### On the Geometric Formalism of Thermodynamics: In the ContextofLiquid Bubble-Boiling and Matter Glassy State

#### Abstract

Modelling of fluids vertical convection in nature by means of our original bubble-boiling method (BBM) allowed us to investigate behavior of the thermodynamic parameters of solutions during the whole process of heating (result of joint action of the processes of temperature conductivity, thermals and vapour bubbles mixing convective motion). There were obtained the universal dependence between the of bubble-boiling temperature and density of the solutions and existence of linear lows between points of discontinuities: T_{dc}, t_{dc}, S_{dc}, and ρ_{dc }which we can write, for q = const., as: (dT/ dρ)_{dc} = const., (dρ/ dt)_{dc} = const., and (dS/ dT)_{dc} = const. This method allowed us to show experimentally a similarity between the temperature-time (T, t)-diagrams of some matters water solutions and Tammann’s glassy state-diagrams. We try to find accordance between well-known Euler’s theorem on right polyhedrons and Gibbs thermodynamic rule about heterogeneous systems. Perhaps, using Gibbs-Tammann method for description of multicomponent system (n = 4, 5 , …), may obtain tetrahedron, octahedron and others. Then, for precise establishment of the moments of the liquids the micro- and macro-scale bubble-boiling regimes beginning, we analyzed our experimental (T, t)-, (dT/dt, T)-, and (d^{2} T/dt^{2}, T)-curves, which showed the existence of the acute maximums near temperatures T = 40 ^{0}C and T = 80 ^{0}C, respectively. Naturally, the same picture shows the temperature dependence of following even derivative of T with respect to t. Thus, this method of processing of T(t)-experimental data allowed us to avoid use of complex high-speed filming technique. Obtained analogy between thermodynamic diagrams of the glassy state of matter and the bubble boiling of liquids is caused by the fluidity of the glass as liquid (that is, “glass is liquid” (Tammann); undoubtedly, this is the best example of the phenomenon supporting well-known Frenkel’s kinetic theory of liquids).More over one can assume that the idea of the kinetic theory was “prompted” to Frenkel by Tammann’s glassy state, as probably form of Gibbs rule was “prompted” to him by Euler theorem about polyhedrons.

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