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Quantum Mechanics_intensive property
Physical properties of materials and systems are often described as intensive and extensive properties. This classification relates to the dependency of the properties upon the size or extent of the system or object in question. The distinction is based on the concept that smaller, non-interacting identical subdivisions of the system may be identified so that the property of interest does or does not change when the system is divided or combined. An intensive property is a bulk property, meaning that it is a physical property of a system that does not depend on the system size or the amount of material in the system. Examples of intensive properties are the temperature, refractive index, density and the hardness of an object. No matter how small a diamond is cut, it maintains its intrinsic hardness. By contrast, an extensive property is one that is additive for independent, noninteracting subsystems.[1] The property is proportional to the amount of material in the system. For example, both the mass and the volume of a diamond are directly proportional to the amount that is left after cutting it from the raw mineral. Mass and volume are extensive properties, but hardness is intensive. The ratio of two extensive properties is scale-invariant, and is therefore an intensive property. For example, when gravity effects can be neglected, the ratio of the extensive properties mass and volume, the density, is an intensive property. This terminology of intensive and extensive properties was introduced by Richard C. Tolman in 1917.[2] Contents
1 Intensive properties 1.1 Combined intensive properties 1.2 Examples 2 Extensive properties 2.1 Combined extensive properties 2.2 Examples 3 Related extensive and intensive properties 4 Generality of classification 5 References Intensive properties
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 temperatureof 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. Additionally, the boiling point of a substance is another example of an intensive property. For example, the boiling point for water is 100°C at a pressure of one atmosphere, a fact which remains true regardless of quantity. According to the state postulate, for a sufficiently simple thermodynamic 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 quantitiesand are not relevant to extremely small systems. Combined intensive properties There are four properties in any thermodynamic system, two are intensive and two are extensive. If the 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). Examples Examples of intensive properties include: chemical potential concentration density (or specific gravity) ductility elasticity electrical resistivity hardness magnetic field magnetization malleability melting point andboiling point
Gibbs energy length mass particle number momentum number of moles volume magnetic moment electrical charge weight Related extensive and intensive properties
Thermodynamics
The classical Carnot heat engine Branches Classical Statistical Chemical Equilibrium / Non-equilibrium Laws Zeroth First Second Third Systems State Equation of state Ideal gas Real gas
State of matter Equilibrium Control volume Instruments Processes Isobaric Isochoric Isothermal Adiabatic Isentropic Isenthalpic Quasistatic Polytropic Free expansion Reversibility Irreversibility Endoreversibility Cycles Heat engines Heat pumps Thermal efficiency
System properties Property diagrams Intensive and extensive properties Functions of state (Conjugate variables in italics) Temperature / entropy Introduction to entropy pressure / volume chemical
Helmholtz free energy
Gibbs free energy
History / Culture Philosophy Entropy and time Entropy and life Brownian ratchet Maxwell's demon Heat death paradox Loschmidt's paradox Synergetics History General Heat Entropy Gas laws "Perpetual motion" machines Theories Caloric theory Vis viva Theory of heat Mechanical equivalent of heat Motive power Key publications "An Experimental Enquiry Concerning ... Heat" "On the Equilibrium of
Heterogeneous Substances" "Reflections on the Motive Power of Fire" Timelines Thermodynamics Heat engines Art Maxwell's thermodynamic surface Education Entropy as energy dispersal
Scientists Bernoulli Carnot Clapeyron Clausius Carathéodory Pierre Duhem Gibbs von Helmholtz Joule Maxwell von Mayer Onsager Rankine Smeaton Stahl Thompson
at constant pressure at constant pressure Corresponding extensive and intensive thermodynamic properties
- L = liter, J = joule ** specific properties, expressed on a per mass basis *** Specific volume is the reciprocal of density. If a molecular weight can be assigned for the substance, or the amount of substance (in moles) can be determined, then each of these thermodynamic properties may be expressed on a molar basis, and their name may be qualified with the adjectivemolar, yielding terms such as molar volume, molar internal energy, molar enthalpy, molar entropy. Standards for the symbols of molar quantities do not exist. A well known molar volume is that of an Ideal gas atstandard conditions for temperature and pressure, with the value22.41liters/mol. Molar Gibbs free energy is commonly referred to as chemical potential, symbolized by μ, particularly when discussing a partial molar Gibbs free energy μi for a component i in a mixture. Generality of classification The general validity of the division of physical properties into extensive and intensive kinds has been addressed in the course of science.[3] Redlich noted that physical properties and especially thermodynamic properties are most conveniently defined as either intensive or extensive,[2] however, these two categories are not all-inclusive and some well-defined physical properties conform to neither definition. Redlich also provides examples of mathematical functions that alter the strict additivity relationship for extensive system, such as the square or square root of volume, which occur in some contexts, altbeit rarely used.[2] Other systems, for which the 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 in which subsystems are arranged. For example, if two identicalgalvanic cells are connected in parallel, the voltage of the system is equal to the voltage of each cell, while the electric charge transferred (electric current) is extensive. However if the same cells are connected in series, the charge becomes intensive and the voltage extensive.[2] The IUPAC definitions do not consider such cases.[1] References Callen, Herbert B. (1985).Thermodynamics and an Introduction to Themostatistics (2nd Ed. ed.). New York: John Wiley & Sons. ISBN 0-471-86256-8. Lewis, G.N.; Randall, M. (1961).Thermodynamics (2nd Edition ed.). New York: McGraw- Hill Book Company.
Linder, Bruno. (2004).Thermodynamics and Introductory Statistical Mechanics. New York: John Wiley & Sons. ISBN 0-471-47459-2.
- ^^ a^ b^ c^ IUPAC Green Book Quantities, Units and Symbols in Physical Chemistry (3rd edn. 2007), page 6 (page 20 of 250 in PDF file)
- ^^ a^ b^ c^ d^ O. Redlich, Journal of chemical education, 47, 154-156 (1970)
- ^ Hatsopoulos G.N. and Keenan J.H.Principles of general thermodynamics, John Wiley and Sons 1965 p.19-
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