Entropy physical

To melt ice we have to put heat into the system. This increases the system entropy via eqn. (5.20). Physically, entropy represents disorder and eqn. (5.20) tells us that water is more disordered than ice. We would expect this anyway because the atoms in a liquid are arranged much more chaotically than they are in a crystalline solid. When water freezes, of course, heat leaves the system and the entropy decreases. 

As a simple example of the reception phenomenon, one can consider the behavior of moving balls in a lottery basket. The basket has several holes in it, and the vyin is determined by the ball that falls stochastically into one of them. In the system, physical entropy relates only to quickly relaxing degrees of freedom, vyhile their behavior is determined by the nature of the ball in the basket but independent of vyhether the ball is in a hole. Hovyever, vyhile for the physical entropy the information quantity is zero, for the second situation, vyhen the ball is already in a given hole, the information equals Thus, the reception of information arises... 

Thus, any information system must comprise statistical and dynamic subsystems. The physical entropy is the measure of numerous nonstored system microstates that are related to statistical subsystem, while macroin formation is the measure of numerous states to be stored in the dynamic subsystem. 

The implication of the word total is that it is possible for entropy of a system to decrease when heat is transferred out however, the increase in entropy outside the system will be greater than the entropy reduction within the system. Physically, entropy is a measure of the amount of energy that is not available to produce work. Work and mechanical energy are fully useable and therefore have no associated entropy and any process that generates entropy is irreversible. 

The entropy Sciaus is the maximum of the physical entropies Sgoitz Scibbs which are bound Shannon entropies and figurred in physical units. 

Further, we define the values of changes of information entropies on the channel K. = C (with an information transfer process being realized by this cycle) by the changes of its physical entropies, for instance, in this way ... 

This is an instructive example, because it tells us that by ignoring the integral measure in the Monte Carlo update processes we effectively would have simulated a different model with modified enfropic properties The term S(uj, v w,) = k ln/u(i/ v w,) is a geometric entropy that accounts for the non-uniformity in the distribution of values of the coordinates of the rth monomer in the chosen coordinate system. It is not a physical entropy, but rather a mathematical counter-term that assigns the physical entropy its correct value. 

The physical entropy of any mass is a function of the quantity of thermal energy it must abscnb in order to exist at a given temperature above absolute zero, the standard temperature usually being taken at 298.15 K for biological purposes, as represented by the following equation. 

W. Von der Linden Maximum-entropy data analysis. J. Appl. Physics. A. NA60, 1995, pp. 155-165. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

The following several sections deal with various theories or models for adsorption. It turns out that not only is the adsorption isotherm the most convenient form in which to obtain and plot experimental data, but it is also the form in which theoretical treatments are most easily developed. One of the first demands of a theory for adsorption then, is that it give an experimentally correct adsorption isotherm. Later, it is shown that this test is insufficient and that a more sensitive test of the various models requires a consideration of how the energy and entropy of adsorption vary with the amount adsorbed. Nowadays, a further expectation is that the model not violate the molecular picture revealed by surface diffraction, microscopy, and spectroscopy data, see Chapter VIII and Section XVIII-2 Steele [8] discusses this picture with particular reference to physical adsorption. 

Thus from an adsorption isotherm and its temperature variation, one can calculate either the differential or the integral entropy of adsorption as a function of surface coverage. The former probably has the greater direct physical meaning, but the latter is the quantity usually first obtained in a statistical thermodynamic adsorption model. 

Brunauer (see Refs. 136-138) defended these defects as deliberate approximations needed to obtain a practical two-constant equation. The assumption of a constant heat of adsorption in the first layer represents a balance between the effects of surface heterogeneity and of lateral interaction, and the assumption of a constant instead of a decreasing heat of adsorption for the succeeding layers balances the overestimate of the entropy of adsorption. These comments do help to explain why the model works as well as it does. However, since these approximations are inherent in the treatment, one can see why the BET model does not lend itself readily to any detailed insight into the real physical nature of multilayers. In summary, the BET equation will undoubtedly maintain its usefulness in surface area determinations, and it does provide some physical information about the nature of the adsorbed film, but only at the level of approximation inherent in the model. Mainly, the c value provides an estimate of the first layer heat of adsorption, averaged over the region of fit. 

This is the result for monatomic fluids and is well approximated by a sum of tliree Lorentzians, as given by the first tliree temis on the right-hand side. The physics of these tliree Lorentzians can be understood by thinking about a local density fluctuation as made up of tliemiodynamically independent entropy and pressure fluctuations p = p s,p). The first temi is a consequence of the themial processes quantified by the entropy... 

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

The subject of entropy is introduced here to illustrate treatment of experimental data sets as distinct from continuous theoretical functions like Eq. (1-33). Thermodynamics and physical chemistry texts develop the equation... 

Along with the curve fitting process, TableCurve also calculates the area under the curve. According to the previous discussion, this is the entropy of the test substance, lead. To find the integral, click on the numeric at the left of the desktop and find 65.06 as the area under the curve over the range of x. The literature value depends slightly on the source one value (CRC Handbook of Chemistry and Physics) is 64.8 J K mol. ... 

Thermodynamics is one of the most well-developed mathematical descriptions of chemistry. It is the held of thermodynamics that dehnes many of the concepts of energy, free energy and entropy. This is covered in physical chemistry text books. 

Solubility in Water A familiar physical property of alkanes is contained m the adage oil and water don t mix Alkanes—indeed all hydrocarbons—are virtually insoluble m water In order for a hydrocarbon to dissolve m water the framework of hydrogen bonds between water molecules would become more ordered m the region around each mole cule of the dissolved hydrocarbon This increase m order which corresponds to a decrease m entropy signals a process that can be favorable only if it is reasonably... 

Remember that the hump which causes the instability with respect to phase separation arises from an unfavorable AH considerations of configurational entropy alone favor mixing. Since AS is multiplied by T in the evaluation of AGj, we anticipate that as the temperature increases, curves like that shown in Fig. 8.2b will gradually smooth out and eventually pass over to the form shown in Fig. 8.2a. The temperature at which the wiggles in the curve finally vanish will be a critical temperature for this particular phase separation. We shall presently turn to the Flory-Huggins theory for some mathematical descriptions of this critical point. The following example reminds us of a similar problem encountered elsewhere in physical chemistry. 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

Bond dissociation energies (BDEs) for the oxygen—oxygen and oxygen— hydrogen bonds are 167—184 kj/mol (40.0—44.0 kcal/mol) and 375 kj/mol (89.6 kcal/mol), respectively (10,45). Heats of formation, entropies, andheat capacities of hydroperoxides have been summarized (9). Hydroperoxides exist as hydrogen-bonded dimers in nonpolar solvents and readily form hydrogen-bonded associations with ethers, alcohols, amines, ketones, sulfoxides, and carboxyhc acids (46). Other physical properties of hydroperoxides have been reported (46). 

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