Absolute Internal Energy of the Real Gas

Albrecht Elsner^{*}

Show more

_{c} and v>v_{v} , where vv is the mass-specific volume of saturated vapor. In the adjacent regions with negative internal energy values U<0 the mean distances between particles are short enough to yield negative energy contributions to U due to interparticle attraction that exceeds the thermal, positive energy contributions due to particle motion. The critical isochor v_{c }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 v_{c} from U>0 to U<0, the change in energy ΔU>0 happens without any discontinuity. The saturation line v_{v} also separates the regions between U>0 and U<0 , but does not represent a line U=0. The internal-energy values of saturated vapor U_{v }and condensate U_{i} can be determined absolutely as functions of vapor pressure p and densities (M/V)_{v} and (M/V)i , repectively, yielding the results U_{i}<0__v, U=U _{i}+U_{v}<0, for T__

References

[1] Gibbs, J.W. (1873) A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces. Transactions of the Connecticut Academy, II, 382-404

[2] Stierstadt, K. (1989) Physik der Materie. VCH, Weinheim, p. 430, T15.

[3] Callen, H.B. (1960) Thermodynamics. John Wiley & Sons, Hoboken, Preface, Chapters 2, 3, 15.3, Figures 9.4, 9.5

[4] Pethick, C.J. and Smith, H. (2004) Bose-Einstein Condensation in Dilute Gases. Cambridge University Press, Cambridge, Equation (2.23)

[5] Strunk, Ch. (2015) Moderne Thermodynamik. De Gruyter Studium, p. 32, Chapter 7.7.3

https://doi.org/10.1515/9783110371062

[6] Elsner, A. (2012) Applied Thermodynamics of the Real Gas with Respect to the Thermodynamic Zeros of the Entropy and Internal Energy. Physica B: Physics of Condensed Matter, 407, 1055-1067.

https://doi.org/10.1016/j.physb.2011.12.118

[7] Elsner, A. (2015) Thermodynamic Equilibrium of the Saturated Fluid with a Free Surface Area and the Internal Energy as a Function of the Phase-Specific Volumes and Vapor Pressure. Engineering, 7, 577-596.

https://doi.org/10.4236/eng.2015.79053

[8] Elsner, A. (2014) Thermodynamic Fit Functions of the Two-Phase Fluid and Critical Exponents. Engineering, 6, 789-826.

https://doi.org/10.4236/eng.2014.612076

[9] Reif, F. (1965) Statistical Physics. Berkeley Physics Course, Volume 5, McGraw-Hill Book Company, Chapter 3.1.