DOCSLIB.ORG

Energy and Entropy Flows in Living Systems Daina Briedis Iowa State University

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Energy and Entropy Flows in Living Systems Daina Briedis Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1981 Energy and entropy flows in living systems Daina Briedis Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Chemical Engineering Commons Recommended Citation Briedis, Daina, "Energy and entropy flows in living systems " (1981). Retrospective Theses and Dissertations. 7399. https://lib.dr.iastate.edu/rtd/7399 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This was produced from a copy of a document sent to us for microfilming. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help you understand markings or notations which may appear on this reproduction. 1. The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure you of complete continuity. 2. When an image on the film is obliterated with a round black mark it is an indication that the film inspector noticed either blurred copy because of movement during exposure, or duplicate copy. Unless we meant to delete copyrighted materials that should not have been filmed, you will find a good image of the page in the adjacent frame. If copyrighted materials were deleted you will find a target note listing the pages in the adjacent frame. 3. When a map, drawing or chart, etc., is part of the material being photo­ graphed the photographer has followed a definite method in "sectioning" the material. It is customary to begin filming at the upper left hand corner of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until complete. 4. For any illustrations that cannot be reproduced satisfactorily by xerography, photographic prints can be purchased at additional cost and tipped into your xerographic copy. Requests can be made to our Dissertations Customer Services Department. 5. Some pages in any document may have indistinct print. In all cases we have filmed the best available copy. UniversiV Micronlms International 300 N /EEBRD, ANN ARBOR, Ml 48106 8209099 Briedis, Daina ENERGY AND ENTROPY FLOWS IN LIVING SYSTEMS loyta State University PH.D. 1981 University Microfilms Intsrnâtionâl W N. Zeeb Roml. Ann Arbor. MI 48106 Copyrigiit 1981 by Briedis, Daina All Riglits Reserved Energy and entropy flows In living systems by Daina Briedis A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major: Chemical Engineering Approved: Signature was redacted for privacy. In Charge of Major |K)rk Signature was redacted for privacy. For the Major Department Signature was redacted for privacy. For the Graduate college Iowa State University Ames, Iowa 1981 Copyright @ Daina Briedis, 1981. All rights reserved. 11 TABLE OF CONTENTS Page DEDICATION V I. INTRODUCTION 1 II. LITERATURE OVERVIEW 5 A. Energy and Biology 5 1. Muscle contraction energetics 5 2. Exercise physiology and energetics 6 3. Development and growth 9 B. Entropy and Biology 10 1. Irreversible thermodynamics 11 2. Development and growth 12 3. Entropy and evolution 15 4. Irreversible thermodynamics and muscle contraction 15 III. TECHNIQUES AND ANALYSIS 17 A. The Mass Balance 17 B. The Energy Balance 22 1. Development 23 2. Discussion of terms 30 3. Special cases 35 C. The Entropy Account 43 1. Development 43 2. Discussion of terms 49 3. Entropy and living systems 54 D. Efficiency 58 1. Thermodynamic efficiencies 58 2. Biochemical efficiencies 61 3. Physiology and efficiency 64 4. General efficiency and efficacy expressions 65 ill Page IV. APPLICATIONS 73 A. Mass Balances 73 B. Energy Consumption Measurements 77 1. Traditional techniques 77 2. The electron balance technique 79 C. Thermodynamics of Growth and Development 83 1. Growth and development 84 2. Analyses of the microbial culture system 85 a. First law analysis 86 b. Second law analysis 93 3. Analyses of the avian egg system 99 a. First law analysis 102 b. Second law analysis 114 4. Entropy and organization 132 D. The Thermodynamics of Muscles and Muscle Systems 140 1. Work and muscles 141 a. Contraction 143 b. Force-velocity relationships 152 c. Muscle energy sources and their evaluation 157 d. In situ studies 164 2. Approaches to muscle experimentation 165 a. The contraction cycle 165 b. Oxygen consumption as a function of state 173 3. Nonequilibrium thermodynamics of muscle 186 4. Work classification 191 a. Exercise without work 192 b. Leg segment analysis 197 c. Work against drag 200 d. Overcoming wind resistance 201 e. Projectiles and propulsion 206 f. Work in a gravitational field 208 V. CONCLUSIONS 220 A. General 220 B. Specific 221 iv Page VI. RECOMMENDATIONS 222 VII. BIBLIOGRAPHY 224 VIII. ACKNOWLEDQIENTS 233 V DEDICATION This work is dedicated to my family; to my parents, Gunars and Antonija Briedis, and to my brother, Robert. 