Macroscopic definition

Entropy is interpreted as the number of microscopic arrangements included in the macroscopic definition of a system. The second law is then used to derive the distribution of molecules and systems over their states. This allows macroscopic state functions to be calculated from microscopic states by statistical methods. 

Because thermodynamics describes macroscopic behaviors, we need a macroscopic definition of the ideal solution in addition to the microscopic description given above. We define an ideal solution as one that, for each of its components, at all T and P and over the entire range of concentrations,... 

See, for example, Chap. 2 in G. Sposito, The Surface Chemistry of Soils, Oxford University Press, New York, 1984. The location of an interface is a molecular-scale concept that macroscopic definitions like Eq. 4.1 cannot make precise. That the interface is likely to be located within three molecular diameters of the periphery of an adsorbent solid is sufficient detail for the application of the concepts in the present section. See D. H. Everett, op. cit.,1 for additional discussion of the interface to which Eq. 4.1 applies (known technically as a Gibbs dividing surface). 

A physical system can be said to be living if it is able to transform external energy/matter into an internal process of self-maintenance and self-generation. This common sense, macroscopic definition, finds its equivalent at the cellular level in the notion of autopoiesis. This can be generalised to describe the general pattern for minimal life, including artificial life. In real life, the autopoietic network of reactions is under the control of nucleic acids and the corresponding proteins. 

Equations (6.299) and (6.300) show that Onsager s reciprocal rules hold. The Js eq and Jweq have a microscopic definition represented by perturbation matrix elements and a macroscopic definition represented by the equilibrium exchange rate. As long as the criteria of linearization are satisfied, the statistical rate theory may be used to describe systems with temperature differences at an interface besides the driving forces of pressure and concentration differences. 

Thus the equal weight-rule rephrases the macroscopic definition of phase coexistence Two phases coexists if they have equal pressure at equal chemical potential. 

Note also that the definition of a pure substance in terms of a combustion analysis ("elemental analysis," going back to von Liebig) is a macroscopic definition, based on weighing macroscopic quantities of material. 

There are two possible definitions of the Gruneisen parameter, one microscopic and the other macroscopic. The microscopic definition involves a model for interactions on an atomic level, while the macroscopic definition involves measurable parameters. 

In the previous section a macroscopic definition of the free and total surface energy as the energy excess within the interface was introduced. An alternative way of addressing this matter is an approximate evaluation of the... 

Equation 3.53 provides a molecular-level interpretation of Eq. 3.50. The exclusion volume, introduced in Eq. 1.9, is related to Eq. 3.53 through the macroscopic definition... 

Fay are independent of the density of constituent e if e a,y. This may be regarded as a macroscopic definition of binary drags, i.e. the drag force between the constituents a and y is independent of the presence of other constituents. 

Equation fl7-421 or f 17-431 are the RT equations for UF. They are particularly sinple because the inherent rejection R° is based on experimental data. Note that the retention definition for UF is microscopic, which is different than the macroscopic definition used for RO (Eq. ri7-24all. The RT equations for UF depend only on the inherent solute rejection and M. For a perfectly mixed membrane module we assume tiiat Xj. = x. Then either Eq. tl7-421 or 117-431 written in terms of can be solved... 

It is indeed interesting to see that there is a perfect compatibility of the macroscopic definitions of pressure, temperature and even entropy, with the microscopic ones, as may be seen at an extremely elementary level, using a model as the Einstein solid for accounting for the distribution of energy (Costa Pereira, 1990e). 

Although it is difficult to give an exact definition of a membrane, a genoal definitipn amid be a selective barrier between two phases, the term selective being inherent to a membrane or a membrane process. It should be noted that this is a macroscopic definition while separation should be considered at the microscopic level. The definition says nothing about membrane structure nor membrane function. 

Gelation is defined as the point during polymerization when the polymer transforms from a hquid to a rubbery state [97]. At the molecular level, this correlates to the moment at which the molecular weight approaches infinity upon incipient formation of a cross-linked network. Macroscopically, gelation is defined as an abrupt increase in viscosity after which the polymer loses its ability to flow and develops viscoelastic properties. The macroscopic definition of gelation does not necessarily correlate to gelation at the molecular level, since hnear polymers... 

Macroscopic definition of elementary steps Consider a thermal reaction of the form -> products... 

According to the first condition of their macroscopic definition (see section 4.1), the elementary reactions proceed in a single zone only, and by applying to them all that has come before and by using the second condition of section 7.4 and relation [7.3], their reactivity can be given as ... 

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