Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. That statement of transitivity is called the "zeroth law of thermodynamics." For example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually, the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium. By the zeroth law, we can conclude that the cold block and the hot block are also in thermal equilibrium.
British physicist Ralph Fowler suggested the number "zeroth" in the 1930s. At that time, the first, second, and third laws of thermodynamics were already named and numbered. The zeroth law had seldom been stated, but it needed to be discussed before the others, so Fowler gave it a smaller number.
Now consider the case where A is a thermometer. The zeroth law tells us that if A reads a certain temperature when in equilibrium with B, and it is then placed in contact with C, it will not exchange energy with C; therefore, its temperature reading will remain the same. In other words, if two objects are in thermal equilibrium, they have the same temperature.
