# Nernst Law of Thermodynamics

Nernst`s heat theorem was formulated by Walther Nernst in the early twentieth century and used in the development of the third law of thermodynamics. An alternative version of the third law of thermodynamics, established in 1923 by Gilbert N. Lewis and Merle Randall: The agreement reached by comparing the values of ΔS for chemical reactions calculated with and without the use of the entropies of the third law and by comparing the entropies of the third law with values calculated from spectroscopic data, He played an important role in determining the third law. In other cases, however, similar comparisons have led to the identification of substances, e.g. CO, NO and H2O, which do not reach a “perfect crystal state” at 0 K and for which S0≠0 is present. The existence of such materials underlines the importance of caution in applying the third law to the determination of entropies from specific thermal data. The third law of thermodynamics, unlike the first and second laws, cannot be expressed by a simple mathematical relation, which is strict in all cases. Its application requires an understanding of its nature, which can be based on a statistical mechanical expression for entropy, Boltzmann`s formula, S = kB ln Ω (where Ω is the number of accessible quantum states subject to the constraint of a fixed energy), as well as the principle that there is only one lowest energy state reached at T = 0 by systems, which are in thermodynamic equilibrium. The case of CO, which is well understood, is a useful illustration of the factors that determine whether S0 = 0: In the solid, the two orientations of a molecule, which differ by an exchange of the C and O atoms, are two distinct states, but because the molecule is relatively symmetrical in terms of shape and distribution of electric charge, The energy difference is small. The lowest energy configuration is one in which there is a perfectly ordered arrangement of molecules, each in a given orientation relative to the others, but the energy is not much lower than that of higher entropy, a random distribution of orientations that is thermodynamically stable at high temperatures. Below ∼5 K, the ordered configuration of low energy becomes thermodynamically stable, but there is a potential barrier to molecular reorientation that exceeds the thermal energy at this temperature, and the perfectly ordered state is not reached. For kinetic reasons, 0 K and S0≠0 have a “frozen perturbation”. In the completely random configuration, there are two possible states for each molecule, Ω = 2NA, S = Rln2 = 5.76J K−1mol−1.

The experimental value is S0=4.2J K−1mol−1, indicating that the molecules are partially ordered, at least in the specific measurement that gave this result. There are other cases, for example NO, H2O and H2O in Na2SO4·10H2O, where the disturbance is complete. These examples help to understand the treatment of nuclear contributions to entropy: the random distribution of different isotopes of the same element across network sites remains at 0 K, the perturbation is frozen, and there is no contribution to specific experimental thermal data. The disorder associated with the orientation of nuclear spin is not frozen, but at temperatures above 1 K it is usually complete, the associated entropy is constant, and there is no contribution to specific heat. The two contributions to entropy cancel each other out in chemical reactions, and although they can be calculated using Boltzmann`s formula, they are omitted from the entropy tables of chemical substances. There are also paramagnetic salts in which the magnetic moments of unpaired electrons, as in the case of nuclear moments, are less than less than 1 K. Measurements with a specific heat up to 1 K would suggest S0≠0, but measurements at a sufficiently low temperature would give S0=0. Harvey, L. S. Proof of the third law of thermodynamics for Ising ferromagnets. A 2, 2368 (1970).

The third law was developed by chemist Walther Nernst in 1906–12 and is therefore often referred to as Nernst`s theorem or Nernst`s postulate. The third law of thermodynamics states that the entropy of a system at absolute zero is a well-defined constant. This is because a system exists at zero temperature in its ground state, so its entropy is determined only by the degeneracy of the ground state. Another method of measuring entropy involves the third law of thermodynamics, which states that the entropy of a perfect crystal of a pure substance in internal equilibrium at a temperature of 0 K is zero. This follows from Eqn 2 and the concept of entropy as disorder. For a perfectly ordered system at absolute zero, t = 1 and S = 0. The “third law of thermodynamics” treats events as T→0, where đQ/T can diverge. First, it is shown that zero temperature is unattainable. Consider the general case where z is a strain coordinate and Z is the conjugate variable, so that the first distribution takes the form dS=T−1[dU+Zdz]=T−1{(∂U/∂T)dT+[Z+(∂U/∂z)]dz}.

