A Single-Component System

Suppose you have a system you want to describe thermodynamically. How do you do it Perhaps most important in your description is what s in the system that is, the components of the system. For our purposes, a component is defined as a unique chemical substance that has definite properties. For example, a system composed of pure UFg has a single chemical component uranium hexafluoride. Granted, UFg is composed of two elements, uranium and fluorine, but each element lost its individual identity when the compound UFg was formed. The phrase chemically homogeneous can be used to describe single-component systems. 

On the other hand, a mixture of iron filings and sulfur powder is composed of the two components iron and sulfur. The mixture may look like a single component, but a close enough inspection reveals two distinct materials in the system that have their own unique properties. This Fe/S mixture is therefore a two-component system. The phrase chemically inhomogeneous is used to describe multicomponent systems. 

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A solution is a homogeneous mixture. Examples of solutions include salt water [NaCl (s) dissolved in H2O] and the alloy brass, which is a solid solution of copper and zinc. Solutions are a little more difficult to consider, because the isolated components might not have the same chemical identity when in solution. For example, NaCl (s) and H2O (f) are two chemical components, but NaCl (aq) consists of Na (aq) and CP (aq) ions as well as excess H2O solvent. When we use solutions as an example of a system, we will be explicit in defining the components of the system. Even though they are homogeneous, properties of solutions will not be considered in this chapter. 

Identify the number of components and phases that exist in each system. Assume no component other than the ones given exists in each system. 

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A similar Marongoni instability can be provoked in a single component system by a temperature gradient [31] as illustrated in Fig. XIII-2. The wavelength of the instability is approximately... 

The example we have reported previously is on a single component system in a 2-D square lattice [3], An atomic position r is written by the polar coordinates, r = (p,6). In the discretization, we draw a circle of radius p=nb where b is a constant and n takes an integer value. On the n-th circle, we choose 8n points. Including the origin, the total number of points on and inside the n=5 circle is 121. As for the... 

The fundamental difference between pure metals and impure metals and alloys arises from the fact that there is only one atomic species present in the former, while there are two or more present in the latter thus a pure metal is a single-component system, a pure binary alloy is a two-component system, while impure metals and alloys, strictly speaking, are multi-component... 

A sequence of multiparticle colhsions may then be carried out. The first MPC event involves particles of all species and is analogous to that for a single component system a rotation operator m is applied to every particle in a cell. The all-species collision step is... 

Two naphthalocyanine derivatives (Scheme 9) were mixed together to improve read-out stability in a write-once optical storage system.220 The Ge derivative has a bulky structure with large side chains on the central atom, whilst the Cu derivative has a flat structure. The stability of the medium under 1 mW laser irradiation for read-out was improved 100-fold compared to that of a single-component system.220... 

This chapter introduces additional central concepts of thermodynamics and gives an overview of the formal methods that are used to describe single-component systems. The thermodynamic relationships between different phases of a single-component system are described and the basics of phase transitions and phase diagrams are discussed. Formal mathematical descriptions of the properties of ideal and real gases are given in the second part of the chapter, while the last part is devoted to the thermodynamic description of condensed phases. 

A phase boundary for a single-component system shows the conditions at which two phases coexist in equilibrium. Recall the equilibrium condition for the phase equilibrium (eq. 2.2). Letp and Tchange infinitesimally but in a way that leaves the two phases a and /3 in equilibrium. The changes in chemical potential must be identical, and hence... 

In this first example, a single-component system consisting of a liquid and a gas phase is considered. If the surface between the two phases is curved, the equilibrium conditions will depart from the situation for a flat surface used in most equilibrium calculations. At equilibrium the chemical potentials in both phases are equal ... 

Pressure and temperature changes with a single-component system qualitative discussion... 

PRESSURE AND TEMPERATURE CHANGES WITH A SINGLE-COMPONENT SYSTEM... 

Quantitative effects of pressure and temperature change for a single-component system... 

Earlier, on p. 181, we looked at the phase changes of a single-component system (our examples included the melting of an ice cube) in terms of changes in the molar Gibbs function AGm. In a similar manner, we now look at changes in the Gibbs function for each component within the mixture and because several components participate, we need to consider more variables, to describe both the host and the contaminant. 

Further experimental work has been carried out on the rates of melting of a solid in a liquid, using a single component system, and Hixson and Baum express their results for the heat transfer coefficient as ... 

