Which law states that if two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other?

The correct answer is the Zeroth Law of Thermodynamics. This law establishes a fundamental principle of temperature and thermal equilibrium. It states that if two systems, say A and B, are both in thermal equilibrium with a third system C, then systems A and B must also be in thermal equilibrium with each other.

This is important because it allows for the definition of temperature as a measurable property. Essentially, the Zeroth Law provides a foundation for the temperature scale; if two systems are in the same thermal state as a third system, they can be considered to have the same temperature. This relationship is crucial in thermodynamics because it underpins the way thermodynamic temperatures are compared and measured, making it fundamental for understanding the interactions between different systems in thermal dynamics.

The other laws of thermodynamics focus on different principles: the First Law deals with the conservation of energy, the Second Law addresses the direction of thermodynamic processes and the concept of entropy, and the Third Law concerns absolute zero and the behavior of systems as they approach this temperature. The Zeroth Law holds distinct significance as it provides the basis for the concept of temperature itself.