What is the zeroth law?

What is the zeroth law?

• A. If two systems are in thermal equilibrium, they have the same entropy.
• B. If two thermodynamic systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other.
• C. All systems at the same temperature are in equilibrium with the surrounding environment.
• D. Thermal equilibrium cannot be established between multiple systems.

Answer: (B)

Transitivity of thermal equilibrium is what the zeroth law is about. If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This establishes temperature as a measurable quantity, because a thermometer can act as that third system to compare temperatures: if System A is in equilibrium with the thermometer and System B is also in equilibrium with the same thermometer, then A and B must share the same temperature and be in equilibrium with each other. The others mix in entropy or environmental ideas or state impossibility, which don’t capture that transitive relationship that defines the zeroth law.

Transitivity of thermal equilibrium is what the zeroth law is about. If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This establishes temperature as a measurable quantity, because a thermometer can act as that third system to compare temperatures: if System A is in equilibrium with the thermometer and System B is also in equilibrium with the same thermometer, then A and B must share the same temperature and be in equilibrium with each other. The others mix in entropy or environmental ideas or state impossibility, which don’t capture that transitive relationship that defines the zeroth law.