Intensive properties, definition

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... 

Definition Two macroscopic systems having all the same numerical values of the independent intensive properties are said to be in the same state (regarded as identical for thermodynamic purposes). 

Comparison of the combined first/second law (4.28) with (4.30) leads to the more general and rigorous thermodynamic definitions for the intensive properties T, —P respectively conjugate to the extensive properties S, V ... 

We have previously emphasized (Section 2.10) the importance of considering only intensive properties Rt (rather than size-dependent extensive properties Xt) as the proper state descriptors of a thermodynamic system. In the present discussion of heterogeneous systems, this issue reappears in terms of the size dependence (if any) of individual phases on the overall state description. As stated in the caveat regarding the definition (7.7c), the formal thermodynamic state of the heterogeneous system is wholly / dependent of the quantity or size of each phase (so long as at least some nonvanishing quantity of each phase is present), so that the formal state descriptors of the multiphase system again consist of intensive properties only. We wish to see why this is so. 

Before studying the properties of gases and liquids, we need to understand the relationship between the two phases. The starting point will be a study of vapor pressure and the development of the definition of the critical point. Then we will look in detail at the effects of pressure and temperature on one of the intensive properties of particular interest to petroleum engineers specific volume. 

Some authors state that the reaction rate is d /dt where t stands for time. But dfydt is proportional to the size of the reactor and, hence, is an extensive property like , and not an intensive property, as should be the reaction rate, according to the definition of the term. The derivative dt /dt is to be called the reactor productivity, but not the reaction rate. 

This section reviews some basic definitions and formulas in thermodynamics. These definitions will be used to develop energy balances to describe cooling tower operations. In our discussions we will use the following terms system, property, extensive and intensive properties, and... 

Comparing Eq. (1.109) with Eq. (1.107) yields the definitions of intensive properties for the partial differentials... 

The compound contains 92.3% carbon, no matter what die size of the sample is. Percent composition is an intensive property that is, compounds have definite compositions. 

The chemical potential provides the fundamental criteria for determining phase equilibria. Like many thermodynamic functions, there is no absolute value for chemical potential. The Gibbs free energy function is related to both the enthalpy and entropy for which there is no absolute value. Moreover, there are some other undesirable properties of the chemical potential that make it less than suitable for practical calculations of phase equilibria. Thus, G.N. Lewis introduced the concept of fugacity, which can be related to the chemical potential and has a relationship closer to real world intensive properties. With Lewis s definition, there still remains the problem of absolute value for the function. Thus,... 

An intensive property is a characteristic of a system that does not depend on the size of the system. That is, doubling the size of the system leave the value of an intensive property unchanged. Examples of intensive properties are pressure, temperature, density, molar volume, etc. By definition, an intensive property can only be a function of other intensive properties. It cannot be a function of properties that are extensive because it would then depend on the size of the system. 

The properties of random copolymers can be estimated by using weighted averages for all extensive properties, and the appropriate definitions for the intensive properties in terms of the extensive properties. Let lrq, m2,. .., mn denote the mole fractions (see Section l.D) of n different types of repeat units in a random copolymer. [The most common random copolymers have n=2. Terpolymers (n=3) are also often encountered.] The n mole fractions then add up to one, and the extensive properties of a random copolymer can be estimated by using mole fractions as weight factors ... 

The symbol Pi was first used by Gibbs and called by him the chemical potential of component i. It can be seen from Eq. (6-52) and the definition of partial molal quantities [Eq. (2-5)] that Pi is the partial molal free energy /( and is an intensive property. 

A heterogeneous system is one consisting of two or more phases. By definition, these are separated from each other by surfaces of discontinuity in one or more of the intensive properties. We will assume that the phases are originally isolated, with each of them in internal equilibrium, and thus that each phase is homogeneous. The problem is thereby reduced to finding conditions on the intensive properties which are necessary and sufficient to ensure equilibrium after the restraint of isolation is removed. The heterogeneous system considered here is an solated system in which no chemical reactions occur. 

The crystal orbital approach (see ref. 94 for a review of the recent computational developments in this field) has dominated the electronic structure calculations on polymers for several years. However, the recently published reports on the finite-cluster calculations reveal that the latter methodology has several definite advantages over the traditional approach. Let P(N) be an extensive property of a finite cluster X-(-A-)j -Y, where N is the number of repeating units denoted by A, while X and Y stand for terminal groups. The corresponding intensive properties, p(N) = P(N)/N, are known only for integer values of N. However, provided the polymer in question is not metallic, P(v) can be approximated by a smooth function p(v) of v = 1/N, which in turn can be extrapolated to v = 0 yielding the property of the bulk polymer. 

These operational distinctions between extensive and intensive avoid ambiguities that can occur in other definitions. Some of those definitions merely say that extensive properties are proportional to the amount of material N in the system, while intensive properties are independent of N. Other definitions are more specific by identifying extensive properties to be those that are homogeneous of degree one in N, while intensive properties are of degree zero (see Appendix A). 

