The zeroth law of thermodynamics states that "if two systems that are in thermal equilibrium with a third system, they are also in equilibrium with each other." It is also known as the zeroth principle of thermodynamics.
If A is in equilibrium with B and A is also in thermal stability with a third body C, we can conclude that B is in thermal equilibrium with C.
Two bodies are in thermodynamic equilibrium when, on contact, their state variables do not change. If they are not in thermal stability, they will transfer heat or energy and reach thermal equilibrium.
The zero law was the last of the laws of thermodynamics to be introduced. It was necessary to place it before the other laws obtain a logical structure. The law was named the Zeroth Law of Thermodynamics by the British Mathematician Ralph H. Fowler.
According to David McKee, a physics professor at Missouri Southern State University, the Zeroth Law "tells us that no matter how much energy two systems have. (...) The Zeroth Law says that the temperature defines the direction of heat flow.”
Examples of Applications of the Zero Law of Thermodynamics
Ice and Water
We put a piece of ice and a glass full of water at room temperature. In this experiment, three elements appear, which are ice, water, and a glass.
Initially, since we have hot and cold elements, all three will exchange heat and energy until they reach thermal equilibrium. After a while, the three parts will get the same temperature that states the zeroth law.
Another example that will help to understand better the concept of thermal equilibrium is that of a thermometer.
Consider a body B consisting of a tube with a capillary containing mercury. Their height levels above the vein represent different temperatures.
Now consider body A, for example, the human body. If you bring the thermometer close to your body and leave it long enough, the thermometer will reach the value corresponding to body temperature.
As the human body has a higher temperature, heat flows to the thermometer since both reach the thermodynamical equilibrium following the rules that zeroth law establishes.