DOCSLIB.ORG

Thermodynamics in Earth and Planetary Sciences

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Thermodynamics in Earth and Planetary Sciences Thermodynamics in Earth and Planetary Sciences Jibamitra Ganguly Thermodynamics in Earth and Planetary Sciences 123 Prof. Jibamitra Ganguly University of Arizona Dept. Geosciences 1040 E. Fourth St. Tucson AZ 85721-0077 Gould Simpson Bldg. USA [email protected] ISBN: 978-3-540-77305-4 e-ISBN: 978-3-540-77306-1 DOI 10.1007/978-3-540-77306-1 Library of Congress Control Number: 2008930074 c 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper 987654321 springer.com A theory is the more impressive the greater the simplicity of its premises, the more different kind of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts. Albert Einstein Preface When the knowledge is weak and the situation is complicated, thermodynamic relations are really the most powerful Richard Feynman Thermodynamics has played a major role in improving our understanding of natural processes, and would continue to do so for the foreseeable future. In fact, a course in thermodynamics has now become a part of Geosciences curriculum in many In- stitutions despite the fact that a formal thermodynamics course is taught in every other department of physical sciences, and also in departments of Chemical Engi- neering, Materials Sciences and Biological Sciences. The reason thermodynamics is taught in a variety of departments, probably more so than any other subject, is that its principles have wide ranging applications but the teaching of thermodynamics also needs special focus depending on the problems in a particular field. There are numerous books in thermodynamics that have usually been written with particular focus to the problems in the traditional fields of Chemistry, Physics and Engineering. In recent years several books have also been written that empha- sized applications to Geological problems. Thus, one may wonder why there is yet another book in thermodynamics. The primary focus of the books that have been written with Geosciences audience in mind has been chemical thermodynamics or Geohemical thermodynamics. Along with expositions of fundamental principles of thermodynamics, I have tried to address a wide range of problems relating to geo- chemistry, petrology, mineralogy, geophysics and planetary sciences. It is not a fully comprehensive effort, but is a major attempt to develop a core material that should be of interest to people with different specialties in the Earth and Planetary Sciences. The conditions of the systems in the Earth and Planetary Sciences to which ther- modynamics have been applied cover a very large range in pressure-temperature space. For example, the P-T conditions for the processes at the Earth’s surface are 1 bar, 25◦C, whereas those for the processes in the deep interior of the Earth ◦ are at pressures of the order of 106 bars and temperatures of the order of 103 C. The pressures for processes in the solar nebula are 10−3–10−4 bars. The extreme range of conditions encompassed by natural processes requires variety of manipu- lations and approximations that are not readily available in the standard text books vii viii Preface on thermodynamics. Earth scientists have made significant contributions in these areas that have been overlooked in the standard texts since the expected audience of these texts rarely deal with the conditions that Earth scientists have to. I have tried to highlight the contributions of Earth scientists that have made possible meaningful applications of thermodynamics to natural problems. In order to develop a proper appreciation of thermodynamic laws and thermody- namic properties of matter, it is useful to look into their physical picture by relat- ing them to the microscopic descriptions. Furthermore, in geological problems, it is often necessary to extrapolate thermodynamic properties of matter way beyond the conditions at which these have been measured, and also to be able to estimate thermodynamic properties because of lack of adequate data to address a specific problem at hand. These efforts require an understanding of the physical or micro- scopic basis of thermodynamic properties. Thus, I have occasionally digressed to the discussion of thermodynamics from microscopic view