Entropy conductivity

Equation (3.116) shows that the rate of change of the entropy per unit volume of substance is due to the convection entropy flow p.w. the conduction entropy flow j v. and the entropy source strength The conduction entropy flow is... 

The conduction entropy flow consists of the heat flow j" and the diffusion flow j,-. The j" is reduced heat flow that is the difference between the change in energy and the change in enthalpy due to matter flow. With the... 

There are substances which conduct entropy very well, such as silver, copper, aluminum, and diamond, and others, such as wood, foamed plastic, or air, which only allow entropy to pass through them very slowly (Fig. 3.4). 

The thinner the surrounding walls are, the greater their area is and the better the substance of which such a wall is composed conducts entropy, the easier the entropy runs through the walls (Fig. 3.18). The correlation is similar to that of the current of electric charge through a wire (see Sect. 20.4). 

Comparison of Eqns (3.47) and (3.51) yields an expression for the conduction entropy flow ... 

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]. 

The most direct effect of defects on tire properties of a material usually derive from altered ionic conductivity and diffusion properties. So-called superionic conductors materials which have an ionic conductivity comparable to that of molten salts. This h conductivity is due to the presence of defects, which can be introduced thermally or the presence of impurities. Diffusion affects important processes such as corrosion z catalysis. The specific heat capacity is also affected near the melting temperature the h capacity of a defective material is higher than for the equivalent ideal crystal. This refle the fact that the creation of defects is enthalpically unfavourable but is more than comp sated for by the increase in entropy, so leading to an overall decrease in the free energy... 

The thermal conductivity of soHd iodine between 24.4 and 42.9°C has been found to remain practically constant at 0.004581 J/(cm-s-K) (33). Using the heat capacity data, the standard entropy of soHd iodine at 25°C has been evaluated as 116.81 J/ (mol-K), and that of the gaseous iodine at 25°C as 62.25 J/(mol-K), which compares satisfactorily with the 61.81 value calculated by statistical mechanics (34,35). 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

The kieveisible phenomena represent entropy gain through irrecoverable heat losses as follows, where X is the thermal conductivity and /is the length ... 

Available data on the thermodynamic and transport properties of carbon dioxide have been reviewed and tables compiled giving specific volume, enthalpy, and entropy values for carbon dioxide at temperatures from 255 K to 1088 K and at pressures from atmospheric to 27,600 kPa (4,000 psia). Diagrams of compressibiHty factor, specific heat at constant pressure, specific heat at constant volume, specific heat ratio, velocity of sound in carbon dioxide, viscosity, and thermal conductivity have also been prepared (5). 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Cp = specific heat e = specific internal energy h = enthalpy k =therm conductivity p = pressure, s = specific entropy t = temperature T = absolute temperature u = specific internal energy [L = viscosity V = specific volume f = subscript denoting saturated hquid g = subscript denoting saturated vapor... 

For sources, units, and remarks, see Table 2-228. v = specific volume, mVkg h = specific enthalpy, kj/kg s = specific entropy, kJ/(kg-K) c = specific beat at constant pressure, kJ/(kg-K) i = viscosity, 10 Pa-s and k = tberni conductivity, VW(m-K). For specific beat ratio, see Table 2-200 for Prandtl number, see Table 2-369. 

For elastic compression the entropy increase is small and can come only from effects of thermal conduction. Thus, to a very good approximation at low compressions in most materials,... 

It must be emphasised that the heat q which appears in the definition of entropy (equation 20.137) is always that absorbed (or evolved) when the process is conducted reversibly. If the process is conducted irreversibly and the heat absorbed is q, then q will be less than q, and q/T will be less than AS the entropy change (equation 20.137). It follows that if an irreversible process takes place between the temperatures Tj and 7 , and has the same heat intake q at the higher temperature 7 2 as the corresponding reversible process, the efficiency of the former must be less than that of the latter, i.e. 

A physically acceptable theory of electrical resistance, or of heat conductivity, must contain a discussion of the explicitly time-dependent hamiltonian needed to supply the current at one boundary and remove it at another boundary of the macrosystem. Lacking this feature, recent theories of such transport phenomena contain no mechanism for irreversible entropy increase, and can be of little more than heuristic value. 

Just as the intrinsic energy of a body is defined only up to an arbitrary constant, so also the entropy of the body cannot, from the considerations of pure thermodynamics, be specified in absolute amount. We therefore select any convenient arbitrary standard state a, in which the entropy is taken as zero, and estimate the entropy in another state /3 as follows The change of entropy being the same along all reversible paths linking the states a and /3, and equal to the difference of the entropies of the two states, we may imagine the process conducted in the following two steps ... 

Inequality (7) shows that the heat absorbed from outside is less than corresponds with the increase of entropy of the system (viz., SQ = Td8, where BQ is the heat absorbed in the process when conducted reversibly), hence some entropy is generated inside the system itself. 

But if the given process is conducted irreversibly, we have proved that there is always more entropy generated in the system than is lost by bodies outside the system, and the excess is called the non-compensatcd entropy. It may happen, and frequently does, that the entropy of the system itself decreases in a particular change, but we have proved that there is an increase outside the system which is greater than the decrease in the system, or at best equal to it in the case of reversible changes. 

Loss of motivity (dissipation of energy) is therefore accompanied by increase of entropy, but the two changes are not wholly co-extensive, because the former is less the lower the temperature T0 of the auxiliary medium, whilst the latter is independent of T0, and depends only on the temperature of the parts of the system. If T0 = 0, i.e., the temperature of the surroundings is absolute zero, there is no loss of motivity, whilst the entropy goes on increasing without limit as the heat is gradually conducted to colder bodies. 

DeCarvalho and Choppin (10, 11) previously have reported the stability constants, complexation enthalpies, and entropies for a series of trivalent lanthanide and actinide sulfates. As their work was conducted a pH 3, the dominant sulfate species was S0 and the measured reaction was as in equation 12. 

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