Temperature scale

Scale of temperature is a way to measure temperature quantitatively. Empirical scales measure the quantity of heat in a system in relation to a fixed parameter, a thermometer. They are not absolute measures, that is why scales vary. Absolute temperature is thermodynamic temperature because it is directly related to thermodynamics. It is the Zeroth Law of Thermodynamics that leads to a formal definition of thermodynamic temperature.

According to the zeroth law of thermodynamics, being in thermal equilibrium is an equivalence relation. Thus all thermal systems may be divided into a quotient set by this equivalence relation, denoted below as M. Assume the set M has the cardinality of c, then one can construct an injective function ƒ: M → R , by which every thermal system will have a number associated with it such that when and only when two thermal systems have the same such value, they will be in thermal equilibrium. This is clearly the property of temperature, and the specific way of assigning numerical values as temperature is called a scale of temperature. In practical terms, a temperature scale is always based on usually a single physical property of a simple thermodynamic system, called a thermometer, that defines a scaling function mapping the temperature to the measurable thermometric parameter. Such temperature scales that are purely based on measurement are called empirical temperature scales.

The second law of thermodynamics provides a fundamental, natural definition of thermodynamic temperature starting with a null point of absolute zero. A scale for thermodynamic temperature is established similarly to the empirical temperature scales, however, needing only one additional fixing point.

Empirical scales are based on the measurement of physical parameters that express the property of interest to be measured through some formal, most commonly a simple linear, functional relationship. For the measurement of temperature, the formal definition of thermal equilibrium in terms of the thermodynamic coordinate spaces of thermodynamic systems, expressed in the zeroth law of thermodynamics, provides the framework to measure temperature.

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