points, although the for- mal aspects of the subject of thermodynamics can be completely developed without appealing to the microscopic picture. On the other hand, I have not spent too much effort to discuss how the thermodynamic laws were developed, as there are many excellent books dealing with these topics, but rather focused on exploring the im- plications of these laws after discussing their essential contents. In several cases, however, I have chosen to provide the derivations of equations in considerable de- tail in order to convey a feeling of how thermodynamic relations are manipulated to derive practically useful relations. This book has been an outgrowth of a course on thermodynamics that I have been teaching to graduate students of Earth and Planetary Sciences at the University of Arizona for over a decade. In this course, I have meshed the development of the fundamental principles with applications, mostly to natural problems. This may not be the most logical way of presenting the subject, but I have found it to be an effective way to keep the interest of the students alive, and answer “why am I doing this?” In addition, I have put problems within the text in appropriate places, and in many cases posed the derivation of some standard equations as problems, with hints wherever I felt necessary based on the questions that I have received from my students when they were given these problems to solve. I have tried to write this book in a self-contained way, as much as possible. Thus, the introductory chapter contains concepts from mechanics and quantum chemistry that were used later to develop concepts of thermodynamics and an understand- ing of some of their microscopic basis. The Appendix II contains a summary of some of the mathematical concepts and tools that are commonly used in classical thermodynamics. Selected sections of the book have been reviewed by a number of colleagues: Sumit Chakraborty, Jamie Connolly, Charles Geiger, Ralph Kretz, Luigi Marini, Denis Norton, Giulio Ottonello, Surendra Saxena, Rishi Narayan Singh, Max Tirone and Krishna Vemulapalli. I gratefully acknowledge their help, but take full respon- sibility for the errors that might still be present. In addition, feedbacks from the graduate students, who took my thermodynamics course, have played an important role in improving the clarity of presentation, and catching errors, not all of which were typographical. Preface ix I started writing the book seriously while I was in the Bayerisches Geoinstit¨ut, Bayreuth, and University of Bochum, both in Germany, during my sabbatical leave in 2002–2003 that was generously supported by the Alexender von Humboldt Foun- dation through a research prize (forschungspreis). I gratefully acknowledge the sup- port of the AvH foundation, and the hospitality of the two institutions, especially those of the hosts, Professors Dave Rubie and Sumit Chakraborty. Research grants from the NASA Cosmochemistry program to investigate thermodynamic and ki- netic problems in the planetary systems provided significant incentives to explore planetary problems, and also made my continued involvement in thermodynamics through the period of writing this book easier from a practical standpoint. I am also very grateful for these supports. I hope that this book would be at least partly successful in accomplishing its goal of presenting the subject of thermodynamics in a way that shows its power in the development of quantitative understanding of a wide variety of geological and planetary processes. And finally, as remarked by the noted thermodynamicist, Kenneth Denbigh (1955) Thermodynamics is a subject which needs to be studied not once but several times over at advancing levels October 25, 2007 Jibamitra Ganguly June 7, 2008 Time: 03:49am t1-v1.3 Contents 1 Introduction ................................................... 1 1.1 Nature and Scope of Thermodynamics . .................... 1 1.2 IrreversibleandReversibleProcesses........................ 3 1.3 Thermodynamic Systems, Walls and Variables . ............. 4 1.4 Work................................................... 5 1.5 Stable and Metastable Equilibrium . ........................ 9 1.6 Lattice Vibrations . ................................... 10 1.7 ElectronicConfigurationsandEffectsofCrystalFields........
