Intensive Property

The physical properties of materials and systems can often be classified as either intensive or extensive , based on how the property changes when the size (or extent) of the system changes. According to IUPAC , an intensive quantity is one whose magnitude is independent of the size of the system [1] while an extensive quantity is one whose magnitude is additive to the subsystem.

An intensive property does not depend on the size of the system or the amount of material in the system. It is not necessarily evenly distributed in space; This can vary from place to place in the body of matter and radiation. Examples of intensive properties include temperature , T ; refractive index , n ; Density , ; _ and the hardness of an object , .

In contrast, broad properties such as mass , volume , and entropy of a system are additive to subsystems.

Although it is often convenient to define physical quantities in order to broaden or broaden them, they do not necessarily fall within those classifications. For example, the square root of mass is neither intensive nor extensive.

Matters were introduced in intensive and extensive quantities into physics by the German author Georg Hull in 1898, and by the American physicist and chemist Richard C. Tolmann in 1917.

intensive properties

An intensive property is a physical quantity whose value does not depend on the quantity of the substance for which it is measured. For example, the temperature of a system in solar equilibrium is the same as the temperature of any part of it. If the system is divided by a wall that is permeable to heat or matter, each subsystem has the same temperature; If a system is divided by a wall that is impervious to heat and matter, the subsystem can have different temperatures. Similarly the density of a homogeneous systemfor ; If the system is split in half, the extensive properties, such as mass and volume, are each split in half, and the intensive property, density, remains the same in each subsystem. Additionally, the boiling point of a substance is another example of an intensive property. For example, the boiling point of water at one atmosphere of pressure is 100 °C , which is true regardless of volume.

The distinction between intensive and extensive properties has some theoretical uses. For example, in thermodynamics, the state of a simple compressible system is entirely specified by two independent, intensive properties as well as a comprehensive property, such as mass. Other intensive properties are derived from those two intensive variables.


Examples of intensive properties include:

  • Chemical potential , μ
  • color [6]
  • concentration , c
  • density , ρ (or specific gravity )
  • Magnetic permeability , μ
  • melting point and boiling point [7]
  • molality , m or b
  • pressure , p
  • Refractive index
  • Specific Conductivity (The Electrical Conductivity)
  • Specific heat capacity , c p
  • Specific internal energy , U
  • specific rotation , [ α ]
  • specific volume , V
  • Standard reduction capacity , [7] E°
  • surface tension
  • temperature, t
  • thermal conductivity
  • viscosity

See List of material properties for a more detailed list specifically relating to materials.

extensive properties

A pervasive property is a physical quantity whose value is proportional to the size of the system it describes, or to the amount of matter in the system. For example, the mass of a sample is a comprehensive quantity; It depends on the amount of substance. The associated intensive quantity is the density that is independent of the amount. The density of water is about 1g/mL whether you consider a drop of water or a swimming pool, but the mass is different in both cases.

Dividing one comprehensive property by another comprehensive property usually gives an intensive value – for example: dividing mass (extensive) by volume (extensive) gives density (intense).


Examples of comprehensive properties include:

  • amount of substance, n
  • energy, e
  • Enthalpy, H
  • entropy, s
  • Gibbs Energy, G
  • heat capacity, c p
  • Helmholtz energy, A or F
  • internal energy, u
  • mass, m
  • Vol. V

conjugate quantity

In thermodynamics, some broad quantities measure the quantities that are conserved in the thermodynamic process of transfer. They are transferred across a wall between two thermodynamic systems, or subsystems. For example, species of matter can be transferred through a semipermeable membrane. Similarly, volume can be considered to be transferred in the process in which the wall movement between the two systems, increasing the volume of one and decreasing the volume of the other by the same amount.

On the other hand, some comprehensive quantities measure quantities that are not conserved in the thermodynamic process of transfer between a system and its surroundings. In a thermodynamic process in which an amount of energy is transferred into or out of a system as heat from the surroundings, an equal amount of entropy in the system increases or decreases, respectively, but in general, not by the same amount as the surroundings. Similarly, a change in the amount of electrical polarization in a system does not necessarily match the corresponding change in electrical polarization in the surroundings.

In a thermodynamic system, extensive quantity transfers are associated with corresponding specific intensive quantity changes. For example, 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 mass quantities and their corresponding intensive quantities have dimensions that multiply to give the dimensions of the energy. Two members of such related distinct alleles are mutually conjugated. Either one of the conjugate pairs, but not both, can be set up as an independent state variable of a thermodynamic system. The conjugate setups are associated with the legendre transformation.

overall quality

The ratio of two broad properties of the same object or system is an intensive property. For example, the ratio of an object’s mass to volume, which are two broad properties, is density, which is an intensive property.

In general, properties can be combined to give new properties, which may be called derived or compound properties. For example, the original quantity [9] mass and volume can be combined to give the derived quantity [10] density. These compound properties can sometimes also be classified as intensive or extensive. Suppose a composite property is a function of a set of intensive properties and a set of comprehensive properties , which can be shown as . If the size of the system is changed by a scaling factor, , only the extensive properties will change, because the intensive properties are independent of the size of the system. Then, the scaled system can be represented as .

