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Applications to Special States of Thermodynamic Equilibrium: Gibbsian Thermodynamics for Physical and Chemical Applications

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A Treatise of Heat and Energy

Part of the book series: Mechanical Engineering Series ((MES))

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Abstract

Gibbs demonstrated in 1878 that the entropy principle (introduced 1865) can be a foundation for the general theory of thermodynamic equilibrium as he noted, “…the general increase of entropy which accompanies the changes occurring in any isolated material system [suggests] that when the entropy of the system has reached a maximum, the system will be in a state of equilibrium.” Such extreme principle has already been discussed in Chap. 7. This chapter provides a more complete but condensed treatment of Gibbsian equilibrium thermodynamics. Though this chapter is not the core of this book, it is noted that its material is easy to grasp due to the mathematical elegance of the content and every engineer (target reader of the book) can benefit from its mastery.

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Notes

  1. 1.

    It is useful to remind the readers that among the following set of equations:\( \begin{array}{*{20}c} {dU = \delta Q - \delta W} \\ {dU = TdS - \delta W} \\ {dU = \delta Q - pdV} \\ {dU = TdS - pdV\,{\text{or}}\,dU = TdS - pdV + \mathop \sum \nolimits_{i = 1}^{n} \mu_{i} dN_{i} ,} \\ \end{array} \)

    only the first and the fourth are always valid for all processes, while the second and third are valid for processes that meet internal reversibility condition (see Sect. 6.5).

References

  1. Callen HB (1st edition, 1960; 2nd edition, 1985) Thermodynamics and an Introduction to Thermostatistics. Wiley, New York

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  2. Gibbs JW (1961) The Scientific Papers of J. W. Gibbs, Vol. 1: Thermodynamics. Dover (p. 354)

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  3. Kestin J (1966) A Treatise in Thermodynamics, Volume 1. Blaisdell Publishing Co

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Authors and Affiliations

  1. Stony Brook University, Stony Brook, NY, USA

    Lin-Shu Wang

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  1. Lin-Shu Wang
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Correspondence to Lin-Shu Wang .

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Wang, LS. (2020). Applications to Special States of Thermodynamic Equilibrium: Gibbsian Thermodynamics for Physical and Chemical Applications. In: A Treatise of Heat and Energy. Mechanical Engineering Series. Springer, Cham. https://doi.org/10.1007/978-3-030-05746-6_9

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  • DOI: https://doi.org/10.1007/978-3-030-05746-6_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05745-9

  • Online ISBN: 978-3-030-05746-6

  • eBook Packages: EngineeringEngineering (R0)

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