1 I. INTRODUCTION Life is a costly, energy consuming process which develops and sus­ tains gradients In temperature, pressure, concentration, and chemical affinity. Living systems fuel this process through the capability of transforming energy from one form to another through Intricate chains of biochemical and physlochemlcal events. In this sense, they have been compared to a complex chemical factory In which the primary purpose Is the creation and maintenance of life. This analogy suggests that the principles of thermodynamics and transport phenomena used for analyzing physical systems may be applied to the study of energy flows in the development, growth, and regulation of living organisms. The application of the principles of conservation of material and of energy to biological systems has appeared frequently In thermodynamics research since the mid-nineteenth century. Calorimetric studies of the heat production of animals were performed in the late 1700s by Lavoisier and Laplace and subsequently served as a basis for more rigorous thermodynamic analyses. In the late 1800s, the link between food as a fuel, the heats of combustion of the nutrients in the food, and the resulting heat production by the system was demonstrated. These later studies warranted assumptions about the applicability of the laws of con­ servation of matter and energy, although the data were not analyzed to represent the proper thermodynamic quantities. The first law of thermodynamics and the concepts and quantities used therein often imply a restriction to measurements done on systems at 2 equilibrium since some of the quantities used In the first law expression are defined rigorously only at equilibrium. Classical thermodynamics Is a study of static situations constrained largely to spatially homogeneous, time-Invariant entitles. Biological systems are Inherently complex and heterogeneous, open, transient, and not at equilibrium. This Indicates the need for additional studies using Irreversible or nonequlllbrlum thermodynamics In which the concept of local equilibrium permits the use of equilibrium thermodynamic variables. The first law, however, does serve as an adequate and useful tool In the macroscopic analysis of biological systems over relatively short time spans. Classical thermodynamic theory can be used In dealing with over­ all features, constraints, and consequences to obtain limiting statements about the system and Its operation. It Is a bookkeeping device and has no predictive capabilities. The concepts of Irreversible thermodynamics allow further insights Into the thermodynamic description of biological systems through the use of ideas such as local equilibrium, entropy flow, entropy production, and stationary states. Many biological processes may be modelled by the phenomenological relations between forces and fluxes developed by Onsager in 1931. The investigation is somewhat simplified in living organisms which operate within a limited temperature range and at nearly constant pressure and which are composed of solutions that may be con­ sidered ideal. The second law of thermodynamics implies that the entropy of an Isolated system in which irreversible processes take place must increase. 3 Since most of the processes In living systems are Irreversible, Prlgoglne (80) has hypothesized that the specific Internal entropy production rate of living systems must be positive but that it continually decreases as a system develops, matures, and ages. These two ideas suggest that life may be placed into a global framework in which living things contribute to the overall entropy increase of the universe. Once the first law analysis has provided a thorough understanding of the energy flows of a system, irreversible thermodynamics, subject to overall energy balance constraints, serves as a predictive tool to characterize and quantify the
Load more

Recommended publications
  • ENERGY, ENTROPY, and INFORMATION Jean Thoma June
    ENERGY, ENTROPY, AND INFORMATION Jean Thoma June 1977 Research Memoranda are interim reports on research being conducted by the International Institute for Applied Systems Analysis, and as such receive only limited scientific review. Views or opinions contained herein do not necessarily represent those of the Institute or of the National Member Organizations supporting the Institute. PREFACE This Research Memorandum contains the work done during the stay of Professor Dr.Sc. Jean Thoma, Zug, Switzerland, at IIASA in November 1976. It is based on extensive discussions with Professor HAfele and other members of the Energy Program. Al- though the content of this report is not yet very uniform because of the different starting points on the subject under consideration, its publication is considered a necessary step in fostering the related discussion at IIASA evolving around th.e problem of energy demand. ABSTRACT Thermodynamical considerations of energy and entropy are being pursued in order to arrive at a general starting point for relating entropy, negentropy, and information. Thus one hopes to ultimately arrive at a common denominator for quanti- ties of a more general nature, including economic parameters. The report closes with the description of various heating appli- cation.~and related efficiencies. Such considerations are important in order to understand in greater depth the nature and composition of energy demand. This may be highlighted by the observation that it is, of course, not the energy that is consumed or demanded for but the informa- tion that goes along with it. TABLE 'OF 'CONTENTS Introduction ..................................... 1 2 . Various Aspects of Entropy ........................2 2.1 i he no me no logical Entropy ........................
