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.
All temperature scales, including the modern thermodynamic temperature scale used in the International System of Units, are calibrated according to thermal properties of a particular substance or device. Typically, this is established by fixing two well-defined temperature points and defining temperature increments via a linear function of the response of the thermometric device. For example, both the old Celsius scale and Fahrenheit scale were originally based on the linear expansion of a narrow mercury column within a limited range of temperature, each using different reference points and scale increments.
Different empirical scales may not be compatible with each other, except for small regions of temperature overlap. If an alcohol thermometer and a mercury thermometer have the same two fixed points, namely the freezing and boiling point of water, their readings will not agree with each other except at the fixed points, as the linear 1:1 relationship of expansion between any two thermometric substances may not be guaranteed.
Empirical temperature scales are not reflective of the fundamental, microscopic laws of matter. Temperature is a universal attribute of matter, yet empirical scales map a narrow range onto a scale that is known to have a useful functional form for a particular application. Thus, their range is limited. The working material only exists in a form under certain circumstances, beyond which it no longer can serve as a scale. For example, mercury freezes below 234.32 K, so temperatures lower than that cannot be measured in a scale based on mercury. Even ITS-90, which interpolates among different ranges of temperature, has a range of only 0.65 K to approximately 1358 K (−272.5 °C to 1085 °C).