Thermodynamics of fluids as a consequence of distribution theory for Diophantine equations
The author introduces the concept of ideal fluid considering the system \( \sum_{i=1}^{s}\varepsilon _{i}N_{i}\leq M\); \(\sum_{i=1}^{s}N_{i}=N\), where \(M \), \(\varepsilon _{i}\) and \(N\) are given numbers, \(N_{i}\) is a positive integer and \(N\) is an integer. \(M\) is the global energy and \(N\) is the total number of particles. Taking \(\varepsilon _{i}=i^{\alpha }\) for some positive number \(\alpha \), the author claims that this leads to an abstract ideal thermodynamics. He then recalls the previous results he obtained concerning the transition via the condensate state in the parastatic, applying them to the scattering problem with Lennard-Jones potential. In a further refinement, he writes a similar problem than above in a two-phase state, separating the gas phase and the liquid phase with dimers and clusters, which leads to the notion of almost-ideal liquid. The last part of the paper contains an application of results concerning Diophantine equations to an abstract thermodynamics without the notion of pressure. The author computes the expression of the compressibility factor at temperatures below the Boyle temperature and finally claims that the values deduced from this expression are in good agreement with experimental graphs.
scientific article; zbMATH DE number 5621797
scientific article