Intensive and extensive properties - wikipedia Intensive and extensive 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 Note : Conjugate variables in italics Property diagrams Intensive and extensive properties Functions of state Temperature / Entropy ( introduction ) Pressure / Volume Chemical potential / Particle number Vapor quality Reduced properties Process functions Work Heat Material properties Property databases Specific heat capacity c = ( displaystyle c = ) T ( displaystyle T ) ∂ S ( displaystyle partial S ) N ( displaystyle N ) ∂ T ( displaystyle partial T ) Compressibility β = − ( displaystyle \beta = - ) 1 ( displaystyle 1 ) ∂ V ( displaystyle partial V ) V ( displaystyle V ) ∂ p ( displaystyle partial p ) Thermal expansion α = ( displaystyle alpha = ) 1 ( displaystyle 1 ) ∂ V ( displaystyle partial V ) V ( displaystyle V ) ∂ T ( displaystyle partial T ) Equations Carnot 's theorem Clausius theorem Fundamental relation Ideal gas law Maxwell relations Onsager reciprocal relations Bridgman 's equations Table of thermodynamic equations Potentials Free energy Free entropy Internal energy U ( S, V ) ( displaystyle U ( S, V ) ) Enthalpy H ( S, p ) = U + p V ( displaystyle H ( S, p ) = U + pV ) Helmholtz free energy A ( T, V ) = U − T S ( displaystyle A ( T, V ) = U-TS ) Gibbs free energy G ( T, p ) = H − T S ( displaystyle G ( T, p ) = H - TS ) History Culture History General Heat Entropy Gas laws `` Perpetual motion '' machines Philosophy Entropy and time Entropy and life Brownian ratchet Maxwell 's demon Heat death paradox Loschmidt 's paradox Synergetics Theories Caloric theory Theory of heat Vis viva ( `` living force '' ) 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 Education Maxwell 's thermodynamic surface Entropy as energy dispersal Scientists Bernoulli Boltzmann Carnot Clapeyron Clausius Carathéodory Duhem Gibbs von Helmholtz Joule Maxwell von Mayer Onsager Rankine Smeaton Stahl Thompson Thomson van der Waals Waterston Book : Thermodynamics Physical properties of materials and systems can often be categorized as being either intensive or extensive quantities, according to how the property changes when the size ( or extent ) of the system changes. According to IUPAC, an intensive property is one whose magnitude is independent of the size of the system. An extensive property is one whose magnitude is additive for subsystems. 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 include temperature, T, refractive index, n, density, ρ, and hardness of an object, η ( IUPAC symbols are used throughout this article ). When a diamond is cut, the pieces maintain their intrinsic hardness ( until the sample reduces to a few atoms thick ), so hardness is independent of the size of the system, for larger samples. By contrast, an extensive property is additive for subsystems. This means the system could be divided into any number of subsystems, and the extensive property measured for each subsystem ; the value of the property for the system would be the sum of the property for each subsystem. For example, both the mass, m, and the volume, V, 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 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. The terms intensive and extensive quantities were introduced by Richard C. Tolman in 1917. Contents 1 Intensive properties 1.1 Examples 2 Extensive properties 2.1 Examples 3 Composite properties 4 `` Specific '' properties 5 Limitations 6 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 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. Additionally, the boiling point of a substance is another example of an intensive property. For example, the boiling point of water is 100 ° C at a pressure of one atmosphere, which remains true regardless of quantity. The distinction between intensive and extensive properties has some theoretical uses. For example, in thermodynamics, according to the state postulate, a sufficiently simple system consisting of a single substance requires only two independent intensive variables to fully specify the system 's entire state. Other intensive properties are derived from those two variables. Examples Examples of intensive properties include : chemical potential, μ color concentration, c density, ρ ( or specific gravity ) magnetic permeability, μ melting point and boiling point molality, m or b pressure, p specific heat capacity, c specific volume, v standard reduction potential, E ° temperature, T Extensive properties The IUPAC Gold Book defines an extensive property as a physical quantity whose magnitude is additive for subsystems. 