ,

Thus, extensive quantities are homogeneous function
Homogeneous function

In mathematics, a homogeneous function is a function with multiplicative scaling behaviour: if the argument is multiplied by a factor, then the result is multiplied by some power of this factor....
s (of degree 1) with respect to . It follows from Euler's homogeneous function theorem that

where the partial derivative
Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant ....
 is taken with all parameters constant except . The converse is also true - any function which obeys the above relationship will be extensive.

Examples

Examples of extensive properties include:
  • mass
    Mass

    In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
  • length
    Length

    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....
  • volume
    Volume

    The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
  • entropy
    Entropy

    In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
  • enthalpy
    Enthalpy

    In thermodynamics and chemistry, the enthalpy is a quotient or description of thermodynamic potential of a system, which can be used to calculate the heat transfer during a quasistatic process taking place in a closed system thermodynamic system under constant pressure....
  • energy
    Energy

    In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
  • electrical resistance
    Electrical resistance

    The electrical resistance of an object is a measure of its opposition to the passage of a steady electrical current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material....
  • texture
    Texture (crystalline)

    In materials science, texture is the distribution of crystallographic orientations of a sample. A sample in which these orientations are fully random is said to have no texture....
  • stiffness
    Stiffness

    Stiffness is the resistance of an Elasticity body to deformation by an applied force. It is an intensive and extensive properties....
  • particle number
    Particle number

    The particle number, N, is the number of constituent particles in a Thermodynamics. The particle number is a fundamental parameter in thermodynamics and it is Conjugate variables to the chemical potential....


Distinction from perceptions

Certain perception
Perception

In psychology and the cognitive sciences, perception is the process of attaining awareness or understanding of sense information. It is a task far more complex than was imagined in the 1950s and 1960s, when it was predicted that building perceiving machines would take about a decade, a goal which is still very far from fruition....
s are often described (or even "measured") as if they are intensive or extensive physical properties, but in fact perceptions are fundamentally different from physical properties. For example, the colour of a solution is not a physical property. A solution of potassium permanganate may appear pink, various shades of purple, or black, depending upon the concentration of the solution and the length of the optical path through it. The colour of a given sample as perceived by an observer (ie, the degree of 'pinkness' or 'purpleness') cannot be measured, only ranked in comparison with other coloured solutions by a panel of observers. Attempts to quantify a perception always involve an observer response, and biological variability is an intrinsic part of the process for many perceived properties. A given volume of permanganate solution of a given concentration has physical properties related to the colour: the optical absorption spectrum is an extensive property, and the positions of the absorption maxima (which are relatively independent of concentration) are intensive properties. A given absorption spectrum, for a certain observer, will always be perceived as the same colour; but there may be several different absorption spectra which are perceived as the same colour: there is no precise one-to-one correspondence between absorption spectrum and colour even for the same observer.

The confusion between perception and physical properties is increased by the existence of numeric scales for many perceived qualities. However, this is not 'measurement' in the same sense as in physics and chemistry. A numerical value for a perception is, directly or indirectly, the expected response of a group of observers when perceiving the specified physical event.

Examples of perceptions related to an intensive physical property:
  • Temperature
    Temperature

    In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
    : in this case all observers will agree which is the hotter of two objects.
  • Loudness
    Loudness

    Loudness is the quality of a sound that is the primary psychological correlate of physical strength .Loudness, a subjective measure, is often confused with objective measures of sound pressure such as decibels or sound intensity....
     of sound; the related physical property is sound pressure level. Observers may disagree about the relative loudness of sounds with different acoustic
    Acoustics

    Acoustics is the interdisciplinary science that deals with the study of sound, ultrasound and infrasound . A scientist who works in the field of acoustics is an acoustician....
     spectra.
  • Hue
    Hue

    Hue is one of the main properties of a color described with names such as "red", "yellow", etc. The two other main properties are lightness and colorfulness....
     of a solution; the related physical property is the position of the spectral absorption maximum (or maxima).
Examples of perceptions related to an extensive physical property:
  • Color
    Color

    Color or colour is the visual perception property corresponding in humans to the categories called red, yellow, blue and others....
     of a solution: The related physical property is the transmission or absorption spectrum
    Spectrum

    A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a Continuum . The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a triangular prism ; it has since been applied by analogy to many fields other than op...


See also

  • Intrinsic and extrinsic properties
    Intrinsic and extrinsic properties

    The term intrinsic denotes a property of some thing or action which is essence and specific to that thing or action, and which is wholly independent of any other object, action or consequence....