The statistical definition of entropy is often used to justify Planck’s form of the third law of thermodynamics in a very graphic form. Statements like for a nondegenerate ground state system at 0 K, the system should be in its lowest energy (ground) state and then S=0 according to the statistical definition of entropy are commonplace in many textbooks. These statements are useful, but might as well be supplemented with more empirical views concerning the physical limits of low temperatures in thermodynamics and the high number of states still accessible for a macroscopic system when the entropy takes small values. The purpose of this note is to emphasize the above points making use of four model systems: the Fermi ideal gas, the confined Bose ideal gas, the photon gas, and the noninteracting particles in a two-level system. Each of these physical systems has a characteristic temperature related to the nature and organization of its microscopic constituents and the third law should perhaps be expressed in terms of the behavior of the system when it approaches this temperature rather than the presumed behavior at exactly T=0 K.

Topics
Bose-Einstein condensate, Laws of thermodynamics, Ideal gas, Entropy, Bosons, Educational aids
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