Zeroth Law of Thermodynamics

Thermal Equilibrium First

When a piece of ice is put into water at room temperature, the water (at the higher temperature) transfers heat to the ice and the ice melts. When hot water is mixed with cold water, the hot water transfers heat and cools down. In both cases the transfer continues until a stage is reached at which there is no further transfer of heat. The two components are then said to be in thermal equilibrium.

• Thermal equilibrium: two systems in thermal contact with each other are in thermal equilibrium if they do not transfer heat between each other.
• Equivalently, when two objects are at the same temperature they are in thermal equilibrium.
• Heat is something transferred from a substance at a higher temperature to one at a lower temperature, and the transfer continues until the two are at the same level.

Statement of the Zeroth Law

If two systems are each in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.

An equivalent and equally examinable form: systems in thermal equilibrium are at the same temperature.

The Diagram

Figure 4.1 is a schematic of three boxes labelled A, B and C, with a double-headed arrow drawn between each pair that is in thermal equilibrium. If A and C are in thermal equilibrium, and A and B are in thermal equilibrium, then B and C must also be in thermal equilibrium — so the third double arrow can be drawn — and A, B and C are all at the same temperature.

Figure 4.2 applies this to measurement: a thermometer brought into contact with an object reaches thermal equilibrium with it, and then the thermometer reading is the temperature of the object.

Why It Matters

• The zeroth law is what allows the concept of a temperature scale to be defined at all.
• It is what permits a thermometer to be used to compare the temperatures of different objects: instead of putting two objects in contact, each is put in contact with the same thermometer.
• It implies that temperature is a measurable quantity. The science of measuring temperature is thermometry.
• It is called the zeroth law because it was proposed after the first and second laws had already been formulated, although it is logically prior to both.

Standard Results

• Zeroth law: if two systems are each in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.
• Systems in thermal equilibrium are at the same temperature.
• Objects lying on a table at room temperature do not exchange heat with the table because they are already at the same temperature, that is, in thermal equilibrium with it.
• A thermocouple must be in physical contact with the object precisely because it must reach thermal equilibrium with it before its reading is the object's temperature.