Physical properties
A physical property is any property that is measurable, whose value describes a state of a physical system. The changes in the physical properties of a system can be used to describe its changes between momentary states. Physical properties are ...

of materials and system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expres ...

s can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...

, an intensive quantity is one whose magnitude is independent of the size of the system, whereas an extensive quantity is one whose magnitude is additive for subsystems.
The terms ''intensive and extensive quantities'' were introduced into physics by German writer Georg Helm
Georg Ferdinand Helm (; 15 March 1851 in Dresden, Saxony – 13 September 1923 in Dresden) was a German mathematician.
Helm graduated from high school from the Annenschule in Dresden in 1867. Thereafter he studied mathematics and natural sci ...

in 1898, and by American physicist and chemist Richard C. Tolman
Richard Chace Tolman (March 4, 1881 – September 5, 1948) was an American mathematical physicist and physical chemist who made many contributions to statistical mechanics. He also made important contributions to theoretical cosmology in ...

in 1917./ref> An intensive property does not depend on the system size or the amount of material in the system. It is not necessarily homogeneously distributed in space; it can vary from place to place in a body of matter and radiation. Examples of intensive properties include

temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...

, ''T''; refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...

, ''n''; density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

, ''ρ''; and hardness
In materials science, hardness (antonym: softness) is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. In general, different materials differ in their hardness; for example har ...

, ''η''.
By contrast, extensive properties such as the mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...

, volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial units, imperial or United States customary units, US customary units (s ...

and entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

of systems are additive for subsystems.
Not all properties of matter fall into these two categories. For example, the square root of the volume is neither intensive nor extensive. For example if a system is doubled in size by juxtaposing a second identical system, the value of an intensive property equals the value for each subsystem and the value of an extensive property is twice the value for each subsystem. However the property √V is instead multiplied by √2 .
Intensive properties

An intensive property is aphysical quantity
A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...

whose value does not depend on the amount of substance which was measured. The most obvious intensive quantities are ratios of extensive quantities. In a homogeneous system divided into two halves, all its extensive properties, in particular its volume and its mass, are divided into two halves. All its intensive properties, such as the mass per volume (mass density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

) or volume per mass (specific volume
In thermodynamics, the specific volume of a substance (symbol: , nu) is an intrinsic property of the substance, defined as the ratio of the substance's volume () to its mass (). It is the reciprocal of density (rho) and it is related to the m ...

), must remain the same in each half.
The temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...

of a system in thermal equilibrium is the same as the temperature of any part of it, so temperature is an intensive quantity. If the system is divided by a wall that is permeable to heat or to matter, the temperature of each subsystem is identical. Additionally, the boiling temperature of a substance is an intensive property. For example, the boiling temperature of water is 100 °C at a pressure of one atmosphere
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A ...

, regardless of the quantity of water remaining as liquid.
Any extensive quantity "E" for a sample can be divided by the sample's volume, to become the "E density" for the sample;
similarly, any extensive quantity "E" can be divided by the sample's mass, to become the sample's "specific E";
extensive quantities "E" which have been divided by the number of moles in their sample are referred to as "molar E".
The distinction between intensive and extensive properties has some theoretical uses. For example, in thermodynamics, the state of a simple compressible system is completely specified by two independent, intensive properties, along with one extensive property, such as mass. Other intensive properties are derived from those two intensive variables.
Examples

Examples of intensive properties include: * charge density, ''ρ'' (or ''ne'') *chemical potential
In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...

, ''μ''
* color
Color ( American English) or colour ( British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are as ...

* concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number concentration'', ...

, ''c''
* energy density, ''ρ''
* magnetic permeability
In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by William ...

, ''μ''
* mass density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

, ''ρ'' (or specific gravity
Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ...

)
* melting point
The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depe ...

and boiling point
The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.
The boiling point of a liquid varies depending upon the surrounding envir ...

* molality
Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution.
A commonly used unit for molali ...

, ''m'' or ''b''
* pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and ...

, ''p''
* refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...

* specific conductance (or electrical conductivity)
* specific heat capacity
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...

, ''cspecific internal energy
The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...

, ''u''
* specific rotation
In chemistry, specific rotation ( '') is a property of a chiral chemical compound. It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance–concentration product, as the light passes through a sample ...

, 'α''* specific volume
In thermodynamics, the specific volume of a substance (symbol: , nu) is an intrinsic property of the substance, defined as the ratio of the substance's volume () to its mass (). It is the reciprocal of density (rho) and it is related to the m ...

