Nemst’s heat theorem

Nevertheless, as noted by Lewis and Randall, certain post-Gibbsian addenda appeared, which will be discussed in the present section. Some of these innovations, such as activity and fugacity (Section 5.8.1), were designed primarily to satisfy practical needs of representing experimental thermochemical data, with no deeper claims on the underlying structure of the theory. In contrast, the developments initiated by Nemst s heat theorem, culminating in what became widely known as the third law of thermodynamics, appear to call into question the structural completeness of the Gibbsian formalism. These developments will be critically discussed in Section 5.8.2. 

Nemst s heat theorem (1906) As T > 0, the entropy change in any reversible process tends to zero. 

Strictly speaking, the equation K =S is an extension of Boltzmann s theory, in so far as we have ascribed a definite value to the entropy constant. According to Boltzmann, the probabihty contains an undetermined factor, which cannot be evaluated without the introduction of new hypotheses. Boltzmann and Clausius suppose that the entropy may assume any positive or negative value, and that the change in entropy alone can be determined by experiment. Of late, however, Planck, in connection with Nemst s heat theorem, has stated the hypothesis that the entropy has always a finite positive value, which is characteristic of the chemical behaviour of the substance. The probabihty must then always be greater than unity, since its logarithm is a positive quantity. The thermodynamical probabihty is therefore proportional to, but not identical with, the mathematical probabihty, which is always a proper fraction. The definition of the quantity w on p. 15 satisfies these conditions, but so far it has not been shown that this definition is sufficient under all circumstances to enable us to calculate the entropy. 

To begin with, we shall discuss a deduction from Nemst s heat theorem which is qualitatively in accord with the facts. If the affinity A converges to a finite value A as the temperature is diminished, its second derivative must have the same... 

Kox, A. Confusion and clarification Albert Einstein and Walther Nemst s heat theorem, 1911-1916. Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Mod. Phys. 37(1), 101-114 (2006)... 

K5rber7 calculated (i) the density at 0°K. from the coefficient of expansion of the liquid at 1 atm. pressure, and (ii) the density at infinite pressure from the compressibility of the liquid at 0° to 50° C. and Tammann s equation, v=v ,- -AKI K- -p), where Ooo=volume at p=oo, and A and K are constants. The first value was somewhat smaller than the second, which was connected with the vanishing of do/dJ at 0°K. according to the Nemst Heat Theorem ( 73.H). The possibility of the compression of the molecules themselves must, however, be taken into account. 

Some examples of the application of the Nemst Theorem m a slightly different form to that already followed have been investigated by J T Barker (Zeitsch physik Chem, 71, 235, 1910) in Nemst s laboratory The following table contains the values of A and - Q (the latent heat of solidification (heat evolved)) in the case of benzene —... 

In justification of the present attempt to deduce Nemst s Theorem theoretically, I must point out, in intro duction, that all endeavours to do so by thermodynamical means, using the experimental rule that heat capacity vanishes at T = o, are to be regarded as having failed.. . ... 

Haber had apparently closed the door on the synthesis of ammonia from its elements. But in 1906, Walther Nemst, using his new heat theorem, calculated the reaction s theoretical ammonia concentration at equilibria corresponding to several pressures. He found that his value at atmospheric pressure disagreed significantly with Haber s, and he publicly challenged Haber s values. 

Since the entropy is S= - dFfdT dAJdTy the Nemst heat theorem (also called the third law of thermodynamics) can be expressed in the form ... 

Afjter much discussion of its range of validity, the Nemst heat theorem has l een stated in the form that the entropy of all factors within a system which are in internal thermodynamic equilibrium disappears at absolute zero temperature. Nemst s other work is considered later (see p. 633). 

Nemst s theorem is applicable only to equilibrium systems. From the third law of thermodynamics, it follows that absolute zero is unattainable because, according to eq. (3.5.27), if near a temperature of absolute zero, a small amount of heat is taken off a system (AT -> 0), a large enough (in a limit infinite) entropy change will take place this contradicts Nemst s theorem. 

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. 

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