The Zeroth Law of Thermodynamics states: If body A is in thermal equilibrium with body C and if body B is in thermal equilibrium with body C, then body A and body B are in thermal equilibrium.
One can begin to understand this law by understanding what is being stated. Image that body A and body B are cubes with each side measuring 1 cm and body C is a cube with each side measuring 0.5 cm. Body C is connects bodies A and B at their centers. The cubes are configured in such a way that body A touches body C which then touches body B. Assuming that all the energy that is being transferred is through body C. If the energy of body A were being released to the air around the bodies it would only affect the entropy, which is the second law of thermodynamics.
Suppose that body A has 5X the amount of energy of body B, then the energy of body A will be transferred to body B through body C because energy is released to a lower order of energy, i.e hot objects give energy to cold objects. An object that is “hot” has more energy than an object is “cold,” therefore, an object of higher temperature will give energy to an object of lower temperature. This concept is based upon all matter wanting to be in the most stable state, an object with greater energy (higher temperature) gives its energy to an object of lower energy (lower temperature). The thermal energy will be transferred back and forth until the objects are in thermal equilibrium. If bodies A and B are connected by body C, then in order for body A and body B to be in thermal equilibrium, than both bodies A and B must be in thermal equilibrium with body C. There are several equations that can calculate this process but to understand the basics of the Zeroth Law just assume concentrate on the following example.
Example: If a hot cup of coffee 45 C is allowed to cool in a room that is 20 C, eventually, the cup of coffee will reach the temperature of the room. The reason for the two objects reaching thermal equilibrium is because the energy of the hot cup of coffee is released into the room until both objects reach an equal temperature. This is the principle of the Zeroth Law. However, depending upon the size of the room and the size of the hot cup of coffee, the thermal equilibrium temperature will not be 20 C because the energy of the hot cup of coffee will cause the temperature of the room to increase. This concept is based upon the 2nd Law of thermodynamics, which states that entropy tends to increase.