On the use of the statistical definition of entropy to justify Planck's form of the third law of thermodynamics

The statistical definition of entropy is often used to justify Planck's for m of the third law of thermodynamics in a very graphic form. Statements lik e for a nondegenerate ground state system at 0 K, the system should be in i ts lowest energy (ground) state and then S=0 according to the statistical d efinition of entropy are commonplace in many textbooks. These statements ar e useful, but might as well be supplemented with more empirical views conce rning the physical limits of low temperatures in thermodynamics and the hig h number of states still accessible for a macroscopic system when the entro py takes small values. The purpose of this note is to emphasize the above p oints making use of four model systems: the Fermi ideal gas, the confined B ose ideal gas, the photon gas, and the noninteracting particles in a two-le vel 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 behavio r at exactly T=0 K. (C) 2000 American Association of Physics Teachers.