Laws of Thermodynamics - Zeroth Law

Zeroth Law

The zeroth law of thermodynamics may be stated as follows:

If system A and system B are individually in thermal equilibrium with system C, then system A is in thermal equilibrium with system B

The zeroth law implies that thermal equilibrium, viewed as a binary relation, is a Euclidean relation. If we assume that the binary relationship is also reflexive, then it follows that thermal equilibrium is an equivalence relation. Equivalence relations are also transitive and symmetric. The symmetric relationship allows one to speak of two systems being "in thermal equilibrium with each other", which gives rise to a simpler statement of the zeroth law:

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

However, this statement requires the implicit assumption of both symmetry and reflexivity, rather than reflexivity alone.

The law is also a statement about measurability. To this effect the law allows the establishment of an empirical parameter, the temperature, as a property of a system such that systems in equilibrium with each other have the same temperature. The notion of transitivity permits a system, for example a gas thermometer, to be used as a device to measure the temperature of another system.

Although the concept of thermodynamic equilibrium is fundamental to thermodynamics and was clearly stated in the nineteenth century, the desire to label its statement explicitly as a law was not widely felt until Fowler and Planck stated it in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable.