Intensive properties, examples

The term ff denotes the number of independent phase variables that should be specified in order to establish all of the intensive properties of each phase present. The phase variables refer to the intensive properties of the system such as temperature (T), pressure (P), composition of the mixture (e.g., mole fractions, x ), etc. As an example, consider the triple point of water at which all three phases—ice, liquid water, and water vapor—coexist in equilibrium. According to the phase rule,... 

Properties are also classified according to their dependence on the mass of a sample. An intensive property is a property that is independent of the mass of the sample. For example, temperature is an intensive property, because we could take a sample of any size from a uniform bath of water and measure the same temperature (Fig. A.2). An extensive property is a property that does depend on the mass ( extent ) of the sample. Volume is an extensive property 2 kg of water occupies twice the volume of 1 kg of water. 

Some intensive properties are ratios of two extensive properties. For example, the property density, d, mentioned above, is a ratio of the mass, m, of a sample divided by its volume, V ... 

Unlike mass and volume, density does not vary with the amount of a substance. Notice in Figure 1-20 that all the corks float, regardless of their sizes. Notice also that all the pieces of lead sink, regardless of their sizes. Dividing a sample into portions changes the mass and volume of each portion but leaves the density unchanged. A property that depends on amount is called extensive. Mass and volume are two examples of extensive properties. A property that is independent of amount is called intensive. Density and temperature are intensive properties. 

This relationship is expressed in extensive properties that depend on the extent of the system, as opposed to intensive properties that describe conditions at a point in the system. For example, extensive properties are made intensive by expressing them on a per unit mass basis, e.g. s = S/m density, p 1 /v, v V/m. For a pure system (one species), Equation (1.2) in intensive form allows a definition of thermodynamic temperature and pressure in terms of the intensive properties as... 

The phase rule states that, when equilibrium conditions are sustained, a minimum number of intensive properties of the (subsurface) system can be used to calculate its remaining properties. An intensive property is a property that is independent of the amount of substance in the domain. Examples of intensive properties include temperature (7), pressure (P), density (p), and chemical potential (p), which is a relative measure of the potential energy of a chemical compound. The phase rule specifies the minimum number of intensive properties that must be determined to obtain a comprehensive thermodynamic depiction of a system. 

A system is homogeneous when the intensive properties are not a function of position, while a system is heterogeneous when the composition of a given mixture varies as a function of position. For example, the subsurface liquid phase usually comprises an aqueous solution incorporating a number of solutes in contaminated subsurface environments, nonaqueous phase liquids also may be present. The air phase of the subsurface includes gases with various partial pressures, and the solid phases comprise a mixture of minerals and organic compounds. 

Properties that do not vary with the amount of mass of a substance - for example, temperature, pressure, surface tension, mole fraction - are termed intensive properties. On the other hand, those properties that vary in proportion to the total mass of substances - for example, total volume, total mass, and heat capacity - are termed extensive properties. 

It should be noted, however, that some extensive properties become intensive properties, in case their specific values - that is, their values for unit mass or unit volume - are considered. For example, specific heat (i.e., heat capacity per unit mass) and density (i.e., mass per unit volume) are intensive properties. 

Sometimes, capital letters and small letters are used for extensive and intensive properties, respectively. For example, Cp indicates heat capacity (kJ C ) and Cp specific heat capacity (kJ kg °C ). Measured values of intensive properties for common substances are available in various reference books [6]. 

It should be emphasized that the criterion for macroscopic character is based on independent properties only. (The importance of properly enumerating the number of independent intensive properties will become apparent in the discussion of the Gibbs phase rule, Section 5.1). For example, from two independent extensive variables such as mass m and volume V, one can obviously form the ratio m/V (density p), which is neither extensive nor intensive, nor independent of m and V. (That density cannot fulfill the uniform value throughout criterion for intensive character will be apparent from consideration of any 2-phase system, where p certainly varies from one phase region to another.) Of course, for many thermodynamic purposes, we are free to choose a different set of independent properties (perhaps including, for example, p or other ratio-type properties), rather than the base set of intensive and extensive properties that are used to assess macroscopic character. But considerable conceptual and formal simplifications result from choosing properties of pure intensive (R() or extensive QQ character as independent arguments of thermodynamic state functions, and it is important to realize that this pure choice is always possible if (and only if) the system is macroscopic. 

The thermodynamic state is therefore considered equivalent to specification of the complete set of independent intensive properties 7 1 R2, Rn. The fact that state can be specified without reference to extensive properties is a direct consequence of the macroscopic character of the thermodynamic system, for once this character is established, we can safely assume that system size does not matter except as a trivial overall scale factor. For example, it is of no thermodynamic consequence whether we choose a cup-full or a bucket-full as sample size for a thermodynamic investigation of the normal boiling-point state of water, because thermodynamic properties of the two systems are trivially related. 

Physical properties are termed either intensive or extensive. Intensive properties are independent of the quantity of material present. Density, specific volume, and compressibility factor are examples. Properties such as volume and mass are termed extensive their values are determined by the total quantity of matter present. 

An intensive property is one whose values are not additive and do not vary with the quantity of the sample in the system. Examples are temperature, pressure and density. 