F\{a_{i}\}\{A_{j}\}F(\{a_{i}\},\{A_{j}\})\lambda {\displaystyle F(\{a_{i}\},\{\lambda A_{j}\})}

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, ,\lambda

{\displaystyle F(\{a_{i}\},\{\lambda A_{j}\})=F(\{a_{i}\},\{A_{j}\}).\,}

(This is equivalent to saying that intensive compound properties are homogeneous functions of degree 0, with respect to .) {Aj}

For example, it follows that the ratio of two comprehensive properties is an intensive property. For example, consider a system with a fixed mass, , and volume, . Density is equal to mass (broad) divided by volume (broad): . If the system is expanded by a factor , then mass and volume become and , and density becomes ; The two s cancel out, so it can be written mathematically , which is analogous to the equation for above.

mV\rho {\displaystyle \rho ={\frac {m}{V}}}\lambda{\displaystyle \lambda m}\lambda V{\displaystyle \rho ={\frac {\lambda m}{\lambda V}}}\lambda
{\displaystyle \rho (\lambda m,\lambda V)=\rho (m,V)}F

Property is a comprehensive asset if for all ,F\lambda

{\displaystyle F(\{a_{i}\},\{\lambda A_{j}\})=\lambda F(\{a_{i}\},\{A_{j}\}).\,}

(This is equivalent to saying that general compound properties are homogeneous functions of degree 1 with respect to .) It follows Euler’s homogeneous function theorem that\{A_{j}\}

F(\{a_{i}\},\{A_{j}\})=\sum _{j}A_{j}\left({\frac {\partial F}{\partial A_{j}}}\right),

where all parameters except the partial derivative are taken with the constant . [11] This last equation can be used to derive thermodynamic relations.A_{j}

Typical Properties

specific property is the intensive property of a system obtained by dividing it by its mass. For example, heat capacity is a widespread property of a system. Dividing the heat capacity, , by the mass of the system gives the specific heat capacity , which is an intensive property. When the broad asset is represented by an upper-case letter, the symbol for the corresponding deep asset is usually represented by a lower-case letter. Common examples are given in the table below. [3]C_{p}c_{p}

SignSI unitsIntensive (Special)
SignSI unitsdeep (molar)
SignSI units
volumeVM3 or LSpecific Quantity*Vm3 / kg or l/kgmolar volumeVM _m3 / mol or l/mol
internal energyYouJspecific internal energyyouJ/kgmolar internal energymJ/mol
EnthalpyhJspecific enthalpyhJ/kgmolar enthalpymJ/mol
gibbs free energyYesJspecific gibbs free energyYesJ/kgchemical potentialor μJ/mol
entropysJ/Kspecific entropysJammu/(kg · Kashmir)molar entropymJammu/(Moll · Kashmir)

heat capacity at constant volume
Specific heat capacity at constant volume
vJammu/(kg · Kashmir)
Molar heat capacity at constant volume
v , mJammu/(Moll · Kashmir)

heat capacity at constant pressure
CP _Jammu/Kashmir
Specific heat capacity at constant pressure
CP _Jammu/(kg · Kashmir)
Molar heat capacity at constant pressure
p , mJammu/(Moll · Kashmir)

* Specific volume is the inverse of density.

If the amount of matter can be quantified in moles, then each of these thermodynamic properties can be expressed in terms of molarity, and their name may be qualified with the adjective molar , as in molar volume, molar volume. Internal energy, molar enthalpy, and molar entropy. The symbol for molar quantities can be indicated by adding a subscript “m” to the corresponding broad property. For example, the molar enthalpy is . [3] The molar Gibbs free energy is usually referred to as the chemical potential, which is symbolized by , especially when discussing the partial molar Gibbs free energy for a component in a mixture.

{\displaystyle H_{\mathrm {m} }}\mu\mu _{i}i

For the characterization of substances or reactions, tables usually report the molar properties referred to a standard state. In that case an additional superscript is added to the symbol. Example:^{{\circ }}

  • {\displaystyle V_{\mathrm {m} }^{\circ }}= 22.41 L/mol is the molar volume of an ideal gas at standard conditions for temperature and pressure.
  • {\displaystyle C_{P,\mathrm {m} }^{\circ }}The standard molar heat capacity of a substance at constant pressure is
  • {\displaystyle \mathrm {\Delta } _{\mathrm {r} }H_{\mathrm {m} }^{\circ }}The standard enthalpy variation of a reaction is (with subcases: formation enthalpy, combustion enthalpy…).
    {\displaystyle E^{\circ }}The standard reduction potential of a redox couple is , i.e. Gibbs energy overload, measured in volts = J/c.


The general validity of the division of physical properties into broad and deep types is addressed in the science curriculum. [12] Radlich noted that, although physical properties, and especially thermodynamic properties, are most easily defined as either intensive or comprehensive, these two categories are not all-inclusive and there are few well-defined physical properties. Properties conform to neither definition. [4] Radlich also provides examples of mathematical functions that replace the strict additive relation for comprehensive systems, such as the volume of a square or square root, which can occur in some contexts, although it is rarely used. [4]

Other systems for which standard definitions do not provide a simple answer are systems in which subsystems interact when combined. Redlich pointed out that the assignment of certain properties as intensive or extensive may depend on the way the subsystems are arranged. For example, if two identical galvanic cells are connected in parallel, the voltage is equal to the voltage of each cell in the system, while the electric charge transferred (or electric current) is widespread. However, if identical cells are connected in series, the charge becomes intensive and the voltage broadens. [4] The IUPAC definitions do not consider such cases. [3]

Some intensive properties do not apply to very small sizes. For example, viscosity is a macroscopic quantity and is not relevant for extremely small systems. Similarly, on very small scales the color is not independent of size, as shown by quantum dots, whose color depends on the size of the “dot”.