    [Show full text]
  • Lecture 4: 09.16.05 Temperature, Heat, and Entropy
    3.012 Fundamentals of Materials Science Fall 2005 Lecture 4: 09.16.05 Temperature, heat, and entropy Today: LAST TIME .........................................................................................................................................................................................2� State functions ..............................................................................................................................................................................2� Path dependent variables: heat and work..................................................................................................................................2� DEFINING TEMPERATURE ...................................................................................................................................................................4� The zeroth law of thermodynamics .............................................................................................................................................4� The absolute temperature scale ..................................................................................................................................................5� CONSEQUENCES OF THE RELATION BETWEEN TEMPERATURE, HEAT, AND ENTROPY: HEAT CAPACITY .......................................6� The difference between heat and temperature ...........................................................................................................................6� Defining heat capacity.................................................................................................................................................................6�
    [Show full text]
  • Chapter 3. Second and Third Law of Thermodynamics
    Chapter 3. Second and third law of thermodynamics Important Concepts Review Entropy; Gibbs Free Energy • Entropy (S) – definitions Law of Corresponding States (ch 1 notes) • Entropy changes in reversible and Reduced pressure, temperatures, volumes irreversible processes • Entropy of mixing of ideal gases • 2nd law of thermodynamics • 3rd law of thermodynamics Math • Free energy Numerical integration by computer • Maxwell relations (Trapezoidal integration • Dependence of free energy on P, V, T https://en.wikipedia.org/wiki/Trapezoidal_rule) • Thermodynamic functions of mixtures Properties of partial differential equations • Partial molar quantities and chemical Rules for inequalities potential Major Concept Review • Adiabats vs. isotherms p1V1 p2V2 • Sign convention for work and heat w done on c=C /R vm system, q supplied to system : + p1V1 p2V2 =Cp/CV w done by system, q removed from system : c c V1T1 V2T2 - • Joule-Thomson expansion (DH=0); • State variables depend on final & initial state; not Joule-Thomson coefficient, inversion path. temperature • Reversible change occurs in series of equilibrium V states T TT V P p • Adiabatic q = 0; Isothermal DT = 0 H CP • Equations of state for enthalpy, H and internal • Formation reaction; enthalpies of energy, U reaction, Hess’s Law; other changes D rxn H iD f Hi i T D rxn H Drxn Href DrxnCpdT Tref • Calorimetry Spontaneous and Nonspontaneous Changes First Law: when one form of energy is converted to another, the total energy in universe is conserved. • Does not give any other restriction on a process • But many processes have a natural direction Examples • gas expands into a vacuum; not the reverse • can burn paper; can't unburn paper • heat never flows spontaneously from cold to hot These changes are called nonspontaneous changes.
    [Show full text]
  • A Simple Method to Estimate Entropy and Free Energy of Atmospheric Gases from Their Action
    Article A Simple Method to Estimate Entropy and Free Energy of Atmospheric Gases from Their Action Ivan Kennedy 1,2,*, Harold Geering 2, Michael Rose 3 and Angus Crossan 2 1 Sydney Institute of Agriculture, University of Sydney, NSW 2006, Australia 2 QuickTest Technologies, PO Box 6285 North Ryde, NSW 2113, Australia; [email protected] (H.G.); [email protected] (A.C.) 3 NSW Department of Primary Industries, Wollongbar NSW 2447, Australia; [email protected] * Correspondence: [email protected]; Tel.: + 61-4-0794-9622 Received: 23 March 2019; Accepted: 26 April 2019; Published: 1 May 2019 Abstract: A convenient practical model for accurately estimating the total entropy (ΣSi) of atmospheric gases based on physical action is proposed. This realistic approach is fully consistent with statistical mechanics, but reinterprets its partition functions as measures of translational, rotational, and vibrational action or quantum states, to estimate the entropy. With all kinds of molecular action expressed as logarithmic functions, the total heat required for warming a chemical system from 0 K (ΣSiT) to a given temperature and pressure can be computed, yielding results identical with published experimental third law values of entropy. All thermodynamic properties of gases including entropy, enthalpy, Gibbs energy, and Helmholtz energy are directly estimated using simple algorithms based on simple molecular and physical properties, without resource to tables of standard values; both free energies are measures of quantum field states and of minimal statistical degeneracy, decreasing with temperature and declining density. We propose that this more realistic approach has heuristic value for thermodynamic computation of atmospheric profiles, based on steady state heat flows equilibrating with gravity.
