Formulation of the Third Law

This assumption states not only that AG approaches AH as T approaches 0 K but also that the AG curve and the AH curve (Fig. 11.1) approach a horizontal limiting tangent. 

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This relationship led to an early formulation of the Third Law known as the Nernst heat theorem, which states that for any isothermal process... 

For convenience and in accordance with a familiar formulation of the third law of thermodynamics, let us take our starting point for entropy measurements such that the entropy of the crystal is zero at the extremely low temperature involved. Starting with the crystal let us then form by reversible evaporation one mole of vapor at the vapor pressure. The entropy of the gas thus formed will evidently be... 

We have pointed out previously that for many reactions the contribution of the TAS term in Equation (7.26) is relatively small thus, AG and AH frequently are close in value even at relatively high temperatures. In a comprehensive series of experiments on galvanic cells, Richards [1] showed that as the temperature decreases, AG approaches AH more closely, in the manner indicated in Figirre 11.1 or Figure 11.2. Although these results were only fragmentary evidence, especially since they required extrapolation from 273 K to 0 K, they did furnish the clues that led Nemst to the first formulation of the third law of thermodynamics. 

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. 

Keywords absolute zero, unattainabiiity formulation of the Third Law of... 

The unattainabiiity formulation of the Third Law of Thermodynamics is briefly reviewed in Sect. 2.1. It puts limitations of the quest for absolute zero, and in its strongest mode forbids the attainment of absolute zero by any method whatsoever. But typically it is stated principally with respect to thermal-entropy-reduction refrigeration (TSRR). TSRR entails reduction of a refrigerated system s thermal entropy, i.e., its localization in the momentum part of phase space (in momentum space for short). The possibility or impossibility of overcoming these limitations via TSRR is considered, in Sects. 2.2. and 2.3. with respect to standard TSRR, and in Sect. 2.4. with respect to absorption TSRR. (In standard TSRR, refrigeration is achieved at the expense of work input in absorption TSRR, at the expense of high-temperature heat input.)... 

Limits imposed by the Second Law and by the unattainability formulation of the Third Law on TSRR... 

The work required to cool any finite sample of matter (and/or of energy such as equilibrium blackbody radiation) maintained within a fixed finite volume V or at constant pressure P from any initial finite fixed, relatively hot ambient temperature Th to what is generally considered to be the ultimate cold temperature Tq = 0 K via standard TSRR is finite — indeed for typical room-temperature T// and for typical laboratory-size samples typically small. Hence the unattainability formulation of the Third Law of Thermodynamics does not forbid attainment of 0 K via standard TSRR by requiring infinite work for the process. Rather, it forbids attainment of 0 K via standard TSRR by forbidding the performance of the required finite, typically small, amount of work. 

The unattainability formulation of the Third Law of Thermodynamics in toto — not merely any particular limit(s) imposed thereby — has been questioned [1], Above all, the question of the attainability of 0 K in a finite number of finite operations (perhaps even in one) by any method whatsoever, and hence the status of the unattainability formulation of the Third Law of Thermodynamics in its strongest mode, according to which this is impossible, remains open [1,26-28], Even so, the question of whether or not OK is attainable by any method whatsoever is sometimes stated to be only of academic interest [27], and it is also sometimes stated that there may be "profound problems [22]" concerning attaining "absolute thermal isolation [22]," i.e., perfect insulation [23], and that infinitely precise measurements [22] may be required to perfectly verify [22] that precisely 0 K has actually been attained [22],... 

It is generally stated that the Nemst formulation of the Third Law of Thermodynamics, according to which all entropy changes vanish at 0 K, and the unattainability formulation thereof, according to which 0 K is unattainable in a finite number of finite operations, are equivalent. But we should note that there are dissensions to this viewpoint [108-113].9... 

Re Entries [17] and [117], Refs. [17] and [117]) The detailed discussions concerning the third law of thermodynamics in Ref. [117] are largely deleted in Ref. [17], which provides only a brief mention of the third law on p. 217. Reference [117] dubs the Nernst formulation of the Third Law of Thermodynamics as the Nernst-Simon formulation thereof. Reference [17] does not render Ref. [117] obsolete, because Ref. [117] discusses aspects not discussed in Ref. [17], and vice versa. 

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... 

Nernsf s formulation of the third law of thermodynamics was originally an ingenious solution to a crucial practical problem in chemical thermodynamics, namely, the calculation of chemical eqtiilibria and the course of chemical reactions from thermal data alone, such as reaction heats and heat capacities. Based on the first two laws of thermodynamics and van t Hoffs equation, chemical equilibria depended on the free reaction enthalpy AG, which was a function of both the reaction enthalpy AH and the reaction entropy AS according to the Gibbs-Helmholtz equation ... 

The third law of thermodynamics, like the first and second laws, is a postulate based on a large number of experiments. In this chapter we present the formulation of the third law and discuss the causes of a number of apparent deviations from this law. The foundations of the third law are firmly rooted in molecular theory, and the apparent deviations from this law can be easily explained using statistical mechanical considerations. The third law of thermodynamics is used primarily for the determination of entropy constants which, combined with thermochemical data, permit the calculation of equilibrium constants. 

It is also often stated that according to the third law of thermodynamics, absolute zero is unattainable by a suitable process through a finite number of steps. This statement is often presented as an alternative formulation of the third law of thermodynamics. 

However, other authors think that this theorem is due to the second and the third law simultaneously. This means that the theorem of the unattainability of absolute zero temperature is not a consequence of the third law exclusively. If this is valid, with the statement of the unattainability of absolute zero we cannot trace back the third law of thermodynamics. Nowadays, there are various formulations of the third law of thermodynamics. 

The theory behind the third law of thermodynamics was initially formulated by Walther Nemst in 1906, which was known as Nemst theorem (https //www.sussex. ac.uk/webteam/gateway/file.php name=a-thermodynamicshistory. pdf site=35). The third law of thermodynamics was conceived from the fact that attaining absolute zero temperature is practically impossible. Lord Kelvin deduced this fact from the second law of thermodynamics with his study of heat transfer, work done, and efficiency of a number of heat engines in series. Kelvin s work was the foundation for the formulation of the third law. It can be stated as follows Absolute zero temperature is not attainable in thermodynamic processes. Another noted scientist, Max Planck, put forward the third law of thermodynamics from his observations in 1913. It states that The entropy of a pure substance is zero at absolute zero temperature. Plank observed that only pure, perfectly crystalline stmctures would have zero entropy at absolute zero temperamre. All other substances attain a state of minimum energy at absolute zero temperature as the molecules of the substance are arranged in their lowest possible energy state. 

Walter H.Nemst, 1864-1941. Professor of Physics in Gottingen and Berlin. Hewasoneof the founders of modem physical chemistry. His formulation of the third law of thermodynamics gained him the 1920 Nobel Prize for Chemistry,... 

Much of conventional thermodynamics developed from electrochemical work. The detailed investigation of the behaviour of reversible electrochemical cells and the reactions occurring within them contributed to the appreciation of the concept of standard free energy and led to the accurate determination of thermodynamic constants for cell reactions. Early work on the temperature dependence of reversible cell e.m.f. s contributed considerably to the formulation of the Third Law of Thermodynamics. 

The constant term may be identified with So we note that So — k log go, where is the statistical weight of the ground state, that is, the number of eigenfunctions corresponding to this state. This is the statistical-mechanical formulation of the third law of thermodynamics. If, as is usually true, the ground state of a system is non-... 

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