Intensive property described

The state (or behaviour) of a system is described by variables or properties which may be classified as (a) extensive properties such as mass, volume, kinetic energy and (b) intensive properties which are independent of system size, e.g., pressure, temperature, concentration. An extensive property can be treated like an intensive property by specifying that it refers to a unit amount of the substance concerned. Thus, mass and volume are extensive properties, but density, which is mass per unit volume, and specific volume, which is volume per unit mass, are intensive properties. In a similar way, specific heat is an intensive property, whereas heat capacity is an extensive property. 

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... 

As described above, the combination of EPR and Mossbauer spectroscopies, when applied to carefully prepared parallel samples, enables a detailed characterization of all the redox states of the clusters present in the enzyme. Once the characteristic spectroscopic properties of each cluster are identified, the determination of their midpoint redox potentials is an easy task. Plots of relative amounts of each species (or some characteristic intensive property) as a function of the potential can be fitted to Nernst equations. In the case of the D. gigas hydrogenase it was determined that those midpoint redox potentials (at pFi 7.0) were —70 mV for the [3Fe-4S] [3Fe-4S]° and —290 and —340mV for each of the [4Fe-4S]> [4Fe-4S] transitions. 

The objective of this section is to establish a relationship between the time rate of change of an extensive property of a system and the behavior of the associated intensive property within a control volume that surrounds the system at an instant in time. This kinematic relationship, described in terms of the substantial derivative, is central to the derivation of conservation equations that describe fluid mechanics. 

Equation (6.35b) shows that the new intensive variable, chemical potential pi, as introduced in this chapter, is actually superfluous for the case c = 1, because its variations can always be expressed in terms of the old variations dT dP. Thus, as stated in Inductive Law 1 (Table 2.1), only two degrees of freedom (independently variable intensive properties) suffice to describe the thermodynamic variability of a simple c = 1 system. This confirms (as expected) that chemical potential pu only becomes an informative thermodynamic variable when chemical change is possible, that is, for c > 2 chemical components. 

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... 

The characteristics, or properties, that are used to describe matter can be classified in several ways. Physical properties are those that can be determined without changing the chemical composition of the sample, whereas chemical properties are those that do involve a chemical change in the sample. Intensive properties are those whose... 

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%. 

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. 

The intensive variables T, P, and nt can be considered to be functions of S, V, and dj because U is a function of S, V, and ,. If U for a system can be determined experimentally as a function of S, V, and ,, then T, P, and /q can be calculated by taking the first partial derivatives of U. Equations 2.2-10 to 2.2-12 are referred to as equations of state because they give relations between state properties at equilibrium. In Section 2.4 we will see that these Ns + 2 equations of state are not independent of each other, but any Ns+ 1 of them provide a complete thermodynamic description of the system. In other words, if Ns + 1 equations of state are determined for a system, the remaining equation of state can be calculated from the Ns + 1 known equations of state. In the preceding section we concluded that the intensive state of a one-phase system can be described by specifying Ns + 1 intensive variables. Now we see that the determination of Ns + 1 equations of state can be used to calculate these Ns + 1 intensive properties. 

This thermodynamic constraint arises because the intensive properties that describe an equilibrium state of a single phase (e.g., T, P, and component activities) cannot all be varied independently. Equation 3.33 can be written in the compact form ... 

In the above equation the exergy is written as an intensive property, e.g. per mol of fuel. The subscript "1" represents the original thermodynamic state, the subscript "o" describes the state when thermodynamic equilibrium with the environment is established. In these considerations it is arbitrarily assumed that any reaction product is in equilibrium with the environment when it has a temperature of T = 300K and a pressure of P = lbar. 

Thermal conductivity is the intensive property of a material that indicates its ability to conduct heat. For one-dimensional heat flow in the x-direction the steady state heat transfer can be described by Fourier s law of heat conduction ... 

Balance equations of extensive quantities describe a change in a system (except in rare gases and shock waves). These balance equations also contain intensive parameters specifying the local state of a continuous medium. Intensive parameters described by the macroscopic properties of the medium are based on the behavior of a large number of particles. 

Practice Problem 1.4 Which is heavier, (a) bricks or straw (b) one package of cheese or two of those packages of cheese (c) Which of these uses of the word heavier describes an intensive property and which an extensive... 

The retention is related to the size, charge, diffusion coefficient, thermal diffusion factor, and so forth of the separated species in polarization FFF. As concerns the focusing FFF, the retention is usually related with the intensive properties of the fractionated species. Consequently, the FFF can be used to characterize the properties related to the retention. Because the entry Focusing FFF of Particles and Macromolecules is fully devoted to the focusing FFF, only the polarization FFF methods will be described here. 

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. 

A state is the physical condition of a system described by a specific set of thermodynamic property values. There are two types of properties that describe the macroscopic state of a system 1) extensive and 2) intensive. Extensive properties are proportional to the size of the system intensive properties are independent of the size of the system. If you combine two identical systems and a property is the same... 

