Nernst Heat Theorem and the Third Law

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. 

An equivalent statement of the third law is It is impossible to reduce the temperature of any system to absolute zero. (A discussion of the equivalence of this formulation with that enunciated by Planck is given in the book E. A Guggenheim, Thermodynamics, p. 161, Interscience Publishers, Inc., New York, 1949.) 

The third law is used for the calculation of absolute entropies. The differential change in entropy in a reversible process is given by 

The difference in entropy between a state at temperature T and the perfect crystalline, solid at absolute zero is obtained by integrating Eq. (5-1) along any reversible path between the state at T and the state at absolute zero. Thus, 

The last term is evaluated from experimental measurements of heat capacities and heats of transition (Sec. 6-1). The extrapolated term is usually evaluated with the aid of the Debye equation for the heat capacity of crystals. The Debye equation for the heat capacity of crystals at low temperature is 

---