Any extensive property can be made intensive by dividing it by the total amount of material in the system however, not all extensive properties are proportional to the amount of material. For example, the interfacial area between the system and its boundary satisfies our definition of an extensive property, but this area changes not only when we change the amount of material but also when we merely change the shape of the system. Further, although some intensive properties can be made extensive by multiplying by the amount of material, temperature and pressure carmot be made extensive. 

For intensive properties, the generic forms for the residual properties are all obtained by combining (4.1.16) with the definition (4.2.11) ... 

Here/represents an intensive property value for the real mixture, and all three terms in (5.2.1) are at the same temperature T, pressure P, composition x, and phase. The excess properties provide a convenient way for measuring how a real mixture deviates from an ideal solution. In general, an excess property/ may be positive, negative, or zero. An ideal solution will have all excess properties equal to zero. Note that the value for depends on the choice of standard state used to define the ideal solution. Further note that the definition (5.2.1) is not restricted to any phase excess properties may be defined for solids, liquids, and gases, although they are most commonly used for condensed phases. 

In Sections 2 to 4 critical phenomena will be of primary importance since they make possible a systematic discussion of all types of phase behaviour in fluid mixtures and of the relationships between them. The definition of a critical point for a mixture is essentially the same as that for a pure component at a critical point all intensive properties of two phases in equilibrium become identical. Whereas pure substances are characterized by a critical point for the equilibrium gas-liquid, binary systems exhibit a critical line in the three-dimensional p-T-x space (where x denotes mole fraction), and systems with n components an ( — l)-dimensional critical surface in the ( i + l)-dimensional p-T-Xi-X2. .. Xn-i space for all kinds of fluid-fluid equilibria. 

What has just been said, to the effect that two intensive properties of a phase usually determine the values of the rest, applies to mixtures as well as to pure substances. Thus a given mixture of alcohol and water has definite properties at a chosen pressure and density. On the other hand, in order to specify which particular mixture is under discussion it is necessary to choose an extra set of variables, namely, those describing the chemical composition of the system. These variables depend on the notion of the pure substance namely, a substance which cannot be separated into fractions of different properties by means of the same processes as those to which we intend to apply our... 

Sometimes a more restricted definition of an extensive property is used The property must be not only additive, but also proportional to the mass or the amount when intensive properties remain constant. According to this definition, mass, volume, amount, and energy are extensive, but surface area is not. 

It should be apparent that a system with thermal equilibrium has a single value of T, and one with meehanieal equilibrium has a single value of p, and this allows the state to be described by a minimal number of independent variables. In contrast, the definition of a nonequifibrium state with nonuniform intensive properties may require a very large number of independent variables. 

These definitions show that a is the fractional volume increase per unit temperaffire increase at constant pressure, and kt is the fractional volume decrease per unit pressure increase at constant temperature. Both quantities are intensive properties. Most substances have positive values of and all substances have positive values of kt, because a pressure increase at constant temperature requires a volume decrease. 

A tall column of gas whose intensive properties are a function of elevation may be treated as an infinite number of uniform phases, each of infinitesimal vertical height. We can approximate this system with a vertical stack of many slab-shaped gas phases, each thin enough to be practically uniform in its intensive properties, as depicted in Fig. 8.1. The system can be isolated from the surroundings by confining the gas in a rigid adiabatic container. In order to be able to associate each of the thin slab-shaped phases with a definite constant elevation, we specify that the volume of each phase is constant so that in the rigid container the vertical thickness of a phase cannot change. 

Consider a system in an equilibrium state. In this state, the system has one or more phases each phase contains one or more species and intensive properties such as T, p, and the mole fraction of a species in a phase have definite values. Starting with the system in this state, we can make changes that place the system in a new equilibrium state having the same kinds of phases and the same species, but different values of some of tbe intensive properties. The number of different independent intensive variables that we may change in this way is the number of degrees of freedom or variance, F, of the system. 

Phase - a physically distinct part of a system whose intensive properties are homogeneous and which has definite bounding surfaces. 

An experimentally determined value is referred to as an apparent property value if it depends on system parameters, for instance, the rate at which the experiment is performed. An example of a rate dependent property is viscosity. By definition, the intrinsic value of a rate dependent property is the extrapolated value in regards of an infinite time period over which the property is obtained. There are properties that are combinations of truly independent properties, e.g., the material density as the mass per unit volume. The properties of foremost interest are intensive properties, i.e., properties that are independent of the size of a system. 

However, it is not impossible that in certain forms of intensive specialization, definite differences may develop in the DNA also, particularly as regards its physico-chemical properties. For example, reports have been published indicating differences between DNA of lymphocytes and neutrophils in their ability to be hydrolyzed by desoxyribonuclease land II (Gokcen, 1962). 

---