Experimental determination of absolute entropies

The postulates of Nernst are those that are required when we wish to determine equilibrium conditions for chemical reactions from thermal data alone. In order to calculate the equilibrium conditions, we need to know the value of AGe for the change of state involved. We take the standard states of the individual substances to be the pure substances at the chosen temperature and pressure. The value of AH° can be determined from measurements of the heat of reaction. We now have 

Planck, in 1912, postulated that the value of the entropy function for all pure substances in condensed states was zero at 0 K. This statement may be taken as a preliminary statement of the third law. The postulate of Planck is more extensive than, but certainly is consistent with, the postulate of Nernst. 

The stable phase of all substances, except helium, at sufficiently low temperatures is the solid phase. We therefore consider the solid phase as the condensed state whose entropy is zero at 0 K, and exclude helium from the discussion for the present. The absolute entropy of a pure substance in some state at a given temperature and pressure is the value of the entropy function for the given state taking the value of the entropy of the solid phase at 0 K 

Equation (15.9) illustrates the type of calculations that must be made to obtain the value of the entropy function of a substance in a given state. We must include all increases in entropy for the increase of temperature of a single phase and for changes of phase that are required to reach the desired state from the state at 0 K. 

Two points concerning the evaluation of the first integral in Equation (15.9) require further discussion. In most experimental determinations of absolute entropies, the lowest temperature attained ranges from 1 to 15 K  

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The condition discussed in the previous paragraph demands certain care in the experimental determination of absolute entropies, particularly in the cooling of the sample to the lowest experimental temperature. In order to approach the condition that all molecules are in the same quantum state at 0 K, we must cool the sample under the condition that thermodynamic equilibrium is maintained within the sample at all times. Otherwise some state may be obtained at the lowest experimental temperature that is metastable with respect to another state and in which all the molecules may not be in the same quantum state at 0 K. 

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