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. For example, the amount of heat required to melt ice at constant temperature and pressure is an extensive property, known as the enthalpy of fusion. The amount of heat required to melt one ice cube would be much less than the amount of heat required to melt an iceberg, so it is dependent on the quantity. Extensive properties are not just dependent on the amount of material in a system ; the relation must be additive. If, say, a property depended on the square of the mass, it would not be an extensive property. ( Consider a system consisting of two 1 gram weights. The total mass is 2 g, squaring that gives 4 g. Squaring and summing the individual masses gives 2 g. This property is not additive for the two subsystems. ) Dividing one extensive property by another extensive property generally gives an intensive value -- for example : mass ( extensive ) divided by volume ( extensive ) gives density ( intensive ). Examples Examples of extensive properties include : amount of substance, mol energy, E enthalpy, H entropy, S Gibbs energy, G heat capacity, C Helmholtz energy, A or F internal energy, U mass, m volume, V Composite properties Properties can be combined to give new properties, which may be called derived, or composite properties. For example, mass and volume can be combined to give density. These composite properties can also be classified as intensive or extensive. Suppose a composite property, F ( displaystyle F ), is a function of a set of intensive properties, ( a i ) ( displaystyle ( a_ ( i ) ) ), and a set of extensive properties, ( A j ) ( displaystyle ( A_ ( j ) ) ), which can be shown as F ( ( a i ), ( A j ) ) ( displaystyle F ( ( a_ ( i ) ), ( A_ ( j ) ) ) ). If the size of the system is changed by some scaling factor, α ( displaystyle alpha ), 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 ( ( a i ), ( α A j ) ) ( displaystyle F ( ( a_ ( i ) ), ( alpha 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, α ( displaystyle alpha ), F ( ( a i ), ( α A j ) ) = F ( ( a i ), ( A j ) ). ( displaystyle F ( ( a_ ( i ) ), ( alpha A_ ( j ) ) ) = F ( ( a_ ( i ) ), ( A_ ( j ) ) ). , ) ( This is equivalent to saying that intensive composite properties are homogeneous functions of degree 0 with respect to ( A j ) ( displaystyle ( A_ ( j ) ) ). ) It follows, for example, that the ratio of two extensive properties is an intensive property. To illustrate, consider a system having a certain mass, m ( displaystyle m ), and volume, V ( displaystyle V ). The density, ρ ( displaystyle \rho ) is equal to mass ( extensive ) divided by volume ( extensive ) : ρ = m V ( displaystyle \rho = ( \frac ( m ) ( V ) ) ). If the system is scaled by the factor α ( displaystyle alpha ), then the mass and volume become α m ( displaystyle alpha m ) and α V ( displaystyle alpha V ), and the density becomes ρ = α m α V ( displaystyle \rho = ( \frac ( alpha m ) ( alpha V ) ) ) ; the two α ( displaystyle alpha ) s cancel, so this could be written mathematically as ρ ( α m, α V ) = ρ ( m, V ) ( displaystyle \rho ( alpha m, alpha V ) = \rho ( m, V ) ), which is analogous to the equation for F ( displaystyle F ) above. The property F ( displaystyle F ) is an extensive property if for all α ( displaystyle alpha ), F ( ( a i ), ( α A j ) ) = α F ( ( a i ), ( A j ) ). ( displaystyle F ( ( a_ ( i ) ), ( alpha A_ ( j ) ) ) = alpha F ( ( a_ ( i ) ), ( A_ ( j ) ) ). , ) ( This is equivalent to saying that extensive composite properties are homogeneous functions of degree 1 with respect to ( A j ) ( displaystyle ( A_ ( j ) ) ). ) It follows from Euler 's homogeneous function theorem that F ( ( a i ), ( A j ) ) = ∑ j A j ( ∂ F ∂ A j ), ( displaystyle F ( ( a_ ( i ) ), ( A_ ( j ) ) ) = sum _ ( j ) A_ ( j ) left ( ( \frac ( partial F ) ( partial A_ ( j ) ) ) \right ), ) where the partial derivative is taken with all parameters constant except A j ( displaystyle A_ ( j ) ). This last equation can be used to derive thermodynamic relations. `` Specific '' properties See also : List of thermodynamic properties A specific property is obtained by dividing an extensive property of a system by the mass of the system. For example, heat capacity is an extensive property of a system. Dividing heat capacity, C, by the mass of the system gives the specific heat capacity, c, 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 properties derived from extensive properties Extensive property Symbol SI units Intensive property Symbol SI units Volume V m or