Entropy, absolute

We shall assume that Cp = 0 at 7 = 0 K. We wish to obtain the absolute entropy of solid lead at 298 K. Each entry in Table 1-2 leads to a value of CpjT. The... 

Draw the curve of Cp vs. T and Cp/T vs. T from the following heat capacity data for solid chlorine and determine the absolute entropy of solid chlorine at 70.0 K... 

Figure 5-11 Pitrtiiil MMII Output Shinvirig Entropy and Heat Capacities for Water. E. perimerital values are 4. i. IS eal K iiiol for the absolute entropy and H.OS eal K iiiol i or the heat eaitaeity.

Ideal gas absolute entropies of many compounds may be found in Daubert et al.,"" Daubert and Danner," JANAF Thermochemical Tables,TRC Thermodynamic Tables,and Stull et al. ° Otherwise, the estimation method of Benson et al. " is reasonably accurate, with average errors of 1-2 J/mol K. Elemental standard-state absolute entropies may be found in Cox et al." Values from this source for some common elements are listed in Table 2-389. ASjoqs may also be calculated from Eq. (2-52) if values for AHjoqs and AGJoqs are known. 

The third law of thermodynamics states that the entropy of any crystalline, perfectly ordered substance must approach zero as the temperature approaches 0 K, and at T = 0 K entropy is exactly zero. Based on this, it is possible to establish a quantitative, absolute entropy scale for any substance as... 

If the heat capacity can be evaluated at all temperatures between 0 K and the temperature of interest, an absolute entropy can be calculated. For biological processes, entropy changes are more useful than absolute entropies. The entropy change for a process can be calculated if the enthalpy change and free energy change are known. 

Thermodynamics is concerned with the relationship between heat energy and work and is based on two general laws, the 1st and 2nd laws of thermodynamics, which both deal with the interconversion of the different forms of energy. The 3rd law states that at the absolute zero of temperature the entropy of a perfect crystal is zero, and thus provides a method of determining absolute entropies. 

In summary, the absolute entropies we calculate and tabulate are, in fact, not so absolute, since they do not include isotopic entropies of mixing nor nuclear spin alignment entropies. The entropies we tabulate are sometimes called practical absolute entropies. They can be used to correctly calculate AS for a chemical process, but they are not true" absolute entropies. 

A cryogenic calorimeter measures Cp,m as a function of temperature. We have seen that with the aid of the Third Law, the Cp,m data (along with AHm for phase changes) can be integrated to give the absolute entropy... 

We note from the derivation that Sm in equation (10.82) is the absolute entropy of the gas, since So.m has been cancelled by the constant of integration. 

Figure 10.14a shows such a plot for Kr.10 The straight line below 7 2 = 4 K2 (Ts= 2 K) demonstrates the validity of equation (10.160). A graph similar to the one shown in Figure 10.14a was used in Chapter 4 to extrapolate Cr resultsgg to zero Kelvin when we used the Third Law to obtain absolute entropies. 

Chapter 4 presents the Third Law, demonstrates its usefulness in generating absolute entropies, and describes its implications and limitations in real systems. Chapter 5 develops the concept of the chemical potential and its importance as a criterion for equilibrium. Partial molar properties are defined and described, and their relationship through the Gibbs-Duhem equation is presented. 

Chapter 4 - The Thrid Law and Absolute Entropy Measurements, Pages 155-202... 

In 1877, the Austrian physicist Ludwig Boltzmann proposed a molecular definition of entropy that enables us to calculate the absolute entropy at any temperature (Fig. 7.6). His formula provided a way of calculating the entropy when measurements could not be made and deepened our insight into the meaning of entropy at the molecular level. The Boltzmann formula for the entropy is... 

The entropies of individual ions in solution are determined by setting the entropy <>1 II in water equal to 0 and then defining the entropies of all other ions relative to this value hence a negative entropy is one that is lower than the entropy of H in water. All absolute entropies are positive, and no sign need he given all entropies of ions are relative to that ot H+ and are listed here with a sign (either + or —). 

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