Nernst-Planck theorem

In a homogeneous body at absolute zero temperature the entropy S is null Nernst-Planck theorem). 

The above discussions treat the change of entropy, and do not give an absolute value of entropy. In 1918 Nernst showed that in its uniform state a material at absolute zero temperature has zero entropy (English version Nernst 1969). This is referred to as the Nernst-Planck theorem or the Third Law of Thermodynamics (cf. Appendix D.3). 

Planck (loc. cit. 276) has observed that the point on which the whole matter turns is the establishment of a characteristic equation for each substance, which shall agree with Nernst s theorem. For if this is known we can calculate the pressure of the saturated vapour by means of Maxwell s theorem ( 90). He further remarks that, although a very large number of characteristic equations (van der Waals, Clausius s, etc.) are in existence, none of them leads to an expression for the pressure of the saturated vapour which passes over into (9) 210, at very low temperatures. Another condition which must be satisfied is... 

The Nernst-Planck Heat Theorem, 68.11, gives 5b =0, hence ... 

In other words, every chemical reaction takes place without change in entropy at the absolute zero. From this it follows that the entropy of a compound is equal to the sum of the atomic entropies. The assumption made by Planck in addition to Nernst s theorem, viz. that the entropy of all substances vanish like the specific heats at the absolute zero, is sufficient but not necessary for the derivation of the heat theorem. 

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. 

Since the last two terms in Eq. (11.74) can be calculated from heat capacities and heats of reaction, the only unknown quantity is ASS, the change in entropy of the reaction at 0 K. In 1906, Nernst suggested that for all chemical reactions involving pure crystalline solids, ASS is zero at the absolute zero the Nernst heat theorem. In 1913, Planck suggested that the reason that ASS is zero is that the entropy of each individual substance taking part in such a reaction is zero. It is clear that Planck s statement includes the Nernst theorem. 

The third law of thermodynamics postulates that the entropy of chemically pure, crystalline substances at absolute zero 0 K is zero. Originally, this postulate was put forward as the Nernst heat theorem (1906) and later proved by quantum mechanics (Planck 1912). From this absolute zero, the standard entropy S T) of substances can formally be determined at an arbitrary temperature T, by adding the entropy increases AS from heating and phase transformations to 5(0). 

Equation (11.4) provides a convenient value for that constant. Planck s statement asserts that 5qk is zero only for pure solids and pure liquids, whereas Nernst assumed that his theorem was applicable to all condensed phases, including solutions. According to Planck, solutions at 0 K have a positive entropy equal to the entropy of mixing. (The entropy of mixing is discussed in Chapters 10 and 14). 

Further work on similar types of cells has been carried out, in which not only is use made of the Nernst Theorem but likewise of the Einstein theory of atomic heat of solids (as modified by Nernst and Lmdemann) This will be taken up after we have discussed Planck s Quantum Theory of radiation and Einstein s application of it to the heat capacity of solids (Vol. Ill)... 

In 1902, T. W. Richards found experimentally that the free-energy increment of a reaction approached the enthalpy change asymptotically as the temperature was decreased. From a study of Richards data, Nernst suggested that at absolute zero the entropy increment of reversible reactions among perfect crystalline solids is zero. This heat theorem was restated by Planck in 1912 in the form The entropy of all perfect crystalline solids is zero at absolute zero.f This postulate is the third law of thermodynamics. A perfect crystal is one in true thermodynamic equilibrium. Apparent deviations from the third law are attributed to the fact that measurements have been made on nonequilibrium systems. 

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