Entropy at absolute zero

The third law (also called the Nernst heat theorem) states that all perfectly ordered crystalline substances have zero entropy at absolute zero temp... 

Studies related to entropy changes revealed that reduction in temperature leads to decrease in entropy change for all processes. It was therefore, postulated that for a process occurring at absolute zero temperature the entropy change would be zero. This has led to a basis from which absolute values of entropy can be determined, taking entropy at absolute zero of temperature to be zero. Thus, unlike i/and F whose changes can be accurately measured but not the absolute value, the absolute value of entropy can indeed be measured. We take, for calculation purposes, enthalpy of elements in a defined standard state to be zero, but that assumption is only for convenience, no molecule or atom can have zero heat content at ambient conditions. On the other hand, a fully ordered (crystalline) solid at absolute zero temperature will have zero entropy. 

Thus, at equilibrium in its lowest energy state the system is in its most stable configuration, for which the entropy at absolute zero. So, has the lowest possible value, whatever the coordinate z under consideration. Moreover, the lowest possible entropy is attained in the limit of vanishing slope dS/dz)T 0 as T - 0. 

Three points are worth making about this third law. First, if it weren t true, it would not be a big deal. We would just have to tabulate entropies at absolute zero as we already do for enthalpies and forego the expression "absolute entropy." Second, some compounds have "residual entropies" at absolute zero as it is, and we can cope with and understand them easily. Third, there are no perfect crystals, there never will be, and there don t need to be in order for the entropy at absolute zero to measure zero. What is the maximum experimental precision of an entropy measurement Perhaps 10 5 eu How big can the degeneracy of a crystal be before its entropy becomes 10 eu ... 

Cp, Cv and S are expressed in units of energy/(m ole-degrees). H and G are expressed in units of energy/mole. Units of J/(mole K) will be used for Cp, Cv and S, and units of J/mole will be used for H and G, in this book. H(0) and S(0) are the residual enthalpy and residual entropy at absolute zero temperature. 

According to this all perfect solids must have the same entropy at absolute zero, which does not necessarily have to be zero. 5(7 = 0) = 0 is an agreement. 

This gives the configurational entropy of mixing for any number of components. It can be used to calculate residual entropies at absolute zero due to impurities, imperfections, nuclear spin, isotojjes, etc., simply by considering the imperfections as one component of a mixture. Equation (6.37) applies equally well to ideal mixtures at higher temperatures, as we shall see in Chapter 10. 

From what has been said it is clear that glassy or amorphous substances will have a random arrangement of constituent particles and so will possess a residual entropy at absolute zero. The third law is therefore restricted to pure crystalline substances. A final restriction should be made in the application of the third law The substance must be in a single quantum state. This last requirement would take care of the difficulty that arises in the case of hydrogen. 

The Third Law of Thermodynamics All Perfect Crystals Have the Same Entropy at Absolute Zero... 

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. 

It should be noted that what one measures in experiments is the difference in the entropy, and not the absolute entropy. Assuming that the entropy is zero at absolute zero in accordance with the Nemst-Planck postulate, one can determine the absolute entropy experimentally. However, it is well known that SCL is a metastable state, and there is no reason for its entropy to vanish at absolute zero [16]. Indeed, it has been demonstrated some time ago that the residual entropy at absolute zero obtained by extrapolation is a nonzero fraction of the entropy of melting [43 ], which is not known a priori. Therefore, it is impossible to argue from experimental data that the entropy indeed falls to zero, since such a demonstration will certainly require calculating absolute entropy though efforts continue to date [61, 62]. 

---