The quantum size effect contribution to heat capacity and the third law of thermodynamics

Abstract

A number of well-known models for finite solids is examined as to their contributions to very-low-temperature specific heats. It is found that finite sample size and quantum energy spacing lead in every case to specific heats which approach zero very rapidly in a Schottky-like manner, so that one has\(\mathop {\lim }\limits_{T \to 0} \left( {{{\partial S} \mathord{\left/ {\vphantom {{\partial S} {\partial T}}} \right. \kern-\nulldelimiterspace} {\partial T}}} \right)_X \equiv 0\) for any dimensionality, a restriction which is in addition to the third law of thermodynamics.