On The Axiomatic Foundations of Temperature

  • M. Pitteri


When the pioneers of thermodynamics deal with temperature, they presume the reader to have an intuitive idea of what temperature is and to be already familiar with the body of common experience with gases upon which much of classical thermometry is based1. From that experience we extract the concept of an ideal gas, that is, of a gas whose pressurep, volumeV and temperatureθ obey the thermal equation of state
$$pV = R\theta ,{\text{ R = const}}{\text{.,}}$$
for all positivep, V andθ. Real gases, air for instance, are good approximations to an ideal gas at temperatures which are not too low, and the best way to measure temperature in a wide range of circumstances is to use the air thermometer. The concept of ideal gas is important in classical thermodynamics and the air thermometer is regarded as giving the ideal-gas temperature most nearly. TRUESDELL [28, §§11B, 11H] discusses this matter and points out that KELVIN [12], who was perhaps the first to conceive that thermometers other than the air thermometer could be used to formulate thermodynamics, “seems to have perceived that the basic ideas of the theory of heat should be independent of the choice of thermometer. He seems also to have wished to excise the concept of ideal- gas temperature”. The latter wish was expressed later by MACH [15], who introduced the concept ofhotness as primitive in thermodynamics.


Thermal Equilibrium Sensory Experience Thermodynamic System Mechanical Concept Classical Thermodynamic 
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  • M. Pitteri

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