    [Show full text]
  • Modeling Two Phase Flow Heat Exchangers for Next Generation Aircraft
    Wright State University CORE Scholar Browse all Theses and Dissertations Theses and Dissertations 2017 Modeling Two Phase Flow Heat Exchangers for Next Generation Aircraft Hayder Hasan Jaafar Al-sarraf Wright State University Follow this and additional works at: https://corescholar.libraries.wright.edu/etd_all Part of the Mechanical Engineering Commons Repository Citation Al-sarraf, Hayder Hasan Jaafar, "Modeling Two Phase Flow Heat Exchangers for Next Generation Aircraft" (2017). Browse all Theses and Dissertations. 1831. https://corescholar.libraries.wright.edu/etd_all/1831 This Thesis is brought to you for free and open access by the Theses and Dissertations at CORE Scholar. It has been accepted for inclusion in Browse all Theses and Dissertations by an authorized administrator of CORE Scholar. For more information, please contact [email protected]. MODELING TWO PHASE FLOW HEAT EXCHANGERS FOR NEXT GENERATION AIRCRAFT A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering By HAYDER HASAN JAAFAR AL-SARRAF B.Sc. Mechanical Engineering, Kufa University, 2005 2017 Wright State University WRIGHT STATE UNIVERSITY GRADUATE SCHOOL July 3, 2017 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Hayder Hasan Jaafar Al-sarraf Entitled Modeling Two Phase Flow Heat Exchangers for Next Generation Aircraft BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Mechanical Engineering. ________________________________ Rory Roberts, Ph.D. Thesis Director ________________________________ Joseph C. Slater, Ph.D., P.E. Department Chair Committee on Final Examination ______________________________ Rory Roberts, Ph.D. ______________________________ James Menart, Ph.D. ______________________________ Mitch Wolff, Ph.D.
    [Show full text]
  • Thermodynamics
    ME346A Introduction to Statistical Mechanics { Wei Cai { Stanford University { Win 2011 Handout 6. Thermodynamics January 26, 2011 Contents 1 Laws of thermodynamics 2 1.1 The zeroth law . .3 1.2 The first law . .4 1.3 The second law . .5 1.3.1 Efficiency of Carnot engine . .5 1.3.2 Alternative statements of the second law . .7 1.4 The third law . .8 2 Mathematics of thermodynamics 9 2.1 Equation of state . .9 2.2 Gibbs-Duhem relation . 11 2.2.1 Homogeneous function . 11 2.2.2 Virial theorem / Euler theorem . 12 2.3 Maxwell relations . 13 2.4 Legendre transform . 15 2.5 Thermodynamic potentials . 16 3 Worked examples 21 3.1 Thermodynamic potentials and Maxwell's relation . 21 3.2 Properties of ideal gas . 24 3.3 Gas expansion . 28 4 Irreversible processes 32 4.1 Entropy and irreversibility . 32 4.2 Variational statement of second law . 32 1 In the 1st lecture, we will discuss the concepts of thermodynamics, namely its 4 laws. The most important concepts are the second law and the notion of Entropy. (reading assignment: Reif x 3.10, 3.11) In the 2nd lecture, We will discuss the mathematics of thermodynamics, i.e. the machinery to make quantitative predictions. We will deal with partial derivatives and Legendre transforms. (reading assignment: Reif x 4.1-4.7, 5.1-5.12) 1 Laws of thermodynamics Thermodynamics is a branch of science connected with the nature of heat and its conver- sion to mechanical, electrical and chemical energy. (The Webster pocket dictionary defines, Thermodynamics: physics of heat.) Historically, it grew out of efforts to construct more efficient heat engines | devices for ex- tracting useful work from expanding hot gases (http://www.answers.com/thermodynamics).
