Theorem of Necessity and Sufficiency of Stable Equilibrium for Generalized Potential Equality between System and Reservoir
Pierfrancesco Palazzo*
Technip, Rome, Italy.
DOI: 10.4236/jmp.2014.518196   PDF   HTML   XML   4,367 Downloads   4,726 Views   Citations


The literature reports that equality of temperature, equality of potential and equality of pressure between a system and a reservoir are necessary conditions for the stable equilibrium of the system-reservoir composite or, in the opposite and equivalent logical inference, that stable equilibrium is a sufficient condition for equality. The aim and the first novelty of the present study is to prove that equality of temperature, potential and pressure is also a sufficient condition for stable equilibrium, in addition to necessity, implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality. The second novelty is that the proof of the sufficiency of equality (or the necessity of stable equilibrium) is attained by means of the generalization of the entropy property, derived from the generalization of exergy property, which is used to demonstrate that stable equilibrium is a logical consequence of equality of generalized potential. This proof is underpinned by the Second Law statement and the Maximum-Entropy Principle based on generalized entropy which depends on temperature, potential and pressure of the reservoir. The conclusion, based on these two novel concepts, consists of the theorem of necessity and sufficiency of stable equilibrium for equality of generalized potentials within a composite constituted by a system and a reservoir.

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Palazzo, P. (2014) Theorem of Necessity and Sufficiency of Stable Equilibrium for Generalized Potential Equality between System and Reservoir. Journal of Modern Physics, 5, 2003-2011. doi: 10.4236/jmp.2014.518196.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Gyftopoulos, E. and Beretta, G.P. (2005) Thermodynamics: Foundations and Applications. Dover Publications, New York.
[2] Beretta, G.P. (2008) International Journal of Thermodynamics, 11, 39-48.
[3] Gyftopoulos, E.P. (2006) International Journal of Thermodynamics, 9, 107-115.
[4] Zanchini, E. (2000) International Journal of Thermal Sciences, 39, 110-116.
[5] Kotas, T.J. (1995) The Exergy Method of Thermal Plant Analysis. Reprint Edition, Krieger Publishing Company, Malabar.
[6] Moran, M.J. and Sciubba, E. (1994) Journal of Engineering for Gas Turbine and Power, 116, 285-290.
[7] Palazzo, P. (2012) International Journal of Energy and Environmental Engineering, 3, 4.
[8] Palazzo, P. (2013) Journal of Modern Physics, 4, 52-58.
[9] Zanchini, E. and Beretta, G.P. (2010) International Journal of Thermodynamics, 13, 67-76.
[10] Zanchini, E. and Barletta, A. (1995) Il Nuovo Cimento, 110B, 10.
[11] Gaggioli, R.A. (1998) International Journal of Applied Thermodynamics, 1, 1-8.

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