Zeroth Law of Thermodynamics

The zeroth law of thermodynamics states that if two systems A and B are each separately in thermal equilibrium with a third system C, then A and B are also in thermal equilibrium with each other -- mathematically, $T_A=T_C$ and $T_B=T_C$ together imply $T_A=T_B$ (Figure 8.18 sets up exactly this scenario). This law, though logically the most basic of all the thermodynamic laws (which is why it is numbered "zeroth," having been recognised as necessary only after the first and second laws were already named), is what actually makes a thermometer work: the thermometer itself plays the role of system C, and once it reaches thermal equilibrium with an object, its reading can be trusted to agree with any other object separately f …