Entropy macroscopic properties

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... 

We see from this discussion that a third generalization is necessary. Up to this point in the text we have been concerned solely with the macroscopic properties. However, in order to obtain an understanding of the third law we must use some concepts concerning the entropy function, based on statistical mechanics. We do so in this chapter with the assumption that the basic concepts that are used are familiar to the reader. 

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 equation, Tm = AHJAS/t is all very well, but like any other thermodynamic equation only gives us a relationship between macroscopic properties. We need to relate the enthalpy and entropy to molecular properties in order to gain insight Fortunately, for this problem we only need to do this qualitatively to gain understanding. 

This definition of entropy shows its exact relationship to probability. However, it is not useful in a practical sense for the typical types of samples used by chemists, because these samples contain so many components. For example, a mole of gas contains 6.022 X 1023 individual particles. In addition, according to one estimate, describing the positions and velocities of this mole of particles would require a stack of paper 10 light years tall—and this description would apply for only an instant. Clearly, we cannot deal directly with this definition of entropy for typical-sized samples. We must find a way to connect entropy to the macroscopic properties of matter. To do so, we will consider an ideal gas that expands isothermally from volume V] to volume 2V] (see Fig. 10.10). 

What we have accomplished here is to use the definition of entropy in terms of probability to derive an expression for AS that depends on volume, a macroscopic property of the gas. We can now relate the change in entropy to heat flow by noting the striking similarity between the above equation for AS and the one derived in Section 10.2 describing qrev for the isothermal expansion-compression of an ideal gas. Compare... 

This very important relationship is the macroscopic (thermodynamic) definition of AS. In our treatment we started with the definition of entropy based on probability, because that definition better emphasizes the fundamental character of entropy. However, it is also very important to know how entropy changes relate to changes in macroscopic properties, such as volume and heat, because these changes are relatively easy to measure. 

On the other hand, some phenomenological distributions of relaxation times, such as the well known Williams-Watts distribution (see Table 1, WW) provided a rather good description of dielectric relaxation experiments in polymer melts, but they are not of considerable help in understanding molecular phenomena since they are not associated with a molecular model. In the same way, the glass transition theories account well for macroscopic properties such as viscosity, but they are based on general thermodynamic concepts as the free volume or the configurational entropy and they completely ignore the nature of molecular motions. 

The focus of this review article will be on the interaction between macromolecules and small-molecule ligands. The discussion will first center on the thermodynamic and kinetic characteristics that are used to measure the extent of binding. Subsequently, we discuss the interactions at the atomic level that drive complex formation. Then, a discussion follows of some tools available to predict macroscopic properties from microscopic properties. We then briefly discuss macromolec-ular motions as well as various aspects of receptor-ligand that have attracted renewed attention, such as conformational selection versus induced-fit, enthalpy-entropy compensation effect, and protein allostery. 

Only just by a (thought) dividing of an equilibrium system A by diaphragms [20], without any influence on its thermodynamic (macroscopic) properties, a non-zero difference of its entropy, before and after its dividing, is evidenced. 

We adopt the premise that matter inside stars consists of an almost perfect gas. The properties of a gas are often referred to as state variables. The macroscopic properties of a gas are described completely by three quantities, i.e. any three of pressure, density, temperature, entropy, and number density. 

A system is said to be in a stationary state if its macroscopic properties such as temperature, pressure, composition and entropy do not change with time inspite of the possible occurrence of irreversible process. Of the macroscopic properties, the intensive ones, though unchanged in time, will generally still vary from point to point in the system. The stationary states may be classified into the following two classes—... 

Thermodynamics, then, is concerned with the relationships between the various macroscopic properties. One of the most important conclusions from thermodynamics is that there are two properties which are particularly important in explaining the behavior of matter. These properties are energy and entropy. The first law of thermodynamics is conveniently summarized in the statement ... 

The most common statement of the third law of thermodynamics is that the entropy of a perfectly crystalline system approaches zero as the temperature of the system approaches zero. (Recall from Macroscopic Properties The World We See that a perfect crystal is a regularly ordered lattice of atoms that exist in a repeating pattern in three dimensions with no defects or irregularities in the lattice.) This is equivalent to saying that a perfectly crystalline system has only one accessible state as the temperature ap-... 

Since AGsqIv is expressed on a per-mole basis, the right sides of these equations should be multiplied by the Avogadro constant iV. ) Although energy is both a molecular and a macroscopic property, both entropy and free energy are macroscopic but not molecular properties. The dielectric continuum model uses the macroscopic property of the solvent, and the macroscopic treatment of the solvent allows us to find AG°oi ei, which is a contribution to a macroscopic property. The dielectric continuum treatment of solvation is a combined quantum-mechanical and statistical-mechanical treatment. 

The most fundamental starting point for any theoretical approach is the quantum mechanical partition function PF), and the fundamental connection between the partition function and the corresponding thermodynamic potential. Once we have a PF, either exact or approximate, we can derive all the thermodynamic quantities by using standard relationships. Statistical mechanics is a general and very powerful tool to connect between microscopic properties of atoms and molecules, such as mass, dipole moment, polarizability, and intermolecular interaction energy, on the one hand, and macroscopic properties of the bulk matter, such as the energy, entropy, heat capacity, and compressibility, on the other. 

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