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In the physical sciences, an intensive property (also called a bulk property, intensive quantity, or intensive variable), is a physical property of a system that does not depend on the system size or the amount of material in the system: it is scale invariant.
By contrast, an extensive property (also extensive quantity, extensive variable, or extensive parameter) is one that is additive for independent, noninteracting subsystems.^{[1]} It is directly proportional to the amount of material in the system.
For example, density is an intensive property of a substance because it does not depend on the amount of that substance; mass and volume, which are measures of the amount of the substance, are extensive properties. In general the ratio of two extensive properties (such as mass and volume) that scale in the same way is scaleinvariant, and hence an intensive property (such as density).
There are also measured physical properties which are neither intensive nor extensive. See counterexamples below.
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An intensive property is a physical quantity whose value does not depend on the amount of the substance for which it is measured. For example, the temperature of a system in thermal equilibrium is the same as the temperature of any part of it. If the system is divided the temperature of each subsystem is identical. The same applies to the density of a homogeneous system: if the system is divided in half, the mass and the volume change in the identical ratio and the density remains unchanged.
According to the state postulate, for a sufficiently simple system, only two independent intensive variables are needed to fully specify the entire state of a system. Other intensive properties can be derived from the two known values.
Some intensive properties, such as viscosity, are empirical macroscopic quantities and are not relevant to extremely small systems.
There are four properties in any thermodynamic system, two intensive ones and two extensive ones.
If a set of parameters, , are intensive properties and another set, , are extensive properties, then the function is an intensive property if for all ,
It follows, for example, that the ratio of two extensive properties is an intensive property  density (intensive) is equal to mass (extensive) divided by volume (extensive).
This section's factual accuracy is disputed. (February 2009) 
Let there be a system or piece of substance a of amount m_{a} and another piece of substance b of amount m_{b} which can be combined without interaction. [For example, lead and tin combine without interaction, but common salt dissolves in water and the properties of the resulting solution are not a simple combination of the properties of its constituents.] Let V be an intensive variable. The value of variable V corresponding to the first substance is V_{a}, and the value of V corresponding to the second substance is V_{b}. If the two pieces a and b are put together, forming a piece of substance "a+b" of amount m_{a+b} = m_{a}+m_{b}, then the value of their intensive variable V is:
which is a weighted mean. Further, if V_{a} = V_{b} then V_{a + b} = V_{a} = V_{b}, 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.
In a thermodynamic system composed of two monatomic ideal gases, 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.
Note that you have to measure the amounts in the same unit that was used to calculate the intensive property from the extensive property. So when you interpolate density, you have to measure the properties in volume, as density is mass per volume. The formula makes no sense when you measure the properties in mass (kg).
Examples of intensive properties include:
An extensive property is defined by the IUPAC Green Book as a physical quantity which is the sum of the properties of separate noninteracting subsystems that compose the entire system.^{[1]} The value of such an additive property is proportional to the size of the system it describes, or to the quantity of matter in the system.
Extensive properties are the counterparts of intensive properties, which are intrinsic to a particular subsystem. Dividing one type of extensive property by a different type of extensive property will in general give an intensive value. For example, mass (extensive) divided by volume (extensive) gives density (intensive).
If a set of parameters are intensive properties and another set are extensive properties, then the function is an extensive property if for all ,
Thus, extensive properties are homogeneous functions (of degree 1) with respect to . It follows from Euler's homogeneous function theorem that
where the partial derivative is taken with all parameters constant except . The converse is also true  any function which obeys the above relationship will be extensive.^{[citation needed]}
Examples of extensive properties include^{[citation needed]}:
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Although not true for all physical properties, there are a number of properties which have corresponding extensive and intensive analogs, many of which are thermodynamic properties. Examples of such extensive thermodynamic properties, which are dependent on the size of the thermodynamic system in question, include volume (V), internal energy (U), enthalpy (H), entropy (S), Gibbs free energy (G), Helmholtz free energy (A), and heat capacities (C_{v} and C_{p}) (in the sense of thermal mass). Note that the main symbols of these extensive thermodynamic properties shown here are capital letters. Except for volume (V), these extensive properties are dependent on the amount of material (substance) in the thermodynamic system in question.
For homogeneous substances, these extensive thermodynamic properties each have analogous intensive thermodynamic properties, which can be expressed on a per mass basis, and the corresponding intensive property symbols would be the lower case letters of the corresponding extensive property. Examples of intensive thermodynamic properties, which are independent on the size of the thermodynamic system in question and are analogous to the extensive ones mentioned above, include specific volume (v), specific internal energy (u), specific enthalpy (h), specific entropy (s), specific Gibbs free energy (g), specific Helmholtz free energy (a), and specific heat capacities (c_{v} and c_{p}, sometimes simply called specific heats). These intensive thermodynamic properties are effectively material properties which are valid at a point in a thermodynamic system or at a point in space at a certain time. These intensive properties are dependent on the conditions at that point such as temperature, pressure, and material composition, but are not considered dependent on the size of a thermodynamic system or on the amount of material in the system. See the table below. Specific volume is volume per mass, the reciprocal of density which equals mass per volume.
Extensive property 
Symbol  SI units  Intensive property** 
Symbol  SI units 

Volume 


Specific volume*** 


Internal energy 


Specific internal energy 


Entropy 


Specific entropy 


Enthalpy 


Specific enthalpy 


Gibbs free energy 


Specific Gibbs free energy 


Heat capacity at constant volume 


Specific heat capacity at constant volume 


Heat capacity at constant pressure 


Specific heat capacity at constant pressure 


If a molecular weight can be assigned for the substance, or the number of moles in the system can be determined, then each of these thermodynamic properties can be expressed on a per mole basis. These intensive properties could be named after the analogous extensive properties but with the word "molar" preceding them; thus molar volume, molar internal energy, molar enthalpy, molar entropy, etc. Although the same small letters can be used as in the analogous specific properties indicating they are intensive, sometimes the corresponding capital letters have been used (and understood to be on a per mole basis), and there seems to be no universally agreed upon symbol convention for these molar properties. A well known molar volume is that of an ideal gas at STP (Standard Temperature and Pressure); this molar volume = 22.41 liters per mole. Molar Gibbs free energy is commonly referred to as chemical potential, symbolized by μ, particularly when discussing a partial molar Gibbs free energy μ_{i} for a component i in a mixture.
There are measured physical properties which are neither intensive nor extensive. For example the electrical resistance of two resistors is the sum of their two resistances only if the resistors are connected in series, but not if they are connected in parallel (if they are placed in parallel, it is instead the electrical conductance – the inverse of the resistance – of the two resistors that is the sum of their two conductances). The electrical resistance of independent noninteracting resistors (subsystems) is therefore not additive in general, and electrical resistance is not an extensive property. Nor is it intensive because the resistance of the two resistors is not equal in general, even if they consist of the same material at the same temperature and pressure.
Another counterexample is invariant mass in special relativity, which is not additive for subsystems in motion relative to each other. Invariant mass is therefore not an extensive quantity, nor it is an intensive quantity.
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リンク元  「広範」「large scale」「precise」「ubiquitous」「ubiquitously」 
拡張検索  「extensively」「extensively drugresistant tuberculosis」「extensive metabolizer」 