# intensive quantity

In physics and chemistry an intensive property (also called a bulk property) of a system is a physical property of the 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. Some intensive properties, such as viscosity, are statistical in nature and not relevant to extremely small quantities.

## Intensive quantity

An intensive quantity (also intensive variable) is a physical quantity 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 not a bulk property, because it depends on the amount of that substance being measured. Density on the other hand, is a bulk property of the substance. The riddle "what weighs more, a pound of feathers or a pound of lead?" is an example where it is easy to confuse the intrinsic and extrinsic.

### Combined intensive quantities

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

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 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 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 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 intensive variable V is:

which is a weighted mean. 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, 60kg of lead, of density 11.34  gÂ·cm−3 and 40kg of tin, of density 6.99  gÂ·cm−3 will combine to form 60 + 40 = 100kg of 60/40 solder of density = 9.60 gÂ·cm−3

In a thermodynamic system composed of two monatomic ideal gases, a and b, if the two gases are mixed, the final temperature T is

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

### Examples

Examples of intensive properties include:

## 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 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 (mass divided by volume gives density).

### 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 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.

### Examples

Examples of extensive properties include:

## Distinction from perceptions

Certain perceptions 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: in this case all observers will agree which is the hotter of two objects.
• Loudness of sound; the related physical property is sound pressure level. Observers may disagree about the relative loudness of sounds with different acoustic spectra.
• Hue 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 of a solution: The related physical property is the transmission or absorption spectrum

## References

• Callen, Herbert B. (1985). Thermodynamics and an Introduction to Themostatistics, 2nd Ed., New York: John Wiley & Sons. ISBN 0-471-86256-8.
• Lewis, G.N.; Randall, M. (1961). Thermodynamics, 2nd Edition, New York: McGraw-Hill Book Company.
Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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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.
Viscosity is a measure of the resistance of a fluid to deform under either shear stress or extensional stress. It is commonly perceived as "thickness", or resistance to flow.
A physical quantity is either a physical property that can be measured (e.g. mass, volume, etc.), or the result of a measurement. The value of a physical quantity Q is expressed as the product of a numerical value and a physical unit [Q].
In physics and chemistry an intensive property (also called a bulk property) of a system is a physical property of the system that does not depend on the system size or the amount of material in the system.
In physics, density is mass m per unit volume V—how heavy something is compared to its size. A small, heavy object, such as a rock or a lump of lead, is denser than a lighter object of the same size or a larger object of the same weight, such as pieces of
A riddle is a statement or question having a double or veiled meaning, put forth as a puzzle to be solved. Riddles are of two types: enigmas, which are problems generally expressed in metaphorical or allegorical language that require ingenuity and careful thinking for their
This article or section is in need of attention from an expert on the subject.
In physics and chemistry an intensive property (also called a bulk property) of a system is a physical property of the system that does not depend on the system size or the amount of material in the system.
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See weight function for the continuous case.

The weighted mean, or weighted average, of a non-empty list of data

with corresponding non-negative weights

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Electronegativity 2.33 (scale Pauling)
Ionization energies
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2nd: 1450.5 kJmol−1
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In physics, density is mass m per unit volume V—how heavy something is compared to its size. A small, heavy object, such as a rock or a lump of lead, is denser than a lighter object of the same size or a larger object of the same weight, such as pieces of
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• Tin

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An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. Additionally, the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container.
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Temperature is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics.
Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface.

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Viscosity is a measure of the resistance of a fluid to deform under either shear stress or extensional stress. It is commonly perceived as "thickness", or resistance to flow.