Statement of the third law

As is well known, Thomsen and Berthelot believed that the tendency of reactions to take place is determined by the heat of reaction, and this view was subsequently modified in favour of the free energy as the correct criterion. Nevertheless it remains true that the majority of reactions take place in the direction in which heat is evolved, especially when the temperature is low, and when none of the substances are gaseous. 

Evidently A4 (or AG) is not very different from AZ7 (or AST) for such processes, and this was substantiated by Richards who showed. 

Instead of considering differences of entropy, as was done by Nemst, Planck subsequently adopted ] the stronger statement as the temperature diminishes indefinitely, the entropy of a chemically homogeneous body of finite density approaches indefinitely near to the value zero . The discussion in 13 11 shows that this statement is not at all satisfactory. In the fiirst place the absolute zero is not attainable, and we must discuss instead the properties of matter as smoothly extrapolated to T = 0 from the lowest attainable temperature T. Secondly, the possibility of giving any value including zero, to the entropy is entirely conventional because nothing is known about the entropy of the nucleus. Finally, we have seen that even the conventional entropy does not necessarily fall to a value of 

X Planck, Treatise on Thermodynamics transl. Ogg (London, Longmans, 1927), 3rd ed., p. 274. 

To be sure, in the great majority of cases the comparison of and i eaior. h dicates that Qq unity, which means that the conventional entropy does approach zero. But it is precisely because there are exceptions that it is difficult to put forward an unambiguous law of nature on the lines of Planck s formulation. Modem versions of the law are much closer to Nemst s original statement, but contain safeguards against unstable states such as supercooled liquids and 

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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. 

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 ... 

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. 

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. 

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 ... 

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. 

The second statement of the third law (which bears Planck s name) is that as the temperature goes to zero, AS goes to zero for any process for which a reversible path could be imagined, provided the reactants and products are perfect crystals. Here, perfect crystals are defined as those which are non-degenerate, that is, they have only a single quantum state in which they can exist at absolute zero. This statement follows rigorously from Boltzmann s equation for entropy,... 

Before we can use this statement, the perfect state must be defined. Here by perfect" we mean without any disturbance in the arrangement of the atoms. That is, the substance must be without any vacancies, dislocations, or defects in the structure of the solid (or liquid) and not contain any impurities. The statement of the third law here is somewhat too constraining. A more correct statement is that all substances in the perfedt state mentioned above should have the same value of entropy at 0 K, not necessarily a value of zero. It is mostly for convenience in the preparation of thermodynamic tables that a value of entropy of zero at 0 K is chosen. 

There are several implications of the above statement. The first obvious one is that there will be no entropy change on a chemical reaction at 0 K if each of the reacting substances is in a perfect state, to produce one or more products in perfect states. In fact, it was this observation that led to the formulation of-the third law. A second implication, which is less obvious and is sonietimes used as an alternative statement of the third law, is... 

In conclusion, we should note that the first statement of the third law of thermodynamics was made by Nernst in 1906, the Nernst heat theorem, which states that in any chemical reaction involving only pure, crystalline sohds the change in entropy is zero at 0 K. This form is less restrictive than the statement of Planck. 

An equivalent statement of the third law is It is impossible to reduce the temperature of any system to absolute zero. (A discussion of the equivalence of this formulation with that enunciated by Planck is given in the book E. A Guggenheim, Thermodynamics, p. 161, Interscience Publishers, Inc., New York, 1949.)... 

The most common statement of the third law of thermodynamics is that the entropy of a perfectly crystalline system approaches zero as the temperature of the system approaches zero. (Recall from Macroscopic Properties The World We See that a perfect crystal is a regularly ordered lattice of atoms that exist in a repeating pattern in three dimensions with no defects or irregularities in the lattice.) This is equivalent to saying that a perfectly crystalline system has only one accessible state as the temperature ap-... 

Nernst heat theorem A statement of the third law of thermodynamics in a restricted form if a chemical change takes place between pure crystalline solids at solute zero there is no change of entropy. 

The statement of the third law by Lewis and Randall (1923) is still useful ... 

A classic statement of the third law principle appears in the 1923 book Thermodynamics and the Free Energy of Chemical Substances by G. N. Eewis and M. Randall ... 

The currently-accepted statement of the third law of thermodynamics is as follows the entropy of any substance tends toward a finite value at the temperature of absolute zero, and that value may be equal to zero in a number of cases. 

In 1911 Planck proposed extending Nemst s statement to assert that the entropies of individual substances actually approach zero as the temperature approaches zero. However, there is no experimental justification for this assertion. In 1923 Lewis proposed the following statement of the third law the entropy of each element in some crystalline state be taken as zero at the absolute zero of temperature, every substance has a finite positive entropy—but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances. We base our entropy calculations on this statement. 

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