According to the zeroth law of thermodynamics, what can be inferred about thermal equilibrium?

The zeroth law of thermodynamics establishes a fundamental principle regarding thermal equilibrium: if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This means that temperature is a fundamental property that can define the state of a system.

In the context provided, if we consider system A and system B being in equilibrium, it implies they have the same temperature. Furthermore, if system A is also in thermal equilibrium with system C, it follows that system C must have the same temperature as system A and, consequently, the same temperature as system B. Therefore, A, B, and C are all in thermal equilibrium with each other.

This statement effectively captures the essence of how the zeroth law allows us to infer relationships of equilibrium based on temperature measurements. Thus, if A is in equilibrium with B and A is in equilibrium with C, we can rightly conclude that B is also in equilibrium with C. This underscores the transitive nature of thermal equilibrium as defined by the zeroth law of thermodynamics.