Temperature dependence of entropy

As the temperature of a perfect crystal is increased, the random vibrational motions increase, and disorder increases within the crystal [see Fig. 10.11(b)]. Thus the entropy of a substance increases with temperature. Since S is zero for a perfect crystal at 0 K, the entropy value for a substance at a particular temperature can be calculated if we know the temperature dependence of entropy. 

For estimation of thermodynamic properties of dissolved species, one can use the Entropy Correspondence Principle ( ), where the entropy of an ion at a given temperature is regarded as a function of the charge, the dielectric constant, mass, radius, and other variables. The function depends mainly upon the choice of the standard state, solvent, and temperature. The temperature dependency of entropy was derived based on the above principles and experimental data. By conducting the a square regression on Criss-Cobble s data ( ), we obtained the following eqtiation for calculating the entropies of species in aqueous solution. 

Fig. 3.1 Left-. Scheme of a hydrogen producing thermoelectrochemical cell Right Temperature dependence of entropy generation in the CuCl cell. From [43], with permission...

For sohd and hquid substances, the influence of pressure on the entropy can be disregarded if there are no extreme changes in pressure. The temperature dependence of entropy can normally be determined from (4.18) assuming constant heat capacity Cp in the considered temperature range. If the temperature deviates by more than 100-200 K from the reference temperature 298.15 K, the temperature dependence of the heat capacity should be taken into consideration for accurate calculations. In such a case, the calculation includes integration of the expression (4.16) with Cp = Cp T). 

Figure 1.20 The temperature dependences of entropy change due to fluctuation free volume formation AS (1, 2) and partial decay of clusters (3, 4) for PC (1,...

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