According to the Zeroth Law of thermodynamics, which statement is correct?

The Zeroth Law of thermodynamics establishes a fundamental principle regarding thermal equilibrium. It states that if two systems, A and B, are in thermal equilibrium with a third system, C, then A and B are also in thermal equilibrium with each other. This foundational concept allows us to define temperature in a consistent way, as it implies that temperature is a property that all objects in thermal equilibrium share.

The correct statement aligns perfectly with this principle. If A is in equilibrium with B, it means that there is no net transfer of heat between A and B, indicating they are at the same temperature. If system C is in equilibrium with A, it must also be at the same temperature as A (and hence B), reinforcing the transitive nature of thermal equilibrium outlined in the Zeroth Law.

In contrast, statements that suggest equilibrium cannot exist among the systems or imply a contradiction to the defined conditions of thermal equilibrium do not align with the Zeroth Law. Thus, the assertion that A and B are in equilibrium with respect to C, and vice versa, supports the logical framework of the Zeroth Law in thermal dynamics.