Load more

Recommended publications
  • Graduate Statistical Mechanics
    Graduate Statistical Mechanics Leon Hostetler December 16, 2018 Version 0.5 Contents Preface v 1 The Statistical Basis of Thermodynamics1 1.1 Counting States................................. 1 1.2 Connecting to Thermodynamics........................ 4 1.3 Intensive and Extensive Parameters ..................... 7 1.4 Averages..................................... 8 1.5 Summary: The Statistical Basis of Thermodynamics............ 9 2 Ensembles and Classical Phase Space 13 2.1 Classical Phase Space ............................. 13 2.2 Liouville's Theorem .............................. 14 2.3 Microcanonical Ensemble ........................... 16 2.4 Canonical Ensemble .............................. 20 2.5 Grand Canonical Ensemble .......................... 29 2.6 Summary: Ensembles and Classical Phase Space .............. 32 3 Thermodynamic Relations 37 3.1 Thermodynamic Potentials .......................... 37 3.2 Fluctuations................................... 44 3.3 Thermodynamic Response Functions..................... 48 3.4 Minimizing and Maximizing Thermodynamic Potentials.......... 49 3.5 Summary: Thermodynamic Relations .................... 51 4 Quantum Statistics 55 4.1 The Density Matrix .............................. 55 4.2 Indistinguishable Particles........................... 57 4.3 Thermodynamic Properties .......................... 59 4.4 Chemical Potential............................... 63 4.5 Summary: Quantum Statistics ........................ 65 5 Boltzmann Gases 67 5.1 Kinetic Theory................................. 68
    [Show full text]
  • Maxwell Relations
    MAXWELLRELATIONS 7.I THE MAXWELL RELATIONS In Section 3.6 we observedthat quantities such as the isothermal compressibility, the coefficientof thermal expansion,and the molar heat capacities describe properties of physical interest. Each of these is essentiallya derivativeQx/0Y)r.r..,. in which the variablesare either extensiveor intensive thermodynaini'cparameters. with a wide range of extensive and intensive parametersfrom which to choose, in general systems,the numberof suchpossible derivatives is immense.But thire are azu azu ASAV AVAS (7.1) -tI aP\ | AT\ as),.*,.*,,...: \av)s.N,.&, (7.2) This relation is the prototype of a whole class of similar equalities known as the Maxwell relations. These relations arise from the equality of the mixed partial derivatives of the fundamental relation expressed in any of the various possible alternative representations. 181 182 Maxwell Relations Given a particular thermodynamicpotential, expressedin terms of its (l + 1) natural variables,there are t(t + I)/2 separatepairs of mixed second derivatives.Thus each potential yields t(t + l)/2 Maxwell rela- tions. For a single-componentsimple systemthe internal energyis a function : of three variables(t 2), and the three [: (2 . 3)/2] -arUTaSpurs of mixed second derivatives are A2U/ASAV : AzU/AV AS, AN : A2U / AN AS, and 02(J / AVA N : A2U / AN 0V. Thecompleteser of Maxwell relations for a single-componentsimple systemis given in the following listing, in which the first column states the potential from which the ar\ U S,V I -|r| aP\ \ M)',*: ,s/,,' (7.3) dU: TdS- PdV + p"dN ,S,N (!t\ (4\ (7.4) \ dNls.r, \ ds/r,r,o V,N _/ii\ (!L\ (7.5) \0Nls.v \0vls.x UITI: F T,V ('*),,.: (!t\ (7.6) \0Tlv.p dF: -SdT - PdV + p,dN T,N -\/ as\ a*) ,.,: (!"*),.
    [Show full text]
  • Thermodynamics, Mnemonic Matrices and Generalized Inverses
    ANZIAMJ. 48(2007), 493-501 THERMODYNAMICS, MNEMONIC MATRICES AND GENERALIZED INVERSES R. B. LEIPNIK1 and C. E. M. PEARCE3 2 (Received 8 August, 2006) Abstract We present an alternative matrix mnemonic for the basic equations of simple thermody- namics. When normalized, this permits an explicit generalized inverse, allowing inversion • of the mechanical and chemical thermodynamic equations. As an application, the natural variables S,V, P and T are derived from the four energies E (internal), F (free), G (Gibbs) and H (enthalpy). 2000 Mathematics subject classification: primary 80A10. Keywords and phrases: thermodynamics, matrix mnemonics, generalized inverses. 1. Introduction The large number of state variables (eight and more) in simple thermodynamics mo- tivated Born's geometrical mnemonic, the thermodynamic square [2, pp. 117-121]. Koenig [6] elaborated on the idea and provided geometrizations of other thermody- namic relationships. A number of these geometrizations have been drawn together by Fox [4] in the thermodynamic cuboctahedron. Thermodynamic squares have also been assembled in the thermodynamic cube by Pate [9]. In this paper we explore another mnemonic which has been found useful for teaching mechanical and chemical thermodynamics at the University of California at Santa Barbara and which is based on matrix representations. This couples the mnemonics with providing a tool for algebraic analysis. In Sections 4 and 5 we derive mathematical consequences of the mnemonic matrix formulation. The basic thermodynamic concepts, besides pressure P, absolute temperature T and volume V are internal energy E, free energy F and entropy S. Useful additions '(Deceased October 10, 2006), Department of Mathematics, UCSB, Ca 93106-3080, USA 2School of Mathematical Sciences, University of Adelaide, Australia 5005; email: [email protected].