    [Show full text]
  • Lecture 6: Entropy
    Matthew Schwartz Statistical Mechanics, Spring 2019 Lecture 6: Entropy 1 Introduction In this lecture, we discuss many ways to think about entropy. The most important and most famous property of entropy is that it never decreases Stot > 0 (1) Here, Stot means the change in entropy of a system plus the change in entropy of the surroundings. This is the second law of thermodynamics that we met in the previous lecture. There's a great quote from Sir Arthur Eddington from 1927 summarizing the importance of the second law: If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equationsthen so much the worse for Maxwell's equations. If it is found to be contradicted by observationwell these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of ther- modynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. Another possibly relevant quote, from the introduction to the statistical mechanics book by David Goodstein: Ludwig Boltzmann who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. There are many ways to dene entropy. All of them are equivalent, although it can be hard to see. In this lecture we will compare and contrast dierent denitions, building up intuition for how to think about entropy in dierent contexts. The original denition of entropy, due to Clausius, was thermodynamic.
    [Show full text]
  • Thermodynamics
    ...Thermodynamics Entropy: The state function for the Second Law R R d¯Q Entropy dS = T Central Equation dU = TdS − PdV Ideal gas entropy ∆s = cv ln T =T0 + R ln v=v0 Boltzmann entropy S = klogW P Statistical Entropy S = −kB i pi ln(pi ) October 14, 2019 1 / 25 Fewer entropy with chickens Counting Things You can't count a continuum. This includes states which may never be actually realised. This is where the ideal gas entropy breaks down Boltzmann's entropy requires Quantum Mechanics. October 14, 2019 2 / 25 Equilibrium and the thermodynamic potentials Second Law : entropy increases in any isolated system. Entropy of system+surroundings must increase. A system can reduce its entropy, provided the entropy of the surroundings increases by more. October 14, 2019 3 / 25 Equilibrium and boundary conditions Main postulate of thermodynamics: systems tend to \equilibrium". Equilibrium depends on boundary conditions. October 14, 2019 4 / 25 A function for every boundary condition Another statement of 2nd Law... System+surroundings maximise S Compare with mechanical equilibrium System minimises energy In thermodynamic equilibrium System minimises ... Free energy October 14, 2019 5 / 25 Free energy Willard Gibbs 1839-1903: A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces, 1873 Equation of state plotted as a surface of energy vs T and P. Volume, entropy are slopes of this surface Heat capacity, compressibility are curvatures. October 14, 2019 6 / 25 Surface and Slopes: Not like this October 14, 2019 7 / 25 Surfaces and slope: More like something from Lovecraft H.P.Lovecraft 1928 \The Call of Cthulhu" PV or TS \space" is completely non-euclidean.
    [Show full text]
  • Thermodynamic Potentials
    THERMODYNAMIC POTENTIALS, PHASE TRANSITION AND LOW TEMPERATURE PHYSICS Syllabus: Unit II - Thermodynamic potentials : Internal Energy; Enthalpy; Helmholtz free energy; Gibbs free energy and their significance; Maxwell's thermodynamic relations (using thermodynamic potentials) and their significance; TdS relations; Energy equations and Heat Capacity equations; Third law of thermodynamics (Nernst Heat theorem) Thermodynamics deals with the conversion of heat energy to other forms of energy or vice versa in general. A thermodynamic system is the quantity of matter under study which is in general macroscopic in nature. Examples: Gas, vapour, vapour in contact with liquid etc.. Thermodynamic stateor condition of a system is one which is described by the macroscopic physical quantities like pressure (P), volume (V), temperature (T) and entropy (S). The physical quantities like P, V, T and S are called thermodynamic variables. Any two of these variables are independent variables and the rest are dependent variables. A general relation between the thermodynamic variables is called equation of state. The relation between the variables that describe a thermodynamic system are given by first and second law of thermodynamics. According to first law of thermodynamics, when a substance absorbs an amount of heat dQ at constant pressure P, its internal energy increases by dU and the substance does work dW by increase in its volume by dV. Mathematically it is represented by 풅푸 = 풅푼 + 풅푾 = 풅푼 + 푷 풅푽….(1) If a substance absorbs an amount of heat dQ at a temperature T and if all changes that take place are perfectly reversible, then the change in entropy from the second 풅푸 law of thermodynamics is 풅푺 = or 풅푸 = 푻 풅푺….(2) 푻 From equations (1) and (2), 푻 풅푺 = 풅푼 + 푷 풅푽 This is the basic equation that connects the first and second laws of thermodynamics.
