Intensive and Extensive Properties

In the study of thermodynamics, extensive and intensive properties are constantly employed. In this chapter we discuss the dependence of extensive properties on the mass of the system and demonstrate how to define a set of intensive properties related to a given extensive property. We shall describe experimental methods for the measurement of these sets of intensive properties. Finally, we present a list of a number of commonly used composition variables and show how these may be related to each other. 

We consider a homogeneous system of r components. No external force may act on this system except for a uniform normal pressure. The system is also assumed to be so large that the configuration of its surface does not affect its bulk properties. Under these conditions, a general extensive property of this system, G, may be considered to be a function of temperature r, pressure/ , and the masses Wj,. . . , m, of the r components. Thus, we may write 

It is found by experiment that the extensive properties are linear homogeneous functions of the masses Wi,. . . at constant Tandp. That is, 

The expression (2-4) provides the definition of a partial molal quantity if the gram-molecular weight (mole) is the unit of mass and of a partial specific quantity if the gram is the unit of mass. In the future, the symbol i will denote a partial molal quantity defined by the relation 

It is sometimes convenient to consider an intensive property a mean molal property, defined by 

A quantitative property of a system describes some macroscopic feature that, although it may vary with time, has a particular value at any given instant of time. 

Most of the properties studied by thermodynamics may be classified as either extensive or intensive. We can distinguish these two types of properties by tbe following considerations. 

If we imagine the system to be divided by an imaginary surface into two parts, any property of the system that is the sum of the property for the two parts is an extensive property. That is, an additive property is extensive. Examples are mass, volume, amount, energy, and the surface area of a solid. 

Thermodynamics and Chemistry, second edition, version 3 2011 by Howard DeVoe. Latest version www.chem.umd.edu/thermobook 

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. 

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Students have severe difficulties in differentiating between heat and temperature. The distinction between extensive and intensive properties is... 

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]. 

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... 

In this chapter we have discussed systems involving PV work and the transfer of species into or out of the system (/t.-du ), but other kinds of work may be involved in a biochemical system. The extensive and intensive properties that are involved in various types of work are given in Table 2.1. 

Extensive and intensive properties Physical properties can be further described as being one of two types. Extensive properties are dependent upon the amount of substance present. For example, mass, which depends on the amount of substance there is, is an extensive property. Length and volume are also extensive properties. Density, on the other hand, is an example of an intensive property of matter. Intensive properties are independent of the amount of substance present. For example, density of a substance (at constant temperature and pressure) is the same no matter how much substance is present. 

This result is an example of a general difference between all corresponding pairs of extensive and intensive properties. The extensive property spans a much wider range, most of which incorporates the effects of the large differences between the sizes of polymeric repeat units. The intensive property, which reflects the true differences between the properties of the polymers independently of the sizes of their repeat units, spans a much narrower range and is hence predicted with somewhat lower accuracy and certainty than the extensive property. 

In this text, no attempt will be made to use nomenclature to distinguish between extensive and intensive properties or between an extensive property and its mass or mole-normalized specific counterpart. You should be aware, then, that quantities appearing in certain equations may represent an extensive property or its specific (e.g., per-mole) counterpart depending on the situation. For example, AG could have units of kilojoules or kilojoules per mole depending on the context. In general, this should not cause confusion, as the context and units involved will almost always be spelled out explicitly. 

These properties may be classified as extensive and intensive properties. 

General Features of SI Units 14 Some Important SI Units in Chemistry 14 Extensive and Intensive Properties 20... 

In thermodynamics it often is necessary to distinguish between extensive and intensive properties. The value of an extensive property changes with the amount of material in the system, whereas the value of an intensive property is independent of the amount of material. Examples of extensive properties are mass, volume, and total free energy, enthalpy and entropy, whereas intensive properties include pressure, temperature, density and molar free energy, enthalpy and entropy. Generally, systems at equilibrium are defined in terms of their intensive properties. 

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