SIPS 2017 Volume 2. Dodds Intl. Symp. / Energy Production

Editors: | Kongoli F, Buhl A, Turna T, Mauntz M, Williams W, Rubinstein J, Fuhr PL, Morales-Rodriguez M |

Publisher: | Flogen Star OUTREACH |

Publication Year: | 2017 |

Pages: | 306 pages |

ISBN: | 978-1-987820-63-8 |

ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |

The Gibbs-Duhem theory of stability of equilibrium states has been extended to determine the stability of irreversible processes. The basic concept of virtual displacement in the reverse direction on the real trajectory, which is involved in the celebrated Gibbs-Duhem theory, has been used. This establishes that all thermodynamically describable processes are thermodynamically stable. This outcome led us to reformulate the fourth law of thermodynamics. Moreover, our present investigations illustrate the basis of the universal inaccessibility principle formulated earlier by one of the present authors (AAB).

[2] F. G. Donnan and A. Haas, eds., A Commentary on the Scientific Writings of J. Willard Gibbs, vol. I, 1936, Yale University Press, London, New Haven.

[3] P. Needham, Commentary on the Principles of Thermodynamics by Pierre Duhem, 2011, Springer, Dordrecht, New York.

[4] P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations, 1971, Wiley, New York.

[5] W. H. Cropper, “Rudolf Clausius and the road to entropy,” Am. J. Phys., 54 (1986), 1068 – 1074.

[6] J. Meixner, “The entropy problem in thermodynamics of processes,” Rheol. Acta., 12(3) (1973), 465 – 467.

[7] K. G. Denbigh, The Principles of Chemical Equilibrium, 1973, Cambridge University Press, Cambridge, UK.

[8] K. G. Denbigh, The Thermodynamics of the Steady State, 1958, Methuen & Company, London.

[9] S. Glasstone, Thermodynamics for Chemists, 1967, D. Van Nostrand, New Jersey.

A. A. Bhalekar, “On the generalized phenomenological irreversible thermodynamic theory (GPITT),” J. Math. Chem., 5(2) (1990), 187 – 196,

[10] A. Bhalekar, “Measure of dissipation in the framework of generalized phenomenological irreversible thermodynamic theory (GPITT),” Proc. Int. Symp. on Efficiency, Costs, Optimization and Simulation of Energy Systems (ECOS’92), Zaragoza, Spain, June 15-18, 1992, A. Valero and G. Tsatsaronis, eds.; Empresa Nacional de Electricidad, Spain and Amer. Soc. Mech. Eng., pp. 121 – 128.

[11] A. Bhalekar, “Universal inaccessibility principle,” Pramana - J. Phys., 50(4) (1998), 281 – 294.

[12] A. Bhalekar, “On the generalized zeroth law of thermodynamics,” Indian J. Phys., 74B( 2) (2000) 153 – 157.

[13] A. Bhalekar, “On the time dependent entropy vis-à-vis Clausius’ inequality: Some of the aspects pertaining to the global and the local levels of thermodynamic considerations,” Asian J. Chem., 12(2) (2000), 417 – 427.

[14] A. Bhalekar, “On the irreversible thermodynamic framework for closed systems consisting of chemically reactive components,” Asian J. Chem., 12(2) (2000), 433 – 444.

[15] A. Bhalekar and B. Andresen, “On the nonequilibrium thermodynamic roots of the additional facets of chemical interaction,” in Recent Advances in Thermodynamic Research Including Nonequilibrium Thermodynamics, Proceedings of 3rd National Conference on Thermodynamics of Chemical and Biological Systems (NCTCBS-2008), G. S. Natarajan, A. A. Bhalekar, S. S. Dhondge, and H. D. Juneja, eds., (Department of Chemistry), 2008, pp. 53 – 62, R. T. M. Nagpur University, Nagpur, Funded by CSIR, New Delhi, October 16– 17.

[16] A. Bhalekar, “The dictates and the range of applicability of the laws of thermodynamics for developing an irreversible thermodynamical framework,” Indian J. Phys., 76B (2002), 715 – 721.

[17] A. Bhalekar, “Irreversible thermodynamic framework using compatible equations from thermodynamics and fluid dynamics. A second route to generalized phenomenological irreversible thermodynamic theory (GPITT),” Bull. Cal. Math. Soc., 94(2) (2002), 209 – 224.

[18] A. Bhalekar, “The universe of operations of thermodynamics vis-à-vis Boltzmann integro-differential equation,” Indian J. Phys., 77B (2003), 391 – 397.

[19] A. Bhalekar, “Thermodynamic insight of irreversibility,” Proceedings of the Third International Conference on Lie-Admissible Treatment of Irreversible Processes (ICLATIP - 3), Dhulikhel, Kavre, Nepal, 2011, C. Corda, ed., pp. 135 – 162, R. M. Santilli Foundation, USA and Kathmandu University.

[20] A, A. Bhalekar and B. Andresen, “A comprehensive formulation of generalized phenomenological irreversible thermodynamic theory (GPITT),” (to appear).

[21] G. Lebon, D. Jou and J. Casas-Vázquez, Understanding of Non-equilibrium Thermodynamics. Foundations, Applications and Frontiers, 2008, Springer, Berlin.

[22] Prigogine and R. Defay, Chemical Thermodynamics, 1954, Longmans Green, London, Translated by D. H. Everett.

[23] Prigogine, Introduction to Thermodynamics of Irreversible Processes, 1967, John Wiley-Interscience, New York.

