Entropy vanishing

This holds for all time intervals x, and so in the optimum state the rate of production of second entropy vanishes. This is entirely analogous to the equilibrium situation, where at equilibrium the rate of change of first entropy vanishes. 

For book-keeping purposes the production of entropy during chemical change is considered as reducing the useful energy of the system by disorderly dispersion. In many cases this waste can be calculated statistically from the increase in disorder. To be in line with other thermodynamic state functions, any system is considered to be in some state of disorder at all temperatures above absolute zero, where entropy vanishes. 

Here SJ and H 0 are the entropy and enthalpy of the crystal at Tm, and ASf and AH( correspond to the entropy of melting and the enthalpy of melting (latent heat). The entropy and enthalpy are calculated this way for A1 and shown in Fig. 2.2 and 2.3. The entropy of the undercooled liquid decreases faster with decreasing temperature than that of the crystal because some entropy of the undercooled melt freezes in with decreasing temperature. This results in a crossover of both curves (extrapolated for the undercooled melt) at an isentropic temperature TAS=0 at approximately 0.25 Tm. Here the difference in the entropy vanishes between the crystal and the undercooled melt. Below this temperature,... 

Finally, it is worth noting that the values of Tq or needed to fit the viscosity data are close to the temperature at which the Kauzmann temperature, Tkau is estimated from extrapolations of other properties such as those shown in Fig. 9.8, lending credence to the model. This model also provides a natural way out of the Kauzmann paradox, since not only do the relaxation times go to infinity as T approaches 7)., but also the configuration entropy vanishes since in glass at T = T only one configuration is possible. 

By applying the requirement according to which also total growth of entropy vanishes, the entropy inequality for the mixture reads... 

If, therefore, the change of entropy vanishes at the absolute zero, the integration constant Jis zero. 

Another method for the solution of Eqs.(7) and (8) for reorienting surfactant molecules can be used. It is possible to assume that the molar areas of the solvent and surfactant are equal. I.e., for two states with the minimal and maximal molar area, cOb = = ((Oiri + (02r2)/r2 . In this case the contribution of the non-ideality of entropy vanishes. Then, the adsorption isotherms for molecules existing in two states (1 and 2) in an ideal (with respect to enthalpy) surface layer become ... 

At the glass transition temperature T of the system the configurational part of entropy vanishes. It is assumed that the transition of the supercooled melt to the glass is a type of second-order transition to obtain Eq. (78), where B is a temperature-independent energy term of transport, R is the gas constant, and A is a temperature-independent quantity, depending on the composition of the solution. 

With T2 = To and Acp 1/T, the VFT equation is obtained. At the Vogel temperature the configurational entropy vanishes, z(T) diverges like z(T) (T — To) but no information about the absolute size of a CRR can be obtained. The approach of Adam and Gibbs was extended by Donth (1992,2001) to obtain the size of a CRR. Within a fluctuation model a formula was developed which allows to calculate a correlation length (or volume Vcrr) from the height of the step in Cp and the temperature fluctuation 8T of a CRR at Tg as... 

At low enough temperatures, the communal entropy vanishes when SCL or CR is confined to a single basin. 

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