Determining the Relationship between Statistical and Phenomenological Models of the Thermodynamic Systems

The paper focuses on conducting a critical analysis of the issues that arise when matching the classical models of statistical and phenomenological thermodynamics.

The analysis reveals that some concepts from the statistical and phenomenological methods of describing classical systems do not quite correlate with one another. Specifically, in these methods, various caloric ideal gas equations of state are used, while the possibility existing in the thermodynamic cyclic processes to obtain the same distributions both due to a change of the particle concentration and owing to a change of temperature is not allowed for in the statistical methods.

The above-mentioned difference of the equations of state is cleared away when using in the statistical functions corresponding to the canonical Gibbs equations instead of the Planck’s constant a new scale factor that depends on the parameters of a system and coincides with the Planck’s constant in going of the system to the degenerate state. The statistical entropy is transformed into one of the forms of heat capacity using this method. The proposed multiplier depends on the parameters of a system and coincides with the Planck’s constant in a particular case in going of a classical system to the degenerate state.

In turn, it appears that the agreement of the methods under consideration in the question of the dependence of molecular distributions on particle concentration will necessitate further refinement of the physical model of ideal gas and the techniques for its statistical description.