    [Show full text]
  • Thermodynamics of Materials
    314: Thermodynamics of Materials L. Lauhon, K. R. Shull March 24, 2021 Contents 1 314: Thermodynamics of Materials4 2 Introduction5 3 Big Ideas of Thermo5 3.1 Classification of Systems....................... 5 3.2 State Variables............................. 7 3.3 Process Variables ........................... 7 3.3.1 Work Done by an External Force.............. 8 3.3.2 Work Done by an Applied Pressure ............ 9 3.4 Extensive and Intensive Props. ................... 9 4 The Laws of Thermodynamics 11 4.1 First Law................................ 11 4.2 Second Law .............................. 12 4.2.1 Reversible and Irreversible Processes ........... 13 4.2.2 Entropy and Heat....................... 13 4.3 Third Law ............................... 14 4.4 Differential Quantities ........................ 15 5 Thermodynamic Variables 17 5.1 Enthalpy................................ 17 5.2 Helmholtz Free Energy ....................... 18 5.3 Gibbs Free Energy .......................... 18 5.4 Other Material Properties ...................... 19 5.4.1 Volume thermal expansion coefficient........... 19 5.4.2 Isothermal Compressibility................. 19 5.4.3 Heat Capacity......................... 19 5.5 Coefficient Relations ......................... 20 5.5.1 Internal Energy........................ 23 1 CONTENTS CONTENTS 5.5.2 Enthalpy............................ 23 5.5.3 Helmholtz Free Energy ................... 23 5.5.4 Gibbs Free Energy ...................... 23 5.6 Equation of State ........................... 23 5.6.1 Expression for dS ....................... 23 5.6.2 Expression for dV ....................... 24 5.6.3 Relationship between CP and CV . 24 6 The Ideal Gas 25 6.1 Thermal Expansion Coefficient ................... 25 6.2 Compressibility............................ 26 6.3 Internal Energy ............................ 26 6.4 Specific Heat.............................. 27 6.5 Examples................................ 27 6.5.1 Free expansion of an ideal gas ............... 27 6.5.2 Isothermal Compression of an Ideal Gas.........
    [Show full text]
  • Icnl-19Q2-P2
    Special Section on Sir J.C. Bose 160th Anniversary Celebration Presentations 1858-1937 Sir J.C. Bose 160th Anniversary Celebration on 17th Feb 2019 at Bangalore IEEE India Info. Vol. 14 No. 2 Apr - Jun 2019 Page 41 Guest Editor Message Sir Jagadish Chandra Bose is a physicist, biologist, biophysicist, botanist and archaeologist. He pioneered plant science, and laid the foundations of experimental science in the Indian subcontinent. He proved by experimentation that both animals and plants share much in common. He demonstrated that plants are also sensitive to heat, cold, light, noise and various other external stimuli. It is widely considered that J.C. Bose was at least 60 years ahead of his time. In 1895, Sir Jagadish Chandra Bose first demonstrated in Presidency College, Calcutta, India, transmission and reception of electromagnetic waves at 60 GHz, over 23 meters distance, through two intervening walls by remotely ringing a bell and detonating gunpowder. For his communication system, Bose pioneered in development of entire millimeter-wave components like a spark-gap transmitter, coherer, dielectric lens, polarizer, horn antenna, and cylindrical diffraction grating. This is the first millimeter-wave communication system in the world, developed about 125 years ago. This is the oldest Milestone achievement from the Asian continent. Bose's experimental work on millimeter-band microwave radio was commemorated as an IEEE Milestone on 14th September 2012 and a plaque in this regard may be viewed in the main corridor of the Acharya Jagadish Chandra Bose Auditorium in the Main Building of Presidency College, Kolkata, India. IEEE celebrated the 160th anniversary of Sir Jagadish Chandra Bose by reflecting on his life and works through eminent speakers compassionately projecting his work to 150 plus IEEE members and engineers on Sunday, 17th February 2019 at the landmark World Trade Center Auditorium in Bengaluru, India.
