Variables, dependent extensive

Before describing these thermodynamic variables, we must talk about their properties. The variables are classified as intensive or extensive. Extensive variables depend upon the amount while intensive variables do not. Density is an example of an intensive variable. The density of an ice crystal in an iceberg is the same as the density of the entire iceberg. Volume, on the other hand, is an extensive variable. The volume of the ocean is very different from the volume of a drop of sea water. When we talk about an extensive thermodynamic variable Z we must be careful to specify the amount. This is usually done in terms of the molar property Zm, defined as... 

This equation is valid for all species Ah a fact that is a consequence of the law of definite proportions. The molar extent of reaction is a time-dependent extensive variable that is measured in moles. It is a useful measure of the progress of the reaction because it is not tied to any particular species A. Changes in the mole numbers of two species j and k can be related to one another by eliminating between two expressions that may be derived from equation 1.1.4. 

In Fig. 2.19, on the contrary, we observe that intermediate solid phases with a variable composition are formed (non-stoichiometric phases). In the diagrams shown here we see therefore examples both of terminal and intermediate phases. (For instance, the Hf-Ru diagram shows the terminal solid solutions of Ru in a and (3Hf and of Hf in Ru and the intermediate compound containing about 50 at.% Ru). These phases are characterized by homogeneity ranges (solid solubility ranges), which, in the case of the terminal phases, include the pure components and which, generally, have a variable temperature-dependent extension. 

The variables whose values are proportional to the total quantity of substances in the system are called extensive variables or extensive properties, such as the volume V and the number of moles n. The extensive variables, in general, depend on the size or quantity of the system. The masses of parts of a system, for instance, sum up to the total mass of the system, and doubling the mass of the system at constant pressure and temperature results in doubling the volume of the system as shown in Fig. 1.2. 

WHO also summarized water quality data from various sources and reported that data on nitrobenzene levels in surface water appear to be more extensive than data on levels in air. While levels are variable depending on location and season, generally low levels ( 0.1-1 pgl ) have been measured. One of the highest levels reported was 67 rgl, in the river Danube, Yugoslavia, in 1990. However, nitrobenzene was not detected in any surface water samples collected near a large number of hazardous waste sites in the United States (reported in 1988). Based on limited data, it appears that there may be greater potential for contamination of groundwater than of surface water several sites measured in the United States in the... 

Extension-contraction of the sea-surface area (by wave motion, by internal waves and by convection) prevents from reaching adsorption equilibrium. Then, the surface properties in the marine environment show a large spatial and temporal variability, depending on amount and nature of the dissolved organic compounds and on the meteo-marine conditions. The actually-occurring surface properties of sea water can be evaluated by measurements at sea (either in situ or by remote sensing). 

It is possible, as a general procedure, to form a new thermodynamic variable dependent solely on the thermodynamic state by combining any two or more of the thermodynamic variables above. An example of which we will make extensive use is specific enthalpy. Specific enthalpy, h (J/kg), is formed by amalgamating specific internal enetgy with two basic thermodynamic variables, pressure and specific volume ... 

Reconstituted spherical HDL can be made by co-sonication of selected HDL components (e.g., apo Al, PC, CE) or by extensively reacting discoidal reconstituted HDL with LCAT in the presence of an exogenous source of cholesterol. The products are spheroidal and, like the discoidal precursor particles, contain two, three, or four apo Al molecules per particle, PC, cholesterol, and a CE core. The diameters of the particles range from 80 to 120 A. Although not well studied, the conformation of apo Al appears distinct from that in the discoidal particles and is variable depending on the particle diameter (A. Jonas, 1990 M.G. Sorci-Thomas, 2002). 

In equilibriim thermodynamics the energy of a system may be considered to be a homogeneous bilinear function of pairs of intensive and extensive variables, either of which can be considered as the independent variable. For example, either pressure or volume may be considered as an independent variable depending upon the environment. The difference between the heat capacity at constant volume and at constant pressure is well known in equilibrium thermodynamics. Thus, in a single component equilibrium system where temperature. 

This chapter begins with a discussion of mathematical properties of the total differential of a dependent variable. Three extensive state functions with dimensions of energy are introduced enthalpy, Helmholtz energy, and Gibbs energy. These functions, together with internal energy, are called thermodynamic potentials. Some formal mathematical manipulations of the four thermodynamic potentials are described that lead to expressions for heat capacities, surface work, and criteria for spontaneity in closed systems. 

The type of system most commonly encountered in chemical engineering apphcations has the primary characteristic variables pressure, volume, temperature and compositiom Such systems are made up of fluids, liquid or gas, and are called PVT systems. The conservation laws concern the accumulation rate of mass, amount of components, energy and momentum of such a system. The variables depend on the extent of a system and are therefore called extensive variables. Extensive properties are additive. When mirltiple systerrrs are combined to a new system, the new value of the variable will be the sum of the initial ones. In contrast, temperature, pressttre, specific volirme and composition are conditions imposed upon or exhibited by the system. These are intensive variables. When systems are combined to a new system, the new value of the variable will be the equilibrium value of the initial ones. 

Generally speaking, intermolecular forces act over a short range. Were this not the case, the specific energy of a portion of matter would depend on its size quantities such as molar enthalpies of formation would be extensive variables On the other hand, the cumulative effects of these forces between macroscopic bodies extend over a rather long range and the discussion of such situations constitutes the chief subject of this chapter. 

Postiilate 5 affirms that the other molar or specific thermodynamic properties of PVT systems, such as internal energy U and entropy S, are also functions of temperature, pressure, and composition. Tnese molar or unit-mass properties, represented by the plain symbols U, and S, are independent of system size and are called intensive. Temperature, pressure, and the composition variables, such as mole fraction, are also intensive. Total-system properties (V U S ) do depend on system size, and are extensive. For a system containing n moles of fluid, M = nM, where M is a molar property. 

---