What is the relationship between temperature and thermal equilibrium as stated in the zeroth law?

The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This implies that thermal equilibrium is achieved when two systems have reached the same temperature. In essence, thermal equilibrium is defined by an absence of heat flow between the systems, which occurs only when they are at the same temperature.

This relationship is foundational in thermodynamics because it establishes the concept of temperature as a measurable property that indicates the thermal state of a system. Therefore, when two systems are at the same temperature, they no longer exchange thermal energy, confirming that they are in thermal equilibrium. Understanding this relationship underscores the importance of temperature in determining heat transfer and thermal interactions among systems.