Pressure macroscopic properties

To define the thennodynamic state of a system one must specify fhe values of a minimum number of variables, enough to reproduce the system with all its macroscopic properties. If special forces (surface effecls, external fields—electric, magnetic, gravitational, etc) are absent, or if the bulk properties are insensitive to these forces, e.g. the weak terrestrial magnetic field, it ordinarily suffices—for a one-component system—to specify fliree variables, e.g. fhe femperature T, the pressure p and the number of moles n, or an equivalent set. For example, if the volume of a surface layer is negligible in comparison with the total volume, surface effects usually contribute negligibly to bulk thennodynamic properties. 

Macroscopic properties often influence tlie perfoniiance of solid catalysts, which are used in reactors tliat may simply be tubes packed witli catalyst in tlie fonii of particles—chosen because gases or liquids flow tlirough a bed of tliem (usually continuously) witli little resistance (little pressure drop). Catalysts in tlie fonii of honeycombs (monolitlis) are used in automobile exliaust systems so tliat a stream of reactant gases flows witli little resistance tlirough tlie channels and heat from tlie exotlieniiic reactions (e.g., CO oxidation to CO,) is rapidly removed. 

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

The fluid is regarded as a continuum, and its behavior is described in terms of macroscopic properties such as velocity, pressure, density and temperature, and their space and time derivatives. A fluid particle or point in a fluid is die smallest possible element of fluid whose macroscopic properties are not influenced by individual molecules. Figure 10-1 shows die center of a small element located at position (x, y, z) with die six faces labelled N, S, E, W, T, and B. Consider a small element of fluid with sides 6x, 6y, and 6z. A systematic account... 

A key problem in the equilibrium statistical-physical description of condensed matter concerns the computation of macroscopic properties O acro like, for example, internal energy, pressure, or magnetization in terms of an ensemble average (O) of a suitably defined microscopic representation 0 r ) (see Sec. IVA 1 and VAl for relevant examples). To perform the ensemble average one has to realize that configurations = i, 5... 

Figure 9-2 shows the result of heating solid CaCOa, initially under a vacuum, to 800°C (part A). Decomposition begins according to reaction (3) and the gas pressure rises (part B). The pressure continues to rise until it reaches 190 mm (part C). Thereafter, no further change is evident. Since we can detect no more evidence of change, we say that the system is at equilibrium. Equilibrium is characterized by constancy of macroscopic properties. 

These include cold drawn, high pressure oriented chain-extended, solid slate extruded, die-drawn, and injection moulded polymers. Correlation of hardness to macroscopic properties is also examined. In summary, microhardness is shown to be a useful complementary technique of polymer characterization providing information on microscopic mechanical properties. 

On the continuum level of gas flow, the Navier-Stokes equation forms the basic mathematical model, in which dependent variables are macroscopic properties such as the velocity, density, pressure, and temperature in spatial and time spaces instead of nf in the multi-dimensional phase space formed by the combination of physical space and velocity space in the microscopic model. As long as there are a sufficient number of gas molecules within the smallest significant volume of a flow, the macroscopic properties are equivalent to the average values of the appropriate molecular quantities at any location in a flow, and the Navier-Stokes equation is valid. However, when gradients of the macroscopic properties become so steep that their scale length is of the same order as the mean free path of gas molecules,, the Navier-Stokes model fails because conservation equations do not form a closed set in such situations. 

Although pressure is caused by molecular collisions, it is a macroscopic property, the collective result of countless collisions. We can get a feel for the macroscopic characteristics of gas pressure by examining Earth s atmosphere. 

The system states (dependent variables) are the pressure, p, and the superficial (Darcy) velocity, v. The density, p, and viscosity, p, are fluid properties, and g is the acceleration of gravity. The porosity, < )(z), and permeability, fc(z), represent the macroscopic properties of the media. Both are spatially dependent and are represented as continuous functions of position z, as explicitly noted. While the per-... 

The macroscopic properties of a material are related intimately to the interactions between its constituent particles, be they atoms, ions, molecules, or colloids suspended in a solvent. Such relationships are fairly well understood for cases where the particles are present in low concentration and interparticle interactions occur primarily in isolated clusters (pairs, triplets, etc.). For example, the pressure of a low-density vapor can be accurately described by the virial expansion,1 whereas its transport coefficients can be estimated from kinetic theory.2,3 On the other hand, using microscopic information to predict the properties, and in particular the dynamics, of condensed phases such as liquids and solids remains a far more challenging task. In these states... 

