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 ENG  Vol.10 No.5 , May 2018
Absolute Reference Values of the Real Gas
Abstract: With his publication in 1873 [1] J. W. Gibbs formulated the thermodynamic theory. It describes almost all macroscopically observed properties of matter and could also describe all phenomena if only the free energy U - ST were explicitly known numerically. The thermodynamic uniqueness of the free energy obviously depends on that of the internal energy U and the entropy S, which in both cases Gibbs had been unable to specify. This uncertainty, lasting more than 100 years, was not eliminated either by Nernst’s hypothesis S = 0 at T = 0. This was not achieved till the advent of additional proof of the thermodynamic relation U = 0 at T = Tc. It is noteworthy that from purely thermodynamic consideration of intensive and extensive quantities it is possible to derive both Gibbs’s formulations of entropy and internal energy and their now established absolute reference values. Further proofs of the vanishing value of the internal energy at the critical point emanate from the fact that in the case of the saturated fluid both the internal energy and its phase-specific components can be represented as functions of the evaporation energy. Combining the differential expressions in Gibbs’s equation for the internal energy, d(μ/T)/d(1/T) and d(p/T)/d(1/T), to a new variable d(μ/T)/d(p/T) leads to a volume equation with the lower limit vc as boundary condition. By means of a variable transformation one obtains a functional equation for the sum of two dimensionless variables, each of them being related to an identical form of local interaction forces between fluid particles, but the different particle densities in the vapor and liquid spaces produce different interaction effects. The same functional equation also appears in another context relating to the internal energy. The solution of this equation can be given in analytic form and has been published [2] [3]. Using the solutions emerging in different sets of problems, one can calculate absolutely the internal energy as a function of temperature-dependent, phase-specific volumes and vapor pressure.
Cite this paper: Elsner, A. (2018) Absolute Reference Values of the Real Gas. Engineering, 10, 270-290. doi: 10.4236/eng.2018.105019.
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, 2, 382-404.
http://www3.nd.edu/-powers/ame.20231/gibbs1873b.pdf

[2]   Elsner, A. (1988) Thermodynamic Representation of the State of a Saturated Fluid. Physics Letters A, 130, 225-233.
https://doi.org/10.1016/0375-9601(88)90598-1

[3]   Elsner, A. (2015) Thermodynamic Equilibrium of the Satu-rated 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

[4]   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

[5]   Strunk, Ch. (2015) Moderne Thermodynamik: Von einfachen Systemen zu Nanostrukturen. 32.
https://doi.org/10.1515/9783110371062

[6]   Lauth, J.G. and Kowalczyk, J. (2015) Thermodynamik. Springer-Verlag, Berlin Heidelberg, 67.
https://doi.org/10.1007/978-3-662-46229-4

[7]   Callen, H.B. (1960) Thermodynamics. John Wiley & Sons, Hoboken, 52.

[8]   Johnson, V.J. (1961) Properties of Materials at Low Temperature (Phase 1). National Bureau of Standards, Cryogenic Engineering Laboratory, Pergamon Press, Oxford, London, New York, Paris.

[9]   Journal of Physical and Chemical Reference Data, Annual Series of Properties of Gases, published since 1972.

[10]   IUPAC Commission on Thermodynamics (1972) International Thermodynamic Tables of the Fluid State. Blackwell Scientific Publications, Hoboken, Vol. 1.

[11]   Selover, T.B. (1987) A Series of Property Tables. Hemisphere Publishing Corporation, New York.

[12]   Reynolds, W.C. (1979) Thermodynamic Properties in SI. Graphs, Tables and Computational Equations for 40 Substances. The Department of Mechanical Engineering, Stanford University, Stanford.

[13]   Grigull, U. and Schmidt, E. (1989) Properties of Water and Steam in SI-Units. Springer-Verlag, Berlin, Heidelberg, New York.

[14]   Wagner, W. and Pruss, A. (1993) International Equations for the Saturation Properties of Ordinary Water Substance. Revised According to the International Temperature Scale of 1990. Addendum to J. Phys. Chem. Ref. Data 16, 893 (1987). Journal of Physical and Chemical Reference Data, 22, 783.
https://doi.org/10.1063/1.555926

[15]   Kohlrausch, F. (1996) Praktische Physik. Band 3, B. G. Teubner Stuttgart.

[16]   Feistel, R. and Wagner, W. (2006) A New Equation of State for H2O Ice Ih. Journal of Physical and Chemical Reference Data, 35, 1021-1047.
https://doi.org/10.1063/1.2183324

[17]   Elsner, A. (2014) The Dominant Role of the Chemical Potential for Driving Currents in Oceans and Air. Journal of Geoscience and Environment Protection, 2, 117-125.

[18]   Pethick, C.J. and Smith, H. (2002) Bose-Einstein Condensation in Dilute Gases. Cambridge University Press, Cambridge.

[19]   Elsner, A. (2017) Absolute Internal Energy of the Real Gas. Engineering, 9, 361-375.

 
 
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