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Application of the Entropy Concept to Thermodynamics and Life Sciences Brigham Young University BYU ScholarsArchive All Theses and Dissertations 2018-06-01 Application of the Entropy Concept to Thermodynamics and Life Sciences: Evolution Parallels Thermodynamics, Cellulose Hydrolysis Thermodynamics, and Ordered and Disordered Vacancies Thermodynamics Marko Popovic Brigham Young University Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Chemistry Commons BYU ScholarsArchive Citation Popovic, Marko, "Application of the Entropy Concept to Thermodynamics and Life Sciences: Evolution Parallels Thermodynamics, Cellulose Hydrolysis Thermodynamics, and Ordered and Disordered Vacancies Thermodynamics" (2018). All Theses and Dissertations. 6996. https://scholarsarchive.byu.edu/etd/6996 This Dissertation is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Application of the Entropy Concept to Thermodynamics and Life Sciences: Evolution Parallels Thermodynamics, Cellulose Hydrolysis Thermodynamics, and Ordered and Disordered Vacancies Thermodynamics Marko Popovic A dissertation submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Brian F. Woodfield, Chair Lee Duane Hansen Harold Dennis Tolley James E. Patterson Jeremy Andrew Johnson Department of Chemistry and Biochemistry Brigham Young University Copyright © 2018 Marko Popovic All Rights Reserved ABSTRACT Application of the Entropy Concept to Thermodynamics and Life Sciences: Evolution Parallels Thermodynamics, Cellulose Hydrolysis Thermodynamics, and Ordered and Disordered Vacancies Thermodynamics Marko Popovic Department of Chemistry and Biochemistry, BYU Doctor of Philosophy Entropy, first introduced in thermodynamics, is used in a wide range of fields. Chapter 1 discusses some important theoretical and practical aspects of entropy: what is entropy, is it subjective or objective, and how to properly apply it to living organisms. Chapter 2 presents applications of entropy to evolution. Chapter 3 shows how cellulosic biofuel production can be improved. Chapter 4 shows how lattice vacancies influence the thermodynamic properties of materials. To determine the nature of thermodynamic entropy, Chapters 1 and 2 describe the roots, the conceptual history of entropy, as well as its path of development and application. From the viewpoint of physics, thermal entropy is a measure of useless energy stored in a system resulting from thermal motion of particles. Thermal entropy is a non-negative objective property. The negentropy concept, while mathematically correct, is physically misleading. This dissertation hypothesizes that concepts from thermodynamics and statistical mechanics can be used to define statistical measurements, similar to thermodynamic entropy, to summarize the convergence of processes driven by random inputs subject to deterministic constraints. A primary example discussed here is evolution in biological systems. As discussed in this dissertation, the first and second laws of thermodynamics do not translate directly into parallel laws for the biome. But, the fundamental principles on which thermodynamic entropy is based are also true for information. Based on these principles, it is shown that adaptation and evolution are stochastically deterministic. Chapter 3 discusses the hydrolysis of cellulose to glucose, which is a key reaction in renewable energy from biomass and in mineralization of soil organic matter to CO2. Conditional thermodynamic parameters, ΔhydG’, ΔhydH’, and ΔhydS’, and equilibrium glucose concentrations are reported for the reaction C6H10O5(cellulose) + H2O(l) ⇄ C6H12O6(aq) as functions of temperature from 0 to 100⁰C. Activity coefficients of aqueous glucose solution were determined as a function of temperature. The results suggest that producing cellulosic biofuels at higher temperatures will result in higher conversion. Chapter 4 presents the data and a theory relating the linear term in the low temperature heat capacity to lattice vacancy concentration. The theory gives a quantitative result for disordered vacancies, but overestimates the contribution from ordered vacancies because ordering leads to a decreased influence of vacancies on heat capacity. Keywords: negentropy, Shannon entropy, information, order, disorder, Gibbs free energy, cellulose hydrolysis, lattice vacancies, heat capacity, samarium and neodymium doped ceria ACKNOWLEDGEMENTS The author expresses his gratitude to Brigham Young University for financial support through an HIDRA graduate fellowship, to the Department of Chemistry and Biochemistry for financial support, to Prof. Brian Woodfield, Department of Chemistry and Biochemistry, Brigham Young University for effort during the research, as well as help in adapting to the American way of life, and to Prof. Emeritus Lee Hansen, Department of Chemistry and Biochemistry, Brigham Young University, for friendliness, inspiring discussions and support. The author also expresses his gratitude to Prof. H. Dennis Tolley, Department of Statistics, Brigham Young University for fruitful team work in the field of statistical mechanics, as well as Prof. James Patterson and Prof. Jeremy Johnson for useful comments. TABLE OF CONTENTS 1 ENTROPY WONDERLAND: A REVIEW OF THE ENTROPY CONCEPT .................................... 1 1.1 Abstract ......................................................................................................................................... 1 1.2 Introduction – What is entropy? .................................................................................................... 2 1.2.1 Entropy in Chemical Thermodynamics ................................................................................ 3 1.2.2 Entropy in Statistical Mechanics ........................................................................................... 9 1.2.3 Residual Entropy ................................................................................................................. 13 1.3 What is the physical meaning of entropy? .................................................................................. 15 1.4 Is entropy a subjective or an objective property ......................................................................... 16 1.5 How to apply entropy to living organisms? ................................................................................ 20 1.6 Conclusions ................................................................................................................................. 22 1.7 Nomenclature .............................................................................................................................. 22 1.8 References ................................................................................................................................... 23 2 LAWS OF EVOLUTION PARALLEL THE LAWS OF THERMODYNAMICS ........................... 30 2.1 Abstract ....................................................................................................................................... 30 2.2 Introduction ................................................................................................................................. 31 2.3 The Macroscopic Definition of Entropy ..................................................................................... 32 2.4 The Microscopic Definition of Entropy ...................................................................................... 34 2.5 Shannon’s Information Entropy .................................................................................................. 39 2.6 Order, disorder and entropy ........................................................................................................ 43 2.7 Evolution and Adaptation of Living Organisms ......................................................................... 46 2.8 Summary ..................................................................................................................................... 50 2.9 Notes ........................................................................................................................................... 53 2.10 Supplement 1: The Second Law of Classical Thermodynamics ................................................. 54 2.10.1 Clausius Inequality Derivation ............................................................................................ 54 2.11 Supplement 2: Clausius’ Entropy ............................................................................................... 59 2.12 Supplement 3: Statistical Entropy Equations .............................................................................. 61 2.13 References: .................................................................................................................................. 64 3 THERMODYNAMICS OF HYDROLYSIS OF CELLULOSE TO GLUCOSE FROM 0 TO 100⁰C: CELLULOSIC BIOFUEL APPLICATIONS AND CLIMATE CHANGE IMPLICATIONS .................. 68 3.1 Abstract ....................................................................................................................................... 68 iv 3.2 Introduction ................................................................................................................................. 68 3.3 Thermodynamic data..................................................................................................................
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