    [Show full text]
  • 1 Where and How Is Entropy Generated in Solar Energy
    Where and How is Entropy Generated in Solar Energy Conversion Systems? Bolin Liao1* 1Department of Mechanical Engineering, University of California, Santa Barbara, CA, 93106, USA Abstract The hotness of the sun and the coldness of the outer space are inexhaustible thermodynamic resources for human beings. From a thermodynamic point of view, any energy conversion systems that receive energy from the sun and/or dissipate energy to the universe are heat engines with photons as the "working fluid" and can be analyzed using the concept of entropy. While entropy analysis provides a particularly convenient way to understand the efficiency limits, it is typically taught in the context of thermodynamic cycles among quasi-equilibrium states and its generalization to solar energy conversion systems running in a continuous and non-equilibrium fashion is not straightforward. In this educational article, we present a few examples to illustrate how the concept of photon entropy, combined with the radiative transfer equation, can be used to analyze the local entropy generation processes and the efficiency limits of different solar energy conversion systems. We provide explicit calculations for the local and total entropy generation rates for simple emitters and absorbers, as well as photovoltaic cells, which can be readily reproduced by students. We further discuss the connection between the entropy generation and the device efficiency, particularly the exact spectral matching condition that is shared by infinite- junction photovoltaic cells and reversible thermoelectric materials to approach their theoretical efficiency limit. * To whom correspondence should be addressed. Email: [email protected] 1 I. Introduction In the context of the radiative energy transfer, the Sun can be approximated as a blackbody at a temperature of 6000 K1, and the outer space is filled with the cosmic microwave background at an effective temperature of 2.7 K.
    [Show full text]
  • AJR Ch6 Thermochemistry.Docx Slide 1 Chapter 6
    Chapter 6: Thermochemistry (Chemical Energy) (Ch6 in Chang, Ch6 in Jespersen) Energy is defined as the capacity to do work, or transfer heat. Work (w) - force (F) applied through a distance. Force - any kind of push or pull on an object. Chemists define work as directed energy change resulting from a process. The SI unit of work is the Joule 1 J = 1 kg m2/s2 (Also the calorie 1 cal = 4.184 J (exactly); and the Nutritional calorie 1 Cal = 1000 cal = 1 kcal. A calorie is the energy needed to increase the temperature of 1 g of water by 1 °C at standard atmospheric pressure. But since this depends on the atmospheric pressure and the starting temperature, there are several different definitions of the “calorie”). AJR Ch6 Thermochemistry.docx Slide 1 There are many different types of Energy: Radiant Energy is energy that comes from the sun (heating the Earth’s surface and the atmosphere). Thermal Energy is the energy associated with the random motion of atoms and molecules. Chemical Energy is stored within the structural units of chemical substances. It is determined by the type and arrangement of the atoms of the substance. Nuclear Energy is the energy stored within the collection of protons and neutrons of an atom. Kinetic Energy is the energy of motion. Chemists usually relate this to molecular and electronic motion and movement. It depends on the mass (m), and speed (v) of an object. ퟏ ke = mv2 ퟐ Potential Energy is due to the position relative to other objects. It is “stored energy” that results from attraction or repulsion (e.g.
    [Show full text]
  • Entropy Is the Only Finitely Observable Invariant
    JOURNAL OF MODERN DYNAMICS WEB SITE: http://www.math.psu.edu/jmd VOLUME 1, NO. 1, 2007, 93–105 ENTROPY IS THE ONLY FINITELY OBSERVABLE INVARIANT DONALD ORNSTEIN AND BENJAMIN WEISS (Communicated by Anatole Katok) ABSTRACT. Our main purpose is to present a surprising new characterization of the Shannon entropy of stationary ergodic processes. We will use two ba- sic concepts: isomorphism of stationary processes and a notion of finite ob- servability, and we will see how one is led, inevitably, to Shannon’s entropy. A function J with values in some metric space, defined on all finite-valued, stationary, ergodic processes is said to be finitely observable (FO) if there is a sequence of functions Sn(x1,x2,...,xn ) that for all processes X converges to X ∞ X J( ) for almost every realization x1 of . It is called an invariant if it re- turns the same value for isomorphic processes. We show that any finitely ob- servable invariant is necessarily a continuous function of the entropy. Several extensions of this result will also be given. 1. INTRODUCTION One of the central concepts in probability is the entropy of a process. It was first introduced in information theory by C. Shannon [S] as a measure of the av- erage informational content of stationary stochastic processes andwas then was carried over by A. Kolmogorov [K] to measure-preserving dynamical systems, and ever since it and various related invariants such as topological entropy have played a major role in the theory of dynamical systems. Our main purpose is to present a surprising new characterization of this in- variant.
    [Show full text]