Properties such as internal energy, volume and entropy are called extensive because their values for a given phase are proportional to the mass or volume of the phase. The value of an extensive property of an entire system is the sum of the values of each of the constituent phases. The molar value of an extensive property is that for a properly defined gram-molecular weight or mole of material. The specific value of an extensive property is that per unit weight (eg, one gram of material). A property is called intensive if its value for a given phase is independent of the mass of the phase. Temp and pressure are examples of such intensive properties... 

In the calorimetric approach, it is necessary to know the heat of fusion of the totally crystalline polymer. This can be obtained from melting-point depression measurements, as described in the following section. The basic idea depends on the fact that the melting temperature is independent of the size of the system, since it is an intensive property. The extent to which it is depressed by the presence of solvent can be used to calculate a heat of fusion characteristic of the crystallites, irrespective of how many are present. This is therefore the heat of fusion of the 100% crystalline polymer. The fractional crystallinity in an actual sample is then the ratio of its calorimetrically measured heat of fusion per gram to that of the 100% crystalline polymer. For example, if the actual polymer has a heat of fusion of 7 cal per gram, and the 100% crystalline polymer a heat of fusion of 10 cal per gram, then the fractional crystallinity is 0.7, and the percentage crystallinity is 70%. 

The state of a system is defined by its properties. Extensive properties are proportional to the size of the system. Examples include volume, mass, internal energy, Gibbs energy, enthalpy, and entropy. Intensive properties, on the other hand, are independent of the size of the system. Examples include density (mass/volume), concentration (mass/volume), specific volume (volume/mass), temperature, and pressure. 

A thermodynamic property is said to be extensive if the magnitude of the property is doubled when the size of the system is doubled. Examples of extensive properties are volume V and amount of substance n. A thermodynamic property is said to be intensive if the magnitude of the property does not change when the size of the system is changed. Examples of intensive properties are temperature, pressure, and the mole fractions of species. The ratio of two extensive properties is an intensive property. For example, the ratio of the volume of a one-component system to its amount is the molar volume Vm = V/n. 

Experience shows that for a system that is a homogeneous mixture of Ns substances, Ns + 2 properties have to be specified and at least one property must be extensive. For example, we can specify T, P, and amounts of each of the Ns substances or we can specify T, P, and mole fractions x, of all but one substance, plus the total amount in the system. Sometimes we are only interested in the intensive state of a system, and that can be described by specifying Ns + 1 intensive properties for a one-phase system. For example, the intensive state of a solution involving two substances can be described by specifying T, P, and the mole fraction of one of substances. 

Unlike free energy G, which is an extensive property (such as for example volume or internal energy), chemical potential p. is an intensive property of the system (such as e. g. temperature and pressure). For this reason the chemical potential of the solute at given temperature and pressure does not depend on the absolute amounts of individual components in the solution but solely on the relative composition, i. e. relative amounts of the substances forming the solution. 

In nonequilibrium systems, the intensive properties of temperature, pressure, and chemical potential are not uniform. However, they all are defined locally in an elemental volume with a sufficient number of molecules for the principles of thermodynamics to be applicable. For example, in a region A , we can define the densities of thermodynamic properties such as energy and entropy at local temperature. The energy density, the entropy density, and the amount of matter are expressed by uk(T, Nk), s T, Nk), and Nk, respectively. The total energy U, the total entropy S, and the total number of moles N of the system are determined by the following volume integrals ... 

Most thermodynamic variables fall into two types. Those representing extensive properties of a phase are proportional to the amount of the phase under consideration they are exemplified by the thermodynamic functions V, E, H, S, A, G. Those representing intensive properties are independent of the amount of the phase they include p and T. Variables of both types may be regarded as examples of homogeneous functions of degree 1 that is, functions having the property... 

A pure substance in the absence of motion, gravity, surface effects, electricity and magnetism, has three intensive properties only two of which are independent, viz., pressure, temperature and concentration (conclusion based on experimental or day-to-day observation). The two independent intensive properties are often referred to as the two degrees of freedom. For example, if we keep water vapour in an evacuated chamber - say, above its critical... 

Some properties of a sample of a substance depend on the quantity of the sample. These properties are called extensive properties. For example, the weight of a solid sample depends on how much of the substance is present. Other properties, such as color and taste, do not depend on how much is present. These properties are known as intensive properties. Intensive properties are much more useful for identifying substances. 

Density is an intensive property, useful in identifying substances. For example, gold can be distinguished from iron pyrite by their greatly differing densities—... 

In the context of how we use the term, intensity refers to the intensive property of the disinfectant. Intensive properties, in turn, are those properties that are independent of the total mass or volume of the disinfectant. For example, concentrations are expressed as mass per unit volume the phrase per unit volume makes concentration independent of the total volume. Hence, concentration is an intensive property and it expresses the intensity of the disinfectant. Another intensive property is radiation from an ultraviolet light. This radiation is measured as power impinging upon a square unit of area. The per unit area here is analogous to the per unit volume. Thus, radiation is independent of total area and is, therefore, an intensive property that expresses the intensity of the radiation, which, in this case, is the intensity of radiation of the ultraviolet light. 

An intensive property may be defined as a property that is unchanged when the size of the system is increased by adding to it any number of systems that are identical to the original system. An extensive property is one that increases in proportion to the size (for example, volume) of the system in such a process. Thus an intensive property may be formed from any extensive property through division by any other extensive property. 

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