Which law states that when two systems are in equilibrium, a third system in equilibrium with them also exists?

The Zeroth Law of Thermodynamics is foundational in establishing the concept of temperature and thermodynamic equilibrium. This law states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This principle allows us to define temperature in a consistent way, as it implies that the systems have the same temperature when they are in equilibrium.

In practical terms, this means that if System A is in equilibrium with System C, and System B is also in equilibrium with System C, then System A must be in equilibrium with System B. This concept is essential in thermodynamics for understanding how heat transfer occurs and for measuring temperature accurately using thermometers, which are based on this principle.

The other laws of thermodynamics deal with different aspects: the First Law focuses on the conservation of energy, the Second Law addresses the direction of energy transfers and the increase of entropy, and the Third Law pertains to the behavior of systems as they approach absolute zero. Each of these laws has a distinct role in thermodynamic principles but does not pertain to the equivalency and relationship outlined in the Zeroth Law.