On the redundancy of the zeroth law of thermodynamics

Abstract

Expositions of classical thermodynamics frequently include the so-called zeroth law amongst its 'fundamental principles'. It is shown here that, given only the first law and the second law (the latter in a formulation manifestly free of any explicit or implicit reference to temperature), the transitivity of the relation 'is in diathermic equilibrium with' can be deduced. The zeroth law which is an assertion of just this transistivity is therefore redundant. The existence of the absolute temperature function of course emerges directly, i.e. without appeal to a prior empirical temperature.