Zeroth law of thermodynamics

If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

When two systems, each in its own thermodynamic equilibrium, are put in purely thermal connection, radiative or material, with each other, there will be a net exchange of heat between them unless or until they are in thermal equilibrium. That is the state of having equal temperature. Although this concept of thermodynamics is fundamental, the need to state it explicitly was not widely perceived until the first third of the 20th century, long after the first three principles were already widely in use. Hence it was numbered zero -- before the subsequent three. The Zeroth Law implies that thermal equilibrium, viewed as a binary relation, is a transitive relation. Since a system in thermodynamic equilibrium is defined to be in thermal equilibrium with itself, and, if a system is in thermal equilibrium with another, the latter is in thermal equilibrium with the former. Thermal equilibrium is furthermore an equivalence relation.