Third law statement

Entropy Changes Near Absolute Zero and Third Law Statements For... 

Critical Assessment of Third Law Statements Each statement of the purported third law may be critically tested in terms of three criteria ... 

Why then should the student of physical chemistry be acquainted with third-law statements such as (5.79) Two motivations may be cited ... 

Critical Assessment of Third Law Statements Each statement of the purported... 

With this, the development of Classical Thermodynamics was complete. Or was it In as late as the middle of twentieth century it was argued and agreed that the principle of unattainability of the absolute zero is synonymous with the third law statement of entropy i.e., entropy of a crystalline substance is zero at absolute zero temperature . 

In the limit, T = 0 K, it is known empirically that the value of the coefficient of thermal expansion of solids approaches zero as a limit. Show that, as a consequence, the entropy is independent of pressure at 0 K so that no specification of pressure is necessary in the third-law statement. 

Because it is necessary to exclude some substances, including some crystals, from the Nemst heat theorem, Lewis and Gibson (1920) introduced the concept of a perfect crystal and proposed the following modification as a definitive statement of the third law of themiodynamics (exact wording due to Lewis and Randall (1923)) ... 

In the Lewis and Gibson statement of the third law, the notion of a perfect crystalline substance , while understandable, strays far from the macroscopic logic of classical thennodynamics and some scientists have been reluctant to place this statement in the same category as the first and second laws of thennodynamics. Fowler and Guggenheim (1939), noting drat the first and second laws both state universal limitations on processes that are experunentally possible, have pointed out that the principle of the unattainability of absolute zero, first enunciated by Nemst (1912) expresses a similar universal limitation ... 

No one doubts the correctness of either of these statements of the third law and they are universally accepted as equivalent. Flowever, there seems to have been no completely satisfactory proof of their equivalence some additional, but very plausible, assumption appears necessary in making the coimection. 

With this in mind Guggenlieim suggested still another statement of the third law of themiodynamics ... 

An alternate statement of the Third Law is the 1912 statement by W. Nernst Absolute zero is unattainable. To show the equivalence of the two statements of the Third Law consider the process... 

That is, S —> 0 as T - 0. The perfect crystal part of this statement of the third law refers to a substance in which all the atoms are in a perfectly orderly array, and so there is no positional disorder. The T— 0 part of the statement implies the absence of thermal motion-—thermal disorder vanishes as the temperature approaches zero. As the temperature of a substance is raised from zero, more orientations become available to the molecules and their thermal disorder increases. Thus we can expect the entropy of any substance to he greater than zero above T = 0. 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

Expressed in words, the rate of change of momentum represents a force. This is a statement of Newton s second law. The third law states that any action is balanced by a reaction, which implies conservation of momentum. 

Statistical mechanics affords an accurate method to evaluate ArSP, provided that the necessary structural and spectroscopic parameters (moments of inertia, vibrational frequencies, electronic levels, and degeneracies) are known [1], As this computation implicitly assumes that the entropy of a perfect crystal is zero at the absolute zero, and this is one of the statements of the third law of thermodynamics, the procedure is called the third law method. 

In Nemst s statement of the third law, no comment is made on the value of the entropy of a substance at 0 K, although it follows from his hypothesis that all pure crystalline substances must have the same entropy at OK. Planck [2] extended Nemst s assumption by adding the postulate that the value of the entropy of a pure solid or a pure liquid approaches zero at 0 K ... 

Lewis and Gibson [3] also emphasized the positive entropy of solutions at 0 K and pointed out that supercooled liquids, such as glasses, even when composed of a single element (such as sulfur), probably retain a positive entropy as the temperamre approaches absolute zero. For these reasons Lewis and Randall [4] proposed the following statement of the third law of thermodynamics ... 

We will adopt this statement as the working form of the third law of thermodynamics. This statement is the most convenient formulation for making calculations of changes in the Gibbs function or the Planck function. Nevertheless, more elegant formulations have been suggested based on statistical thermodynamic theory [5]. 

The preceding statement of the third law has been formulated to exclude solutions and glasses from the class of substances that are assumed to have zero entropy at 0 K. Let us examine one example of each exclusion to see that this limitation is essential. 

In the statement that we have adopted for the third law, it is assumed (arbitrarily) that the entropy of each element in some crystalline state is zero at 0 K. Then for every perfect crystalline substance, the entropy is also zero at 0 K. Consequently we can set S(0 K) in Equation (11.14) equal to zero. Thus, we may write... 

Third Law of Thermodynamics. Also referred to as the Nernst heat theorem, this law states that it is impossible to reduce the temperature of any system, via a finite set of operations, to absolute zero. For any changes involving perfectly crystalline solids at absolute zero, the change in total entropy is zero (thus, A5qk = 0). A corollary to this statement is that every substance, at T > 0 K, must have a positive and finite entropy value. The entropy of that substance is zero only at absolute zero when that substance is in pure, perfect crystalline form. See Entropy... 

R. H. Fowler and E. A. Guggenheim [Statistical Thermodynamics (Cambridge University Press, Cambridge, 1939)] criticized this statement as well as similar statements (to be quoted below) which imply that the entropy of perfect crystalline substances is zero. According to Fowler and Guggenheim, the only valid third-law inference is the unattainability of absolute zero, as expressed in the following statement ... 

Still more questionable statements (e.g., 5 = 0 at T = 0 ) can be found in other textbooks. The multiplicity of statements of the third law suggests its problematic character compared with other laws. 

Let us begin with the common statement (5.79) of the third law. If we inquire What is the meaning of a perfect crystal , the most direct answer appears to be It is a crystal with S0 = 0. This circular definition insures that (5.79) is impervious to falsification, but reduces the statement to a meaningless tautology. 

Finally, it will be shown (Section 11.8) that the basic observation (5.77a) is already a consequence of inductive laws that were previously incorporated in the Gibbsian formalism. Thus, even the Nemst heat theorem and Fowler-Guggenheim unattainability statement (although meaningful and valid) are essentially superfluous, bringing no new content to the thermodynamic formalism. We therefore conclude that all formulations of the third law fail one or more of the above criteria, and thus play no useful thermodynamic role as addenda to the Gibbsian formalism. 

Planck, in 1912, postulated that the value of the entropy function for all pure substances in condensed states was zero at 0 K. This statement may be taken as a preliminary statement of the third law. The postulate of Planck is more extensive than, but certainly is consistent with, the postulate of Nernst. 

Planck s statement of the Third law suggests that a scale for the absolute value of entropy can be set up ... 

The normal isotopic abundances for Li are 92.48 mole % for 7Li and 7.52 mole % for 6Li. Making reasonable approximations, determine the entropy, enthalpy, and Gibbs free energy changes on mixing the pure isotopes. Discuss your results in terms of the statements made in Section 1.21 in conjunction with the Third Law of Thermodynamics. 

Clausius himself, later on, introduced the concept of entropy. Studies on entropy led to the evolution of the Third Law of Thermodynamics in 1906 by Nemst (1907). This was many times debated and revised till 1912, when Plank (1927) went back to practically the same statement as that of Nemst. 

However, we can assign absolute entropy values. Consider a solid at 0 K, at which molecular motion. virtually ceases. If it is a perfect crystal, its internal arrangement is absolutely regular [see Fig. 10.11(a)]. There is only one way to achieve this perfect order every particle must be in its place. For example, with N coins there is only one way to achieve the state of all heads. Thus a perfect crystal represents the lowest possible entropy that is, the entropy of a perfect crystal at 0 K is zero. This is a statement of the third law of thermodynamics. 

---