[24] H. Lavenda, Thermodynamics of Irreversible Processes, 1978, Macmillan Press, London.

[25] S. A. Kamal, “The fourth law of thermodynamics,” The Pakistan Institute of Physics Conference, Lahore, March 2011, 1 – 5,. Paper # PIPC-11-25.

[26] P. Glansdorff and I. Prigogine, “Non-Equilibrium stability theory,” Physica, 46 (1970), 344 – 366.

[27] P. Glansdorff, G. Nicolis, and I. Prigogine, “The thermodynamic stability theory of non-equilibrium states,” Proc. Nat. Acad. Sci. USA, 71 (1974), 197–199.

[28] G. Malkin, “Theory of stability of motion,” in ACE-tr-3352 Physics and Mathematics, 1952, US Atomic Energy Commission, Washington, New York, Moscow, Leningrad.

[29] N. G. Chetayev, The Stability of Motion. 1961, Pergamon Press, Oxford, M. Nadler, Transl.

[30] Z. Shtokalo, Linear Differential Equations with Variable Coefficients. Criteria of Stability and Instability of Their Solutions, 1961, Hindustan Publishing, Delhi, India.

[31] G. Malkin, Stability and Dynamic Systems, 1962, American Mathematical Society, Providence, Rhode Island.

[32] Reference 31, pp. 291– 297.

[33] W. Hahn, Theory and Applications of Lyapunov’s Direct Method. 1963, Prentice-Hall, Englewood Cliffs, New Jersey.

[34] P. LaSalle and S. Lefschetz, eds., Nonlinear Differential Equations and Nonlinear Mechanics. 1963, Academic Press, New York.

[35] Elsgolts, Differential Equations and the Calculus of Variations, 1970, Mir Publications, Moscow, G. Yankuvsky, Transl.

[36] H. H. E. Leipholz, Stability Theory: An Introduction to the Stability of Dynamic Systems and Rigid Bodies, 1987, B. G. Teubner/John Wiley, Stuttgart/Chichester.

[37] P. LaSalle and S. Lefschetz, Stability by Liapunov’s Direct Method with Applications, 1961,

[38] Academic Press, New York.

[39] A. Sànchez, Ordinary Differential Equations and Stability Theory. An Introduction, 1979,

[40] Dover, New York.

[41] Keizer and R. F. Fox, “Qualms regarding the range of validity of the Glansdorff-Prigogine criterion for stability of non-equilibrium states,” Proc. Nat. Acad. Sci. USA, 71 (1974), 192 – 196, 2919.

[42] P. T. Landsberg, “The fourth law of thermodynamics,” Nature, 238 (1972), 229 – 231.

[43] J. Laidler, Chemical Kinetics, 1967, Tata McGraw-Hill, New Delhi.

[44] R. Wayne, The Theory of the Kinetics of Elementary Gas Phase Reactions,

[45] in Comprehensive Chemical Kinetics, 1969, Eds. C. H. Bamford and C. F. H Tipper, Vol. 2, Elsevier, New York, Ch. 3, pp. 189 – 301.

[46] H. Eyring, “The activated complex in chemical reactions,” J. Chem. Phys., 3 (1935), 107 – 115.

[47] S. Glasstone, K. J. Laidler, and H. Eyring, Theory of Rate Processes, 1941, First ed., McGraw-Hill, New York.

[48] G. Evans and M. Polanyi, “Some applications of the transition state method to the calculation of reaction velocities, especially in solution,” Trans. Faraday Soc., 31 (1935), 875 – 894.

[49] J. Laidler and J. C. Polanyi, “Theories of the Kinetics of Bimolecular Reactions”, Progress in Reaction Kinetics, Vol. 3, 1965, Pergamon Press, London, Ch. 1, pp. 1 – 61.

[50] L. Arnot, “Activated complex theory of bimolecular gas reactions,” J. Chem. Educ., 49 (1972), 480 – 482.

A. A. Bhalekar “The transition state theory of bimolecular reaction rates via the Bodenstein steady state for activated complexes,” CACAA, 4 (2015), 309 – 340.

[51] A. Bhalekar, “On a comprehensive thermodynamic theory of stability of irreversible processes: A brief introduction,” Far East J. Appl. Math., 5 (2001), 199 – 210.

[52] A. Bhalekar, “Comprehensive thermodynamic theory of stability of irreversible processes (CTTSIP). I. The details of a new theory based on Lyapunov’s direct method of stability of motion and the second law of thermodynamics,” Far East J. Appl. Math., 5 (2001), 381 – 396.

[53] A. Bhalekar, “Comprehensive thermodynamic theory of stability of irreversible processes (CTTSIP). II. A study of thermodynamic stability of equilibrium and nonequilibrium stationary states,” Far East J. Appl. Math., 5 (2001), 397 – 416.

[54] A. Bhalekar, “The generalized set-up of comprehensive thermodynamic theory of stability of irreversible processes (CTTSIP) and a few illustrative applications,” J. Indian Chem. Soc., 81 (2004), 1119 – 1126.

[55] V. M. Tangde, S. G. Rawat, and A. A. Bhalekar, “Comprehensive thermodynamic theory of stability of irreversible processes (CTTSIP): The set-up for autonomous systems and application,” Int. J. Eng. Tech. Res., 3 (2015), 182 – 191.

A. A. Bhalekar and V. M. Tangde, “Thermodynamic Stability of Irreversible Processes Based on Lyapunov Function Analysis,” 2017, SIPS 2017 Proceedings, (Accepted).