A sublimation process is controlled primarily by the conditions under which phase equilibria occur in a single-component system, and the phase diagram of a simple one-component system is shown in Figure 15.30 where the sublimation curve is dependent on the vapour pressure of the solid, the vaporisation curve on the vapour pressure of the liquid, and the fusion curve on the effect of pressure on the melting point. The slopes of these three curves can be expressed quantitatively by the Clapeyron equation ... 

Since TOC, for some solid wastes, was used as a criterion to measure leachate sorption for organic compounds, TOC by itself is considered as a single component system (i.e., SCS, see Sect. 2.1). To represent the SCS equilibrium system for various waste materials, the sorption characteristics of different soils and sediments were analyzed and evaluated using three different sorption iso-... 

To a certain extent the expression multicomponent catalysts is an arbitrary one. There is no doubt that the pure chemical elements and pure chemical compounds have to be called single component catalysts. It is, however, questionable whether a material such as steel should be classified as a single component system or as a multicomponent system. Some of the multicomponent catalysts, for instance, the iron-alumina catalyst consist of two separate solid phases but it would be misleading to accept the presence of more than one phase as the decisive criterion for multicomponent catalysts. The more than additive catalytic action of Cu-ions and Fe-ions in an homogeneous aqueous medium represents obviously a case of multicomponent catalysis, although it occurs in a single-phase system. As to solid multicomponent catalysts, they usually consist of more than one single phase, but there are exceptions to this rule, such as in cases in which mixed crystals or solid solutions are formed from the components. 

Apart from water, the major constituents of most foods are carbohydrates, proteins, and lipids. These organic components of foods are less sensitive to irradiation than they are in their pure solutions as a single-component system. 

Two primary aspects to the practical implementation of molecular dynamics are (i) the numerical integration of the equations of motion along with the boundary conditions and any constraints on the system and (ii) the choice of the interatomic potential. For a single-component system, the potential energy can be written as an expansion in terms of -body potentials ... 

Other conditions at the critical point of a single-component system can... 

In the three-dimensional diagram, the curve formed by the intersection of the two surfaces represents all of the equilibrium points of the two-phase system. Such a curve is obtained for each type of a two-phase equilibrium existing in a single-component system. At any triple point of the system three such curves meet at a point, giving the temperature and pressure of the triple point. 

This order indicates that the aG-type host framework is more favorable than the other two trans-types ((TP or aT), and the 1 1 aG type is more favorable than 2 1 aG. In addition, this order agrees with the fact that less-selective enclathrations (entry 1, 12 and 21) were observed when they construct the same host frameworks at the same host-guest ratios in a single-component system. For example, both benzene and toluene can be included in the same 1 1 aG type. In the same way, less-selective enclathrations were also observed in the cases of ethylbenzene vs. n-propylbenzene (1 1 (3P) and n-amylbenzene vs. n-hexylbenzene (2 1 aG). 

As we have seen from our previous discussions of heat capacities, thermal expansion coefficients, and compressibilities, partial derivatives are the key to discussing changes in thermodynamic systems. In a single-component system of fixed size, the specification of two state variables completely determines the state of the system. Calling one of the molar energy quantities Z, we can write Z = Z(X, Y), where Xand Tare any two state variables, such as Tand I] or Tand V. Using the general mathematical properties of functions of two variables that are discussed in Appendix A,... 

In addition to being a function of T, the partition function is also a function of V, on which the quantum description of matter tells us that the molecular energy levels, , depend. Because, for single-component systems, all intensive state variables can be written as functions of two state variables, we can think of q(T, V) as a state function of the system. The partition function can be used as one of the independent variables to describe a single-component system, and with one other state function, such as T, it will completely define the system. All other properties of the system (in particular, the thermodynamic functions U, H, S, A, and G) can then be obtained from q and one other state function. 

Does Eq. (8) imply that for a single-component system, the chemical potential is the molar internal energy as well as the molar Gibbs free energy ... 

The evaluation of D by fitting an error function, which is based upon an undisturbed diffusion model in a single component system, will not lead to a proper description of the fluorine uptake in a natural multi-component system. 

Improved raw materials procurement and flow by replacing two containers associated with dualcomponent adhesive with a single-component system Elimination of pot life consideration and line downtime resulting from adhesive advancement Elimination of mix ratio tolerance concerns with resulting improvement in product consistency Elimination of variations from the coating process with resulting improvement in product consistency Improved worker safety and reduced hazardous materials exposure to liquid and paste systems... 

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