TITLE:
Absolute Internal Energy of the Real Gas
AUTHORS:
Albrecht Elsner
KEYWORDS:
Energy Reference Value Zero in Microscopic and Macroscopic Particle Systems, State of Transition from Bound to Freely-Moving Particles, Internal Energy Regions in the State Chart of Gas, Critical Point and Critical Isochor Loci of Vanishing Internal Energy, Critical Opalescence, BEC, Calculation of Internal Energies of Saturated Liquid and Vapor
JOURNAL NAME:
Engineering,
Vol.9 No.4,
April
30,
2017
ABSTRACT: The internal energy U of the real, neutral-gas particles of total mass M in the volume V can have positive and negative values, whose regions are identified in the state chart of the gas. Depending on the relations among gas temperature T, pressure p and mass-specific volume v=V/M, the mass exists as a uniform gas of freely-moving particles having positive values U or as more or less structured matter with negative values U. In the regions U>0above the critical point [Tc , pc , vc] it holds that p(T,v)>pc and v>vc, and below the critical point it holds that p(T,v)c and v>vv , where vv is the mass-specific volume of saturated vapor. In the adjacent regions with negative internal energy values Uc is the line of equal positive and negative energy contributions and thus represents a line of vanishing internal energy U=0. At this level along the critical isochor the ever present microscopic fluctuations in energy and density become macroscopic fluctuations as the pressure decreases on approaching the critical point; these are to be observed in experiments on the critical opalescence. Crossing the isochor vc from U>0 to UΔU>0 happens without any discontinuity. The saturation line vv also separates the regions between U>0 and U , but does not represent a line U=0. The internal-energy values of saturated vapor Uv and condensate Ui can be determined absolutely as functions of vapor pressure p and densities (M/V)v and (M/V)i , repectively, yielding the results Uiv, U=Ui+Uvc and U=Ui=Uv=0 at the critical point. Crossing the line Vv from U=Uv>0 to U=Uv+UiΔU=-Ui>0 to be removed from the particle system. The thermodynamic and quantum-mechanical formulations of the internal energy of a particle system only agree if both the macroscopic and microscopic energy scales have the same absolute energy reference value 0. Arguments for the energy reference value in the state of transition from bound to freely- moving particles in macroscopic classical and microscopic quantum particle systems are discussed.