The observable (macroscopic) properties of a system at equilibrium are constant. At equilibrium, there is no overall change in the properties that depend on the total quantity of matter in the system. Examples of these properties include colour, pressure, concentration, and pH. 

The macroscopic properties of the three states of matter can be modeled as ensembles of molecules, and their interactions are described by intermolecular potentials or force fields. These theories lead to the understanding of properties such as the thermodynamic and transport properties, vapor pressure, and critical constants. The ideal gas is characterized by a group of molecules that are hard spheres far apart, and they exert forces on each other only during brief periods of collisions. The real gases experience intermolecular forces, such as the van der Waals forces, so that molecules exert forces on each other even when they are not in collision. The liquids and solids are characterized by molecules that are constantly in contact and exerting forces on each other. 

Transport properties are often given a short treatment or a treatment too theoretical to be very relevant. The notion that molecules move when driven by some type of concentration gradient is a practical and easily grasped approach. The mathematics can be minimized. Perhaps the most important feature of the kinetic theory of gases is the recognition that macroscopic properties such as pressure and temperature can be derived by suitable averages of the properties of individual molecules. This concept is an important precursor to statistical thermodynamics. Moreover, the notion of a distribution function as a general... 

To understand heterogeneous catalysis it is necessary to characterize the surface of the catalyst, where reactants bond and chemical transformations subsequently take place. The activity of a solid catalyst scales directly with the number of exposed active sites on the surface, and the activity is optimized by dispersing the active material as nanometer-sized particles onto highly porous supports with surface areas often in excess of 500m /g. When the dimensions of the catalytic material become sufficiently small, the properties become size-dependent, and it is often insufficient to model a catalytically active material from its macroscopic properties. The structural complexity of the materials, combined with the high temperatures and pressures of catalysis, may limit the possibilities for detailed structural characterization of real catalysts. 

A principal theme of this text is the direct relation of macroscopic properties to molecular structure. In concluding the discussion on the si and sll cavity size ratios, two examples are given of how macroscopic engineering properties (equilibrium pressure and temperature, and heat of dissociation) are determined by the size ratios in Table 2.4. 

The second example of microscopic structure reflected in macroscopic properties is almost as important as determining phase equilibria conditions. After establishing that hydrates will form (or dissociate) at certain pressure and temperature conditions, engineers are often interested in the amount of energy required for the phase transition. 

The method presented in this chapter serves as a link between molecular properties (e.g., cavities and their occupants as measured by diffraction and spectroscopy) and macroscopic properties (e.g., pressure, temperature, and density as measured by pressure guages, thermocouples, etc.) As such Section 5.3 includes a brief overview of molecular simulation [molecular dynamics (MD) and Monte Carlo (MC)] methods which enable calculation of macroscopic properties from microscopic parameters. Chapter 2 indicated some results of such methods for structural properties. In Section 5.3 molecular simulation is shown to predict qualitative trends (and in a few cases quantitative trends) in thermodynamic properties. Quantitative simulation of kinetic phenomena such as nucleation, while tenable in principle, is prevented by the capacity and speed of current computers however, trends may be observed. 

Figure 2. Schematic representation of the four conceptually different paths (the heavy lines) one may utilize to attack the phase-coexistence problem. Each figure depicts a configuration space spanned by two macroscopic properties (such as energy, density. ..) the contours link macrostates of equal probability, for some given conditions c (such as temperature, pressure. ..). The two mountaintops locate the equilibrium macro states associated with the two competing phases, under these conditions. They are separated by a probability ravine (free-energy barrier). In case (a) the path comprises two disjoint sections confined to each of the two phases and terminating in appropriate reference macrostates. In (b) the path skirts the ravine. In (c) it passes through the ravine. In (d) it leaps the ravine.

Every chemistry student is familiar with the ideal gas equation PV = nRT. It turns out that this equation is a logical consequence of some basic assumptions about the nature of gases. These simple assumptions are the basis of the kinetic theory of gases, which shows that the collisions of individual molecules against the walls of a container creates pressure. This theory has been spectacularly successful in predicting the macroscopic properties of gases, yet it really uses little more than Newton s laws and the statistical properties discussed in the preceding chapters. 

