The Entropy of a Crystalline Solution of Silver Bromide and Silver Chloride in Relation to the Third Law of Thermodynamics

Abstract

With the object of testing experimentally the third law of thermodynamics as applied to crystalline solutions, the chief thermodynamic properties of such a solution of silver bromide and silver chloride have been studied. Measurements described and recorded include: the free energy of formation, obtained from measurements of the e.m.f. of appropriate silver-silver halide electrodes against hydrogen; the heat of formation, from measurements of heat absorbed in dissolving the various phases in a thiosulfate solution; the specific heats between 15°K and 298°K of the pure constituents and the solid solution. The entropy of silver bromide and of silver chloride is calculated from the specific heat curves. The entropy change in the formation of the solid solution at 298°K is calculated from the experimental data and is found to agree with the result calculated statistically. The latter is identical in form and magnitude with the entropy as calculated thermodynamically for an ideal solution, though the heat content and free energy show that the solution is far from perfect. From the specific heat curves it appears that the entropy of mixing persists essentially unchanged in magnitude to the lowest temperature of the measurements, and presumably to the absolute zero. The existence of finite entropies, or entropy differences, at the absolute zero is regarded as established thermodynamically, and the requisite interpretation of statistical ideas to secure concordance with this result is discussed. Finally, although the existence of a valid but limited third law is accepted, and a concise general statement of it suggested, it is pointed out that the ``principle of the unattainability of the absolute zero'' must be regarded as extra-thermodynamic in character.

High Purity Isotopically Enriched29Si and30Si Single Crystals: Isotope Separation, Purification, and Growth

“…Figure 5 shows a good agreement with the experiment up to 15K from which we obtain y = 6.12 x For T > 15 K the Debye approximation fails in AgBr as is known from specific heat measurements (Eucken et all931, Eastman and Milner 1933). Therefore the deviation of the theory from experiment above 15 K does not necessarily invalidate the model; moreover at this temperature the linear approximation for A t j also breaks down.…”

Modeling the relaxation of polymer glasses under shear and elongational loads

“…The paradox is avoided if we are correct that an entropic polymer stress can persist within a frozen solvent. Note that closely analogous arguments concerning the persistence of entropic contributions to the chemical potential in frozen systems have been confirmed in both experiment 52 and simulation.…”

“…We believe we have the right answer to this question (the entropic force is maintained but its response to further deformation is altered), which mirrors similar discussions of phase equilibria involving nonergodic materials that date back over 80 years. 52,53,60 This type of question might remain a technical nicety if the predominant polymer stress in glasses is never entropic, but comes to the fore if the opposite is ever true.…”

The quasi-low temperature behaviour of specific heat

“…From this graph or directly from the C m / T 3 values, we can find the characteristic temperature of AgCl, which is T 0 = 10.6 K. If we plot T θ for AgCl specific heat data, figure 7 (in units 10 −4 K), we find that the minimum of this graph coincides with the maximum of the graph in figure 6: it is the same T 0 as expected.

Figure 6. C m / T 3 vs T for AgCl [35,36].

Figure 7. T θ ( T ) for AgCl [35].

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