Zeroth Law of Thermodynamics

The zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle establishes transitivity: if object A equilibrates with object B, and object B equilibrates with object C, then A and C are also in equilibrium. This foundational concept enables temperature measurement and comparison across multiple systems.

When a thermometer measures an object's temperature, it reaches thermal equilibrium by changing its own temperature. The measured reading reflects the thermometer's temperature, not the object's initial state. By the zeroth law, if the thermometer and object are in equilibrium, they share the same temperature, making thermometers reliable measurement tools.

British physicist Ralph Fowler suggested the name 'zeroth' in the 1930s because the first, second, and third laws of thermodynamics were already established and numbered. The zeroth law needed to be discussed before the others logically, so Fowler assigned it a smaller number to reflect its foundational importance in thermodynamic theory.

When beakers A and B are connected, heat transfers until they reach thermal equilibrium. When B and C are then connected, they also equilibrate. Eventually, all three beakers reach the same uniform temperature, demonstrating the zeroth law experimentally. This shows that thermal equilibrium is transitive across multiple bodies.

A cold metal block and hot metal block placed on a room-temperature metal plate will each reach equilibrium with the plate separately. By the zeroth law, since both blocks equilibrate with the plate, they must also be in thermal equilibrium with each other, even without direct contact. This illustrates that equilibrium is transitive through an intermediary.

If two objects are in thermal equilibrium, they have the same temperature. This relationship is central to the zeroth law: it defines temperature as the property that is equal when objects are in equilibrium. Without this principle, temperature measurement and comparison between different systems would be impossible.

When a thermometer is placed in contact with an object already in thermal equilibrium, no temperature difference exists between them. Since energy transfer requires a temperature gradient, no heat flows. The thermometer's reading remains unchanged, confirming that both objects share the same temperature and are in equilibrium.