This is the defining equation for the fundamental material function Lx, the spectral intensity, it describes the directional and wavelength dependence of the energy radiated by a body and has the character of a distribution function. The (thermodynamic) temperature T in the argument of Lx points out that the spectral intensity depends on the temperature of the radiating body and its material properties, in particular on the nature of its surface. The adjective spectral and the index A show that the spectral intensity depends on the wavelength A and is a quantity per wavelength interval. The Si-units of Lx are W/(m2/um sr). The units pm and sr refer to the relationship with dA and dec. 

The other group of properties are the intensive properties these are characteristic of the substance (or substances) present, and are independent of its (or their) amount. Temperature and pressure are intensive properties, and so also are refractive index, viscosity, density, surface tension, etc. It is because pressure and temperature are intensive properties, independent of the quantity of matter in the system, that they are frequently used as variables to describe the thermodynamic state of the system. It is of interest to note that an extensive property may become an intensive property by specifying unit amount of the substance concerned. Thus, mass and volume are extensive, but density and specific volume, that is, the mass per unit volume and volume per unit mass, respectively, are intensive properties of the substance or system. Similarly, heat capacity is an extensive property, but specific heat is intensive. 

The twelve structural parameters defined above are all extensive variables. In order to convert them into intensive variables for use in the correlation for Tg, which is an intensive property, they will all be scaled by the number N of vertices in the hydrogen-suppressed graph of the repeat unit, as described by Equation 2.8 in Section 2.C. In other words, xj/N, x2/N,. .., x12/N, will be used as linear regression variables in the correlation for Tg. 

The state of an equilibrium phase is specified by its chemical composition and a relatively few intensive properties, generally two, e.g., temperature and pressure, temperature and mass density, or density and pressure. The number and kind of intensive properties required are determined by experience. To specify the state of a nonequilibrium system generally requires more than the values of a few intensive properties. Thus a system undergoing heat transfer may require a mathematical function to describe its temperature distribution and thus its state. 

Temperature, one of the seven basic physical quantities of the International System (SI) of units, is that property which describes the thermodynamic states of a system and is a measure of that system s hotness, as expressed in terms of any of several arbitrary scales. It is an indicator of the direction in which energy will flow spontaneously when two bodies are brought into contact, that is, from the hotter body to the colder one. Temperature, unlike mass and volume, is an intensive property, that is, it is independent of the quantity of matter. 

The state of the system is given by a set of values of properly chosen physical variables. To determine unambiguously the state of the simplest system (a pure substance in one phase) one should know two properties (e.g. temperature and pressure) in addition to the quantity (moles). To describe the state of more complex systems one should know more properties (e.g. the concentrations of individual species). The thermodynamic properties of the system depending only on the state and not on the way by which the system has reached the given state, are called state functions. The typical fundamental state functions are temperature, pressure, volume and concentration of the individual components of the system. The thermodynamic properties are usually classified into extensive and intensive ones. The extensive properties are proportional to the quantity of the substance in the system. Therefore, they are additive, i.e. the total extensive property of the system equals the sum of the extensive properties of the individual parts of the system. Typical extensive quantities are weight, energy, volume, number of moles. On the other hand, the intensive properties do not depend on the quantity of the substance in the system (pressure, temperature, concentration, specific quantities, specific resistance, molar heat, etc.). 

It is possible to subdivide the properties used to describe a thermodynamic system (e.g., T, P, V,U,...) into two main classes termed intensive and extensive variables. This distinction is quite important since the two classes of variables are often treated in significantly different fashion. For present purposes, extensive properties are defined as those that depend on the mass of the system considered, such as volume and total energy content, indeed all the total system properties (Z) mentioned above. On the other hand, intensive properties do not depend on the mass of the system, an obvious example being density. For example, the density of two grams of water is the same as that of one gram at the same P, T, though the volume is double. Other common intensive variables include temperature, pressure, concentration, viscosity and all molar (Z) and partial molar (Z, defined below) quantities. ... 

The ideal gas law, pV = is a relation between the four variables that describe the state of any gas. As such, it is an equation of state. The variables in this equation fall into two classes n and V are extensive variables (extensive properties), while p and T are intensive variables (intensive 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. 

In this section we describe two methods for determining partial molal quantities for two-component systems from experimental data. In both cases the experimental data necessary are the behavior of the extensive property G or, equivalently, the intensive property as a function of the mole fraction of one of the components. (More details can be found in the book Gilbert Newton Lewis and Merle Randall, Thermodynamics and the Free Energy of Chemical Substances, pp. 36-41, McGraw-Hill Book Company, Inc., New York, 1923.)... 

The atomic theory focuses on the extensive properties of matter such as mass and volume, whereas the kinetic theory states that particles are dynamic and separated by a vacuum describing the intensive properties of matter (Krnel, Watson Glazar, 1998). The next five propositions - taken from de Vos Verdonk, (1996, p.658) and Garnett (1984, p. 153) -summarise the kinetic theory. 

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