    [Show full text]
  • Applied Thermodynamics: Software Solutions Part-III (Refrigeration Cycles, Air Compressor, Thermodynamic Relations)
    Dr. M. Thirumaleshwar Applied Thermodynamics: Software Solutions Part-III (Refrigeration cycles, Air compressor, Thermodynamic relations) 2 Download free eBooks at bookboon.com Applied Thermodynamics: Software Solutions: Part-III 1st edition © 2014 Dr. M. Thirumaleshwar & bookboon.com ISBN 978-87-403-0753-5 3 Download free eBooks at bookboon.com Applied Thermodynamics: Software Solutions: Part-III Contents Contents Dedication Part I Preface Part I About the Author Part I About the Software used Part I To the Student Part I 360° How to use this Book? Part I 1 Gas Power Cycles Part I thinking 1.1 Definitions, Statements and Formulas360° used[1-6]: Part I . 1.2 Problems on Otto cycle (or, constant volume cycle): Part I 1.3 Problems on Diesel cycle (or, constantthinking pressure cycle): Part I 1.4 Problems on Dual cycle (or, limited pressure cycle): . Part I 1.5 Problems on Stirling cycle: Part I 1.6 References: Part I 360° thinking . 360° thinking. Discover the truth at www.deloitte.ca/careers Discover the truth at www.deloitte.ca/careers © Deloitte & Touche LLP and affiliated entities. Discover the truth at www.deloitte.ca/careers © Deloitte & Touche LLP and affiliated entities. © Deloitte & Touche LLP and affiliated entities. Discover the truth4 at www.deloitte.ca/careersClick on the ad to read more Download free eBooks at bookboon.com © Deloitte & Touche LLP and affiliated entities. Applied Thermodynamics: Software Solutions: Part-III Contents 2 Cycles for Gas Turbines and Jet propulsion Part II 2.1 Definitions, Statements and Formulas
    [Show full text]
  • Maxwell Relations
    Maxwell relations Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. ese relations are named for the nineteenth- century physicist James Clerk Maxwell. Contents Equations The four most common Maxwell relations Derivation Derivation based on Jacobians General Maxwell relationships See also Equations Flow chart showing the paths between the Maxwell relations. P: e structure of Maxwell relations is a pressure, T: temperature, V: volume, S: entropy, α: coefficient of statement of equality among the second thermal expansion, κ: compressibility, CV: heat capacity at derivatives for continuous functions. It constant volume, CP: heat capacity at constant pressure. follows directly from the fact that the order of differentiation of an analytic function of two variables is irrelevant (Schwarz theorem). In the case of Maxwell relations the function considered is a thermodynamic potential and xi and xj are two different natural variables for that potential: Schwarz' theorem (general) where the partial derivatives are taken with all other natural variables held constant. It is seen that for every thermodynamic potential there are n(n − 1)/2 possible Maxwell relations where n is the number of natural variables for that potential. e substantial increase in the entropy will be verified according to the relations satisfied by the laws of thermodynamics e four most common Maxwell relations e four most common Maxwell relations are the equalities of the second derivatives of each of the four thermodynamic potentials, with respect to their thermal natural variable (temperature T; or entropy S) and their mechanical natural variable (pressure P; or volume V): Maxwell's relations (common) where the potentials as functions of their natural thermal and mechanical variables are the internal energy U(S, V), enthalpy H(S, P), Helmholtz free energy F(T, V) and Gibbs free energy G(T, P).
