Verification of the Third Law

In a chemical reaction at a given temperature, this relationship can be used to give 

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

The conclusion that can be reached from the Nernst heat theorem is that the total entropy of the products and the reactants in a chemical reaction must be the same at 0 Kelvin. But nothing in the statement requires that the entropy of the individual substances in the chemical reaction be zero, although a value of zero for all reactants and products is an easy way to achieve the result of equation (4.17). 

Within experimental error, S0m (monoclinic) = 5o.m (rhombic), and it seems more probable that they both have zero entropy at 0 K than that both have the same non-zero entropy. 

In a procedure similar to that described earlier for N , the entropy at T = 49.44 K point (a) can be calculated from the heat capacities and the enthalpies of transition, by following two different paths. Sm 49 44 was found to be 34.06 J-K-1 mol-1 following the solid III— solid II path and Sm.49.44 = 34.02 JK 1 mol l following the (solid V— solid IV— solid II) path. The two results agree well within experimental error, which requires that the entropy of solid III and solid V be the same at 0 K, an occurrence that is unlikely unless Sm 0 = 0 for both forms. 

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W. F. Giauque was one of those pioneers whose work led to the verification of the Third Law. He received the Nobel Prize in 1949 for his work. 

Comparison and agreement with the calorimetric value verifies the assumption that So = 0. For example, we showed earlier that the entropy of ideal N2 gas at the normal boiling point as calculated by the Third Law procedure had a value of 152.8 0.4 J-K mol. The statistical calculation gives a value of 152.37 J K -mol-1, which is in agreement within experimental error. For PH3, the Third Law and statistical values at p 101.33 kPa and T— 185.41 K are 194.1 0.4 J K, mol 1 and 194.10 J-K 1-mol 1 respectively, an agreement that is fortuitously close. Similar comparisons have been made for a large number of compounds and agreement between the calorimetric (Third Law) and statistical value is obtained, all of which is verification of the Third Law. For example, Table 4.1 shows these comparisons for a number of substances. 

At such low temperatures, most matter is solid, and the best type of solid sample to study is a crystal. Studies of crystals showed some intriguing thermodynamic behavior. For instance, in the measurement of entropy it was found that absolute entropy approached zero as the temperature approached absolute zero. This is experimental verification of the third law of thermodynamics. But a measurement of the heat capacity of the solid showed something interesting The heat capacity of the solid approached zero as the temperature approached absolute zero, also. But for virtually all crystalline solids, the heat-capacity-versus-temperature plot took on a similar shape at low temperatures, typified by Figure 18.3 The curves have the distinct shape of a cubic function, that is, y = x. In this case, the variable is absolute temperature, so experimentally it was found that the constant-volume heat capacity Cy was directly related to T ... 

Method With the exception of installation of a thermocouple between two alum crystals pressed up together [1-3], no simple and reliable methods for the experimental determination of the magnitude of self-cooling in a decomposing solid existed until recent years. Verification of the above calculations was thus difficult. The situation changed for the better only very recently with the appearance of third-law methodology in TA [8]. 

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