Q.State the Zeroth law of thermodynamics. Explain how this law makes it logically possible to define temperature as a physical quantity, and to construct thermometers.

The Zeroth law of thermodynamics states that if a system $A$ is in thermal equilibrium with a system $C$, and a system $B$ is separately also in thermal equilibrium with $C$, then $A$ and $B$ must be in thermal equilibrium with each other as well.

This makes temperature a logically well-defined quantity: taking $C$ to be a thermometer, if the thermometer reads the same value when placed in contact with $A$ as it does when placed (separately) in contact with $B$, the Zeroth law guarantees $A$ and $B$ are at the same temperature, even without $A$ and $B$ ever being placed directly in contact with one another. Without this guarantee, there would be no logical basis for using a single thermometer reading to compare the temperatures of two different bodies measured at different times, and building and calibrating any thermometer at all would not be justified.

State the law precisely, then explain the thermometer application by substituting a thermometer for the third system $C$.

• Only stating the law without explaining WHY it matters for defining temperature/thermometers.
• Getting the transitivity backwards (e.g. claiming $C$ must be in equilibrium with both $A$ and $B$ simultaneously in direct contact, rather than the correct separate-contact statement).