Liquids entropy

One of the most convincing tests of the AG relationship appeared in the work of Scala et al.92 for the SPC/E model of water,57 which is known to reproduce many of water s distinctive properties in its super-cooled liquid state qualitatively. In this study, the dynamical quantity used to correlate with the configurational entropy was the self-diffusivity D. Scala et al. computed D via molecular dynamics simulations. The authors calculated the various contributions to the liquid entropy using the methods described above for a wide range of temperature and density [shown in Figure 12(a-c)]. 

Consider a molecule with a smaller symmetry number of ctj and an isomer molecule with a larger symmetry number of a2, the liquid entropy of the less symmetrical molecule is higher than the more symmetrical molecule by F ln(cT2/cri). As a consequence, the more symmetric molecule has a smaller entropy of melting, A5m,2 = A5m,i - R ln(a2/ai), which would lead to a higher melting temperature—if symmetry does not have a big effect on the enthalpy of melting or the entropy of the solid. 

Selected thermodynamic properties of liquid COFj have been estimated [1683]. These calculated values for the Helmholtz free energy function (-G/RT), liquid entropy (5), and heat capacity at constant volume (C,) are recorded in Table 13.11. 

First-order solid-state amorphization occurs due to an entropy catastrophe [39] causing melting of superheated graphite and decompressed diamond below Pg when the entropy of the ordered crystal would exceed the entropy of the disordered liquid. This condition is resolved with the occurrence of a kinetic transition to a (supercooled) glass whereby the exact kinetic conditions during carbon transformation will be critically Pg-depen-dent [39]. It is important to consider the crystal to liquid transition and the effect of a superheated crystal whereof the ultimate stability is determined by the equality of crystal and liquid entropies [40]. When this condition is met, a solid below its Pg will melt to an amorphous solid, particularly... 

Here 7J, is a new nonzero vanishing mobility temperature that is characteristic of each liquid and lies far below the temperature at which each diffusivity plot in Fig. 3 tends to zero on the linear scale. The claim of to physical significance is that it falls below the observed normal 7, such that 7 1.1 to 1.3 Tq and is usually coincident with the temperature at which the supercooled liquid entropy, measured below the fusion temperature, extrapolates to the same value as for the crystal (though the free energy of the latter remains lower Equation 5 implies an apparent activation energy that varies with temperature according to... 

The AS " term is a measure of the increase or decrease in the order of a system. A more ordered system has less entropy and is less probable than a disordered one. The main factors that influence AS° in a chemical reaction are the number of moles of material on each side of the balanced equation and their physical state. The liquid phase of a substance has more entropy (less order) than the solid, and the gas phase has much more entropy than the liquid. Entropy increases when more molecules are formed at the expense of fewer ones, as for example in elimination reactions. Conversely, addition reactions convert more molecules to fewer ones and are characterized by a negative sign for AS ". 

Morsi,B.E., Midoux,N., Laurent,A. et J.C.Charpentier. "Hydrodynamique et aire interfacials des ecoulements gaz-liquide a co-courant vers le bas en lit fixe. Influence de la nature du liquide". Entropie 16 No 91 (1980) 39. 

The significance of flash fractions is that they give the maximum possible vapor fraction formed in an isentropic process for discharges into the atmosphere. This statement could be derived mathematically starting from Eq. (27.7) and equations for the temperature dependency of the vapor and liquid entropies in saturated state. For instance, in choked isentropic pipe flow the vapor fraction of the fluid at the aperture is always smaller than the flash fraction (because the exit pressure is higher than the atmospheric pressure). 

Limas-Ballesteros R, Riba JP, Couderc JP. Expansion de couches de particules non spheriques fluidisees par un liquide. Entropie 106 37-45, 1982a. 

FIGURE 19 (a) The entropy Sof liquid and solid He (upper diagram) measured in units of the gas constant R, plotted as functions of temperature T and the melting pressure Pm of He as a function of T. It may be noted that the minimum in the melting curve occurs at the temperature where the difference between the solid and liquid entropies changes sign. [From values tabulated by Betts, D. S. (1976). Refrigeration and Thermometry Below One Kelvin, Sussex Univ. Press, London.]... 

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