Foundation of Temperature
The zeroth law establishes thermal equilibrium as an equivalence relationship. An equivalence relationship on a set (such as the set of thermally equilibrated systems) divides that set into a collection of distinct subsets ("disjoint subsets") where any member of the set is a member of one and only one such subset. In the case of the zeroth law, these subsets consist of systems which are in mutual equilibrium. This partitioning allows any member of the subset to be uniquely "tagged" with a label identifying the subset to which it belongs. Although the labeling may be quite arbitrary, temperature is just such a labeling process which uses the real number system for tagging. The zeroth law justifies the use of suitable thermodynamic systems as thermometers to provide such a labeling, which yield any number of possible empirical temperature scales, and justifies the use of the second law of thermodynamics to provide an absolute, or thermodynamic temperature scale. Such temperature scales bring additional continuity and ordering (i.e., "hot" and "cold") properties to the concept of temperature.
In the space of thermodynamic parameters, zones of constant temperature form a surface, that provides a natural order of nearby surfaces. One may therefore construct a global temperature function that provides a continuous ordering of states. The dimensionality of a surface of constant temperature is one less than the number of thermodynamic parameters, thus, for an ideal gas described with three thermodynamic parameters P, V and n, it is a two-dimensional surface.
For example, if two systems of ideal gases are in equilibrium, 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.
The surface PV/N = const defines surfaces of equal thermodynamic temperature, and one may label defining T so that PV/N = RT, where R is some constant. These systems can now be used as a thermometer to calibrate other systems. Such systems are known as "ideal gas thermometers".
Read more about this topic: Zeroth Law Of Thermodynamics
Famous quotes containing the words foundation of, foundation and/or temperature:
“In a country where misery and want were the foundation of the social structure, famine was periodic, death from starvation common, disease pervasive, thievery normal, and graft and corruption taken for granted, the elimination of these conditions in Communist China is so striking that negative aspects of the new rule fade in relative importance.”
—Barbara Tuchman (1912–1989)
“Beautiful credit! The foundation of modern society. Who shall say that this is not the golden age of mutual trust, of unlimited reliance upon human promises? That is a peculiar condition of society which enables a whole nation to instantly recognize point and meaning in the familiar newspaper anecdote, which puts into the mouth of a distinguished speculator in lands and mines this remark:M”I wasn’t worth a cent two years ago, and now I owe two millions of dollars.””
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“This pond never breaks up so soon as the others in this neighborhood, on account both of its greater depth and its having no stream passing through it to melt or wear away the ice.... It indicates better than any water hereabouts the absolute progress of the season, being least affected by transient changes of temperature. A severe cold of a few days’ duration in March may very much retard the opening of the former ponds, while the temperature of Walden increases almost uninterruptedly.”
—Henry David Thoreau (1817–1862)