In a similar way, we should examine the heat transfer between a thermodynamic system and its environment or between the different parts of the system, and its balance should dictate the thermal equilibrium of the system. Intuitively, such a balance is reached if the temperature becomes the same for different objects or parts of the system in thermal contact, and the net heat transfer over time becomes zero. Thus, when we say two objects (a thermodynamic system and its environment, for example) are in thermal equilibrium, we mean that they are at the same temperature. How do we know whether they are in thermal equilibrium? The governing principle here is the zeroth law of thermodynamics: Let us consider three objects at temperatures \(T_1, \, T_2\), and \(T_3\) respectively.
Mathematically, we can simply write the zeroth law of thermodynamics as If object 1 is in thermal equilibrium with objects 2 and 3, respectively, then objects 2 and 3 must also be in thermal equilibrium.