L Specific volume * m / kg or L / kg Internal energy U J Specific internal energy u J / kg Entropy J / K Specific entropy s J / ( kg K ) Enthalpy J Specific enthalpy h J / kg Gibbs free energy J Specific Gibbs free energy g J / kg Heat capacity at constant volume J / K Specific heat capacity at constant volume J / ( kg K ) Heat capacity at constant pressure J / K Specific heat capacity at constant pressure J / ( kg K ) * Specific volume is the reciprocal of density. If 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 adjective molar, yielding terms such as molar volume, molar internal energy, molar enthalpy, and molar entropy. The symbol for molar quantities may be indicated by adding a subscript `` m '' to the corresponding extensive property. For example, molar enthalpy is H. A well known molar volume, V, is that of an ideal gas at standard conditions for temperature and pressure, with the value 22.41 L / mol. Molar Gibbs free energy is commonly referred to as chemical potential, symbolized by μ, particularly when discussing a partial molar Gibbs free energy μ for a component i in a mixture. 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 physical properties conform to neither definition. Redlich also provides examples of mathematical functions that alter the strict additivity relationship for extensive systems, such as the square or square root of volume, which may occur in some contexts, albeit rarely used. 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 identical galvanic cells are connected in parallel, the voltage of the system is equal to the voltage of each cell, while the electric charge transferred ( or the electric current ) 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 is a macroscopic quantity and is not relevant for extremely small systems. Likewise, at a very small scale color is not independent of size, as shown by quantum dots, whose color depends on the size of the `` dot ''. References ^ Jump up to : McNaught, A.D. ; Wilkinson, A. ; Nic, M. ; Jirat, J. ; Kosata, B. ; Jenkins, A. ( 2014 ). IUPAC. Compendium of Chemical Terminology, 2nd ed. ( the `` Gold Book '' ). 2.3. 3. Oxford : Blackwell Scientific Publications. ISBN 0 - 9678550 - 9 - 8. doi : 10.1351 / goldbook. E02281. ^ Jump up to : Cohen, E.R. ; et al. ( 2007 ). IUPAC Green Book ( PDF ) ( 3rd ed. ). Cambridge : IUPAC and RSC Publishing. pp. 6 ( 20 of 250 in PDF file ). ISBN 978 0 85404 433 7. Jump up ^ Canagaratna, Sebastian G. ( 1992 ). `` Intensive and Extensive : Underused Concepts ''. J. Chem. Educ. 69 ( 12 ) : 957 -- 963. Bibcode : 1992JChEd... 69... 957C. doi : 10.1021 / ed069p957. ^ Jump up to : Tolman, Richard C. ( 1917 ). `` The Measurable Quantities of Physics ''. Phys. Rev. 9 ( 3 ) : 237 -- 253. ^ Jump up to : Redlich, O. ( 1970 ). `` Intensive and Extensive Properties ''. J. Chem. Educ. 47 ( 2 ) : 154 -- 156. Bibcode : 1970JChEd... 47... 154R. doi : 10.1021 / ed047p154. 2. Jump up ^ Chang, R. ; Goldsby, K. ( 2015 ). Chemistry ( 12 ed. ). McGraw - Hill Education. p. 312. ISBN 978 - 0078021510. ^ Jump up to : Brown, T.E. ; LeMay, H.E. ; Bursten, B.E. ; Murphy, C. ; Woodward ; P. ; Stoltzfus, M.E. ( 2014 ). Chemistry : The Central Science ( 13th ed. ). Prentice Hall. ISBN 978 - 0321910417. Jump up ^ Alberty, R.A. ( 2001 ). `` Use of Legendre transforms in chemical thermodynamics '' ( PDF ). Pure Appl. Chem. 73 ( 8 ) : 1349 -- 1380. doi : 10.1351 / pac200173081349. Jump up ^ George N. Hatsopoulos, G.N. ; Keenan, J.H. ( 1965 ). Principles of General Thermodynamics. John Wiley and Sons. pp. 19 -- 20. ISBN 9780471359999. CS1 maint : Multiple names : authors list ( link ) Retrieved from `` https://en.wikipedia.org/w/index.php?title=Intensive_and_extensive_properties&oldid=801130508 '' Categories : Physical quantities Thermodynamic properties Hidden categories : CS1 maint : Multiple names : authors list Articles with specifically marked weasel - worded phrases from July 2017 Talk Contents About Wikipedia Català Español فارسی Français 한국어 हिन्दी Bahasa Indonesia Italiano עברית 日本 語 Norsk Русский 中文 Edit links This page was last edited on 17 September 2017, at 21 : 08. Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia ® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. About Wikipedia

Question: is the boiling point of water an extensive or intensive property why do you say so
Answer: the boiling point of a substance is another example of an intensive property. For example, the boiling point of water is 100 °C at a pressure of one atmosphere, which remains true regardless of quantity.