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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>0 above 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 U 0 to U 0 happens without any discontinuity. The saturation line vv also separates the regions between U>0 and U 0 to U=Uv+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.

Absolute Internal Energy of the Real Gas