The kinetic theory of gases, coupled with the Boltzmann distribution, lets us predict a wide variety of the macroscopic properties of gases, and the agreement with experiment is excellent—even though we are making extremely crude approximations to the microscopic structure of the individual molecules. Molecules are much more complicated than tiny billiard balls, yet at standard temperature and pressure, the answers we get from the simplest theories are good to within a few percent. 

Thermodynamics deals with relations among bulk (macroscopic) properties of matter. Bulk matter, however, is comprised of atoms and molecules and, therefore, its properties must result from the nature and behavior of these microscopic particles. An explanation of a bulk property based on molecular behavior is a theory for the behavior. Today, we know that the behavior of atoms and molecules is described by quantum mechanics. However, theories for gas properties predate the development of quantum mechanics. An early model of gases found to be very successftd in explaining their equation of state at low pressures was the kinetic model of noninteracting particles, attributed to Bernoulli. In this model, the pressure exerted by n moles of gas confined to a container of volume V at temperature T is explained as due to the incessant collisions of the gas molecules with the walls of the container. Only the translational motion of gas particles contributes to the pressure, and for translational motion Newtonian mechanics is an excellent approximation to quantum mechanics. We will see that ideal gas behavior results when interactions between gas molecules are completely neglected. 

PhysChem Batch Advanced Chemistry Development Inc. www.acdlabs.com pKa, log Kow, log D, K c, bioconcentration factor, solubility at a certain pH, boiling point, vapor pressure, enthalpy of vaporization, flash point, macroscopic properties... 

Chemical thermodynamics deals with the physicochemical state of substances. All physical quantities corresponding to the macroscopic property of a physicochemical system of substances, such as temperature, volume, and pressure, are thermodynamic variables of the state and are classified into intensive and extensive variables. Once a certain number of the thermodynamic variables have been specified, then all the properties of the system are fixed. This chapter introduces and discusses the characteristics of intensive and extensive variables to describe the physicochemical state of the system. 

All observable quantities of the macroscopic property of a thermodynamic system, such as the volume V, the pressure p, the temperature T, and the mass m of the system, are called variables of the state, or thermodynamic variables. In a state of the system all observable variables have their specified values. In principle, once a certain number of variables of the state are specified, all the other variables can be derived from the specified variables. The state of a pure oxygen gas, for example, is determined if we specify two freely chosen variables such as temperature and pressure. 

The idea of hidden variables is fairly common in chemical models such as the kinetic gas model. This theory is formulated in terms of molecular momenta that remain hidden, and evaluated against measurements of macroscopic properties such as pressure, temperature and volume. Electronic motion is the hidden variable in the analysis of electrical conduction. The firm belief that hidden variables were mathematically forbidden in quantum systems was used for a long time to discredit Bohm s ideas. Without joining the debate it can be stated that this proof has finally been falsified. 

Classical thermodynamics is based on a description of matter through such macroscopic properties as temperature and pressure. However, these properties are manifestations of the behavior of the countless microscopic particles, such as molecules, that make up a finite system. Evidently, one must seek an understanding of the fundamental nature of entropy in a microscopic description of matter. Because of the enormous number of particles contained in any system of interest, such a description must necessarily be statistical in nature. We present here a very brief indication of the statistical interpretation of entropy, t... 

The properties of a system based on the behavior of molecules are related to the microscopic state, which is the main concern of statistical thermodynamics. In contrast, classical thermodynamics formulate the macroscopic state, which is related to the average behavior of large groups of molecules leading to the definitions of macroscopic properties such as temperature and pressure. 

The equilibrium state is reached when there is no change with time in any of the system s macroscopic properties. The phase rule by Gibbs gives the general conditions for equilibrium between phases in a system. It is assumed that the equUibrium is only influenced by temperature and pressure, that is, surface, magnetic, electrical, and magnetic... 

The macroscopic properties of homogeneous PVT systems at internal equilibrium can be expressed as functions of temperature, pressure, and composition only. 

All quantities corresponding to a macroscopic property of the system under consideration are called thermodynamic variables. These may be for example, its volume F, the pressure p, the absolute temperature T, the mass m of the system, or its refractive index. 

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