Do we know what the temperature is?

Abstract

Temperature, the central concept of thermal physics, is one of the most frequently employed physical quantities in common practice. Even though the operative methods of the temperature measurement are described in detail in various practical instructions and textbooks, the rigorous treatment of this concept is almost lacking in the current literature. As a result, the answer to a simple question of "what the temperature is" is by no means trivial and unambiguous. There is especially an appreciable gap between the temperature as introduced in the frame of statistical theory and the only experimentally observable quantity related to this concept, phenomenological temperature. Just the logical and epistemological analysis of the present concept of phenomenological temperature is the kernel of the contribution.

The quandary aspects of non-isothermal kinetics beyond the ICTAC kinetic committee recommendations

“…1. It is somehow distressing to learn that this effect of thermal inertia has been known since 1933 from the fundamental work by Tian [118,143] but not addressed in most calorimetric books, with the exception of [144,145] serving thus as a good evidence of thermoanalysts' reluctance about such a crucial theme distorting the as-observed shapes of DTA [116][117][118][119][120][121][122][123][124][125]144,145]. Thermal inertia is habitually abandoned because its value is considered insignificant even if forever associated with the mass of studied sample (including its holder) executive regardless its decreasing size preserving levelheaded down to micro-states.…”

“…As a matter of fact, the temperature of any material body exposed to a heat changes is not uniform. Even if the material is thermally inert (not exhibiting any heat consumption and/or generation) and identified with a termoscopic state [117] it involves a temperature field [106,107,115,116]. The estimation of this time-dependent non-uniform temperature field and its impact on the shape of DTA curve represented the main objective of our recent book chapter [106].…”

“…It appears making possible to numerically monitor processing temperature at as speedy cooling rates as million Kelvin's per second [110,[130][131][132]. However, it is well known that the temperature as a physical quantity is a numerical measure of the degree of warmness (so called hotness manifold [117]) the measurement of which is realized by the way of instrumental detection. Temperature and its measurement ought to stay in accordance of the thermodynamic law declaring that measured physical systems are in thermal equilibrium.…”

Šesták’s proposal of term “tempericity” for non-equilibrium temperature and modified Tykodi’s thermal science classification with regard to methods of thermal analysis

“…3. The information on temperature of solid sample T s at a given time t does not represent the instantaneous thermal state (thermoscopic state-see [60]) of the sample nor average (weighted) temperature T u of the sample but only temperature of the sample surface T sS (or of sample holder T sH ). 4.…”

On relativistic transformation of temperature

“…Astonishingly, a satisfying definition of the physical quantity called temperature is practically lacking in the current literature. That is why we are referring here almost exclusively to our recent concise paper [52], devoted to this subject. The phenomenological temperature is not a simple concept and even its empirical basis is twofold.…”