The zeroth law of thermodynamics states that two thermodynamic systems, each in thermal equilibrium with a third, are in thermal equilibrium with each other.
Consider two systems, A and B, in contact with each other via an immovable thermally conducting boundary and achieving thermal equilibrium over time. B is then brought in contact with a third system, C, via the same type of boundary.
If no net energy and matter transfer is observed between B and C, we can deduce that A is also in thermal equilibrium with C. When this happens, there must be at least one measurable thermodynamic property that is common among the three systems.
We call this common thermodynamic property, temperature, and the above-mentioned principle that allows us to define temperature, the zeroth law of thermodynamics. Temperature is therefore defined as the thermodynamic property that has the same magnitude in two systems that are in thermal equilibrium.
The principle that eventually became the zeroth law of thermodynamics was first mentioned in 1871 by James Maxwell, who said, “bodies whose temperatures are equal to that of the same body have themselves equal temperatures”. A modern version of the zeroth law of thermodynamics utilises the term ‘thermal equilibrium’ and states that
Two thermodynamic systems, each in thermal equilibrium with a third, are in thermal equilibrium with each other.
Question
Which of the three systems that are described above, the thermometer?
Answer
B, as it indicates that A and C have the same temperature. If B contains a substance with relatively high coefficient of thermal expansion, e.g. helium, it can be used to assess A and C at various temperatures by monitoring its volume at constant pressure. Thus, the zeroth law of thermodynamics forms the basis of thermometry.