, ''v''
* standard reduction potential
Redox potential (also known as oxidation / reduction potential, ''ORP'', ''pe'', ''E_'', or E_) is a measure of the tendency of a chemical species to acquire electrons from or lose electrons to an electrode and thereby be reduced or oxidised respe ...

, ''E°''
* surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to ...

* temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...

, ''T''
* thermal conductivity
The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa.
Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...

* velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is ...

''v''
* viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inter ...

See List of materials properties for a more exhaustive list specifically pertaining to materials.
Extensive properties

An extensive property is a physical quantity whose value is proportional to the size of thesystem
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expres ...

it describes, or to the quantity of matter in the system. For example, the mass of a sample is an extensive quantity; it depends on the amount of substance. The related intensive quantity is the density which is independent of the amount. The density of water is approximately 1g/mL whether you consider a drop of water or a swimming pool, but the mass is different in the two cases.
Dividing one extensive property by another extensive property generally gives an intensive value—for example: mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...

(extensive) divided by volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial units, imperial or United States customary units, US customary units (s ...

(extensive) gives Examples

Examples of extensive properties include: *amount of substance
In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...

, ''n''
* enthalpy, ''H''
* entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

, ''S''
* Gibbs energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pr ...

, ''G''
* heat capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat capacity i ...

, ''Cinternal energy
The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...

, ''U''
* spring stiffness, ''K''
* mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...

, ''m''
* volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial units, imperial or United States customary units, US customary units (s ...

, ''V''
Conjugate quantities

In thermodynamics, some extensive quantities measure amounts that are conserved in a thermodynamic process of transfer. They are transferred across a wall between two thermodynamic systems or subsystems. For example, species of matter may be transferred through a semipermeable membrane. Likewise, volume may be thought of as transferred in a process in which there is a motion of the wall between two systems, increasing the volume of one and decreasing that of the other by equal amounts. On the other hand, some extensive quantities measure amounts that are not conserved in a thermodynamic process of transfer between a system and its surroundings. In a thermodynamic process in which a quantity of energy is transferred from the surroundings into or out of a system as heat, a corresponding quantity of entropy in the system respectively increases or decreases, but, in general, not in the same amount as in the surroundings. Likewise, a change in the amount of electric polarization in a system is not necessarily matched by a corresponding change in electric polarization in the surroundings. In a thermodynamic system, transfers of extensive quantities are associated with changes in respective specific intensive quantities. For example, a volume transfer is associated with a change in pressure. An entropy change is associated with a temperature change. A change in the amount of electric polarization is associated with an electric field change. The transferred extensive quantities and their associated respective intensive quantities have dimensions that multiply to give the dimensions of energy. The two members of such respective specific pairs are mutually conjugate. Either one, but not both, of a conjugate pair may be set up as an independent state variable of a thermodynamic system. Conjugate setups are associated byLegendre transformation
In mathematics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involutive transformation on real-valued convex functions of one real variable. In physical problems, it is used to convert functions ...

s.
Composite properties

The ratio of two extensive properties of the same object or system is an intensive property. For example, the ratio of an object's mass and volume, which are two extensive properties, is density, which is an intensive property. More generally properties can be combined to give new properties, which may be called derived or composite properties. For example, the base quantities mass and volume can be combined to give the derived quantity density. These composite properties can sometimes also be classified as intensive or extensive. Suppose a composite property $F$ is a function of a set of intensive properties $\backslash $ and a set of extensive properties $\backslash $, which can be shown as $F(\backslash ,\backslash )$. If the size of the system is changed by some scaling factor, $\backslash lambda$, only the extensive properties will change, since intensive properties are independent of the size of the system. The scaled system, then, can be represented as $F(\backslash ,\backslash )$. Intensive properties are independent of the size of the system, so the property F is an intensive property if for all values of the scaling factor, $\backslash lambda$, :$F(\backslash ,\backslash )\; =\; F(\backslash ,\backslash ).\backslash ,$ (This is equivalent to saying that intensive composite properties arehomogeneous function
In mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the ''d ...

s of degree 0 with respect to $\backslash $.)
It follows, for example, that the ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to th ...

