  The Kelvin-Planck statement of the Second Law of Thermodynamics is a
stricture on the nature of heat receipt by any body suffering a cyclic process.
It makes no mention of temperature or of entropy. Beginning with a
Kelvin-Planck statement of the Second Law, we show that entropy and temperature
-- in particular, existence of functions that relate the local specific entropy
and thermodynamic temperature to the local state in a material body -- emerge
immediately and simultaneously as consequences of the Hahn-Banach Theorem.
Existence of such functions of state requires no stipulation that their domains
be restricted to equilibrium states. Further properties, including uniqueness,
are addressed in a companion paper.
