Rescaling Temperature and Entropy

Abstract

Temperature and entropy traditionally are expressed in units of kelvin and joule/kelvin. These units obscure some important aspects of the natures of these thermodynamic quantities. Defining a rescaled temperature using the Boltzmann constant, T′ = kBT, expresses temperature in energy units, thereby emphasizing the close relationship between temperature and energy. When temperature is rescaled, entropy must also be rescaled, S′ = S/kB. Rescaled entropy is dimensionless. Rescaling reveals that the Boltzmann constant (and the gas constant) can be viewed as unit conversion factors between two energy units, kelvin and joule. The machinery of chemical thermodynamics remains intact upon rescaling, inasmuch as T and S appear together. Similar to entropy, however, heat capacities become dimensionless upon rescaling. Rescaling provides several insights into the nature of thermodynamic quantities: temperature is a measure of energy intensity; entropy is a measure of distribution; heat capacity states the number of ...