In the following, we need the result of the cross-differentiation of this expression with respect to T and z, namely Z+(∂U/∂z)=T(∂Z/∂T). The case of dS = 0 is now particularly interesting, because one can only hope to reach the lowest possible temperature under adiabatic conditions. The imposition of this requirement leads to There is no formula associated with the third law of thermodynamics, In the limit of T = 0, the equation is reduced to only ΔG = ΔH, as shown in the figure shown here, which is supported by experimental data. [2] From thermodynamics, however, we know that the slope of the ΔG curve is -ΔS. Since the slope shown here reaches the horizontal limit of 0 as T → 0, the implication is that ΔS → 0, which is Nernst`s heat theorem. Aizenman, M. & Elliott, L. H. The third law of thermodynamics and ground state degeneracy for lattice systems. 24, 279-297 (1981).

A modern understanding of entropy and quantum theory takes the heat theorem out of the realm of thermodynamics. Nernst`s version states: At zero temperature, a finite-sized system has an entropy S independent of external parameters x, i.e. S(T, x1)âS(T, x2)â0 as temperature Tâ0. Since we now understand zero-temperature entropy as the logarithm of ground-state degeneracy, the validity of the heat theorem depends on whether the degeneracy changes for different parameters of Hamilton`s Hamilton. It is easy to find Hamiltonian families who encounter or injure the heating rate.6,7 Here, however, we deal with the issue of Nernst`s principle of inaccessibility8, which Nernst introduced to support his attempts to derivate from his heat theorem and to counter Einstein`s objections. We can understand that it takes an infinite amount of time or an infinite number of steps to bring a system to its ground state. Nernst argues that if the heat theorem could be violated, it would be possible to violate the principle of inaccessibility (Fig. 1). We will see that this is not the case. Although one can potentially cool faster in systems that violate the heat theorem, we show that the principle of inaccessibility still applies. The bond we obtain quantifies the extent to which a change in entropy at T=0 affects the cooling rate.

Horodecki, M. & Oppenheim, J. Fundamental limitations for quantum and nanoscale thermodynamics. Nat. Common. 4, 2059 (2013). The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero. The entropy of an absolute zero system is typically zero and, in any case, is determined only by the number of different ground states it has. In particular, the entropy of a pure crystalline substance (perfect order) at absolute zero temperature is zero.

This statement applies when the perfect crystal has only one state with minimal energy. We hope that the present work will better align the third law with those of the other laws of thermodynamics. These have long been established, although they have recently been reformulated in the context of other resource theories.19,20,25,27,38,39,40 As described in ref. 30, the first law (energy saving) and unitarity (or microscopic reversibility) describe the class of operations that are permissible in thermodynamics. The zero law is the fact that the only state that can be added to the theory without making it trivial is the equivalence class of thermal states at temperature T. This allows the temperature to rise naturally. The second act tells us what state transformations are permitted in the category of transactions. For macroscopic systems with short-range interactions, there is only one function, entropy, that tells you whether you can switch from one state to another, but in general, there are many limitations.25,30,31,32 The third law quantifies the time it takes to cool a system. We propose to generalize it further: while the second law tells us which thermodynamic transitions are possible, the third generalized laws quantify the timing of these transitions. In this context, it would be interesting to study the time and resource costs of other thermodynamic transitions. It would also be interesting to examine the third law in more constrained physical environments, as well as other theoretical frameworks of resources, particularly those discussed in ref. 30.

As stated in one of the many formulations of the third law of thermodynamics, the entropy of any substance in a perfect crystalline state is zero within the T→0 limit. The importance for chemical thermodynamics is that entropy values can be obtained from specific thermal data alone: the “third law entropy” is obtained by extrapolating specific thermal data to 0 K, CP/T is integrated to obtain S(T)-S0, and assuming, as proposed in the third law, that S0, the entropy in state 0 K, obtained by extrapolation is equal to zero.

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