of two extensive properties is an intensive property. To illustrate, consider a system having a certain mass, $m$, and volume, $V$. The density, $\backslash rho$ is equal to mass (extensive) divided by volume (extensive): $\backslash rho=\backslash frac$. If the system is scaled by the factor $\backslash lambda$, then the mass and volume become $\backslash lambda\; m$ and $\backslash lambda\; V$, and the density becomes $\backslash rho=\backslash frac$; the two $\backslash lambda$s cancel, so this could be written mathematically as $\backslash rho\; (\backslash lambda\; m,\; \backslash lambda\; V)\; =\; \backslash rho\; (m,\; V)$, which is analogous to the equation for $F$ above.
The property $F$ is an extensive property if for all $\backslash lambda$,
:$F(\backslash ,\backslash )=\backslash lambda\; F(\backslash ,\backslash ).\backslash ,$
(This is equivalent to saying that extensive composite properties are homogeneous function
In mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the ''d ...

s of degree 1 with respect to $\backslash $.) It follows from Euler's homogeneous function theorem
In mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the ''d ...

that
:$F(\backslash ,\backslash )=\backslash sum\_j\; A\_j\; \backslash left(\backslash frac\backslash right),$
where the 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 (as opposed to the total derivative, in which all variables are allowed to vary). Pa ...

is taken with all parameters constant except $A\_j$. This last equation can be used to derive thermodynamic relations.
Specific properties

A ''specific'' property is the intensive property obtained by dividing an extensive property of a system by its mass. For example, heat capacity is an extensive property of a system. Dividing heat capacity, $C\_p$, by the mass of the system gives the specific heat capacity, $c\_p$, which is an intensive property. When the extensive property is represented by an upper-case letter, the symbol for the corresponding intensive property is usually represented by a lower-case letter. Common examples are given in the table below. : *Specific volume is the reciprocal ofchemical potential
In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...

, symbolized by $\backslash mu$, particularly when discussing a partial molar Gibbs free energy $\backslash mu\_i$ for a component $i$ in a mixture.
For the characterization of substances or reactions, tables usually report the molar properties referred to a standard state
In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. A superscript circle ° (degree symbol) or a Plimsoll (⦵) character is used ...

. In that case an additional superscript $^$ is added to the symbol. Examples:
* $V\_^$ = is the molar volume of an ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is am ...

at standard conditions for temperature and pressure
Standard temperature and pressure (STP) are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union o ...

.
* $C\_^$ is the standard molar heat capacity of a substance at constant pressure.
* $\backslash mathrm\; \backslash Delta\_\; H\_^$ is the standard enthalpy variation of a reaction (with subcases: formation enthalpy, combustion enthalpy...).
* $E^$ is the standard reduction potential
Redox potential (also known as oxidation / reduction potential, ''ORP'', ''pe'', ''E_'', or E_) is a measure of the tendency of a chemical species to acquire electrons from or lose electrons to an electrode and thereby be reduced or oxidised respe ...

of a redox couple, i.e. Gibbs energy over charge, which is measured in volt
The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827).
Defi ...

= J/C.
Limitations

The general validity of the division of physical properties into extensive and intensive kinds has been addressed in the course of science. Redlich noted that, although physical properties and especially thermodynamic properties are most conveniently defined as either intensive or extensive, these two categories are not all-inclusive and some well-defined concepts like the square-root of a volume conform to neither definition. Other systems, for which standard definitions do not provide a simple answer, are systems in which the subsystems interact when combined. Redlich pointed out that the assignment of some properties as intensive or extensive may depend on the way subsystems are arranged. For example, if two identicalgalvanic cell
A galvanic cell or voltaic cell, named after the scientists Luigi Galvani and Alessandro Volta, respectively, is an electrochemical cell in which an electric current is generated from spontaneous Oxidation-Reduction reactions. A common apparatus ...

s are connected in parallel
Parallel is a geometric term of location which may refer to:
Computing
* Parallel algorithm
* Parallel computing
* Parallel metaheuristic
* Parallel (software), a UNIX utility for running programs in parallel
* Parallel Sysplex, a cluster of I ...

, the voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge t ...

of the system is equal to the voltage of each cell, while the electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectiv ...

transferred (or the electric current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving ...

) is extensive. However, if the same cells are connected in series, the charge becomes intensive and the voltage extensive. The IUPAC definitions do not consider such cases.
Some intensive properties do not apply at very small sizes. For example, viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inter ...

is a macroscopic
The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic.
Overview
When applied to physical phenomena an ...

quantity
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a uni ...

and is not relevant for extremely small systems. Likewise, at a very small scale color
Color ( American English) or colour ( British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are as ...

is not independent of size, as shown by quantum dots
Quantum dots (QDs) are semiconductor particles a few nanometres in size, having optical and electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanotechnology. When the ...

, whose color depends on the size of the "dot".
References

{{DEFAULTSORT:Intensive And Extensive Properties Physical quantities Thermodynamic properties