It provides an independent definition of temperature without reference to entropy, which is defined in the second law.
[1][2][3] Two systems are said to be in thermal equilibrium if they are linked by a wall permeable only to heat, and they do not change over time.
The zeroth law is needed for the definition of such scales, and justifies the use of practical thermometers.
Empirical temperature provides further relations of thermally equilibrated systems, such as order and continuity with regard to "hotness" or "coldness", but these are not implied by the standard statement of the zeroth law.
[8]This statement asserts that thermal equilibrium is a left-Euclidean relation between thermodynamic systems.
Thus, again implicitly assuming reflexivity, the zeroth law is therefore often expressed as a right-Euclidean statement:
The zeroth law belongs to the thermodynamic concept, but this is no longer the primary international definition of temperature.
In the case of the zeroth law, these subsets consist of systems which are in mutual equilibrium.
One may therefore construct a global temperature function that provides a continuous ordering of states.
For example, if two systems of ideal gases are in joint thermodynamic equilibrium across an immovable diathermal wall, then P1V1/N1 = P2V2/N2 where Pi is the pressure in the ith system, Vi is the volume, and Ni is the amount (in moles, or simply the number of atoms) of gas.
[4] It is the opinion of Elliott H. Lieb and Jakob Yngvason (1999)[7] that the derivation from statistical mechanics of the law of entropy increase is a goal that has so far eluded the deepest thinkers.
[7]: 5 Thus the idea remains open to consideration that the existence of heat and temperature are needed as coherent primitive concepts for thermodynamics, as expressed, for example, by Maxwell and Max Planck.
[13] Writing long before the term "zeroth law" was coined, in 1871 Maxwell[5] discussed at some length ideas which he summarized by the words "All heat is of the same kind".
[5] Modern theorists sometimes express this idea by postulating the existence of a unique one-dimensional hotness manifold, into which every proper temperature scale has a monotonic mapping.
[6]: 23 This might also be expressed by saying that there is precisely one kind of non-mechanical, non-matter-transferring contact equilibrium between thermodynamic systems.
According to Sommerfeld, Ralph H. Fowler coined the term zeroth law of thermodynamics[15] while discussing the 1935 text by Meghnad Saha and B.N.
Any of the physical properties of A which change with the application of heat may be observed and utilised for the measurement of temperature.
It is not explicitly evident in the existence statement of Fowler and Edward A. Guggenheim that temperature refers to a unique attribute of a state of a system, such as is expressed in the idea of the hotness manifold.