    [Show full text]
  • Thermodynamic Potentials
    Thermodynamic Potentials a.cyclohexane.molecule March 2016 We work with four key potentials in thermodynamics: the internal energy U, the enthalpy H ≡ U +PV , the Helmholtz potential F ≡ U −TS, and the Gibbs potential G ≡ U + PV − TS = H − TS. dU = T dS − P dV dH = dU + P dV − V dP = T dS − P dV + P dV − V dP = T dS − V dP dF = dU − T dS − SdT = T dS − P dV − T dS − SdT = −SdT − P dV dG = dH − T dS − SdT = T dS − V dP − T dS − SdT = −SdT − V dP (We are most interested in changes in these potentials|the zeroes of these potentials are not defined, and absolute values for these quantities are thus of no significance.) We only see T being paired with S and V being paired with P , suggesting some relationship between these linked variables, which we call conjugate variables. Conjugate variables represent generalized-force{generalized-displacement pairs, the product of each pair having units of energy. One member of each pair is intensive; the other is extensive. The most common of these pairs are P and V , and T and S, but other pairs include f and L, and γ and A. Where relevant, they appear in the expression for dU and the differentials of other thermodynamic potentials: elastic rod: dU = T dS + fdL liquid film: dU = T dS + γdA These potentials identify the availability of free energy in different conditions. Consider a system in contact with its surroundings at a temperature T0 and a pressure P0. From the first and second laws, dU = δq + δw = δq + δwnon-exp − P0 dV dS ≥ δq=T0 () δq ≤ T0 dS where we have distinguished expansive from non-expansive work.
    [Show full text]
  • The Thermoelastic Square
    THE THERMOELASTIC SQUARE A mnemonic for remembering thermodynamic identities The state of a material is the collection of variables such as stress, strain, temperature, entropy. A variable is a state variable if its integral over any closed path in the other state variables is zero. Clearly, this definition is circular unless we assume there exists a minimal set postulated state variables. For example, the zeroth law of thermodynamics postulates the existence of a temperature. The pressure is usually postulated to be a state variable. For typical applications involving inviscid fluids, only these two state variables — temperature and pressure — are needed in order to determine the other state variables. For solids, more state variables are needed. The state postulate of thermodynamics says that the minimum number of state variables needed to determine all other state variables is equal to one plus the number of quasistatic work modes. For a gas, there is only one work mode, namely pdV where pressure p works to produce a volume change dV. For a more general material, there are a total of six work modes, corresponding to the six independent components of stress causing changes in the six components of strain. In addition to the six state variables that characterize stress or strain, the state postulate says there must be one more variable such as temperature or entropy that characterizes the thermal state of the material. Suppose we take strain and entropy to be our primitive state variables. Such a material is said to be thermoelastic, and the first law of thermodynamics implies that the specific stress tensor (i.e., stress divided by density) is given by a derivative of the internal energy function with respect to strain, while the temperature is the derivative of energy with respect to entropy.
    [Show full text]
  • THE]THERMODORM, a Mnemonic Octahedron of Thermodynamics
    [jn a classroom THE]THERMODORM, A Mnemonic Octahedron of Thermodynamics k (8) d(- PV) =-SdT - PdV - l NidJJi = dU[T,µi] A. F. GANGI, N. E. LAMPING, AND P. T. i=l EUBANK and Texas A&M University k (9) College Station, Texas 77843 O =- SdT + VdP - l NidJJi • dU[T,P,JJi ] , i=l The development, use, and construction of the the last relation is also called the Gibbs-Duhem THERMODORM*1, a mnemonic octahedron in equation. U, H, A, G, TS-PV, TS, and -PV will be termed the energy functions with S V P T terms of the energy functions of thermodynamics ' ' ' ' and their variables is described. This easily con­ N1 and µ.1 as their independent variables. The structed, pocket-sized device provides at a glance natural variables of U are S, V, and N1 while the complete set of Maxwell relations and energy those of G are T, P, and Ni, etc.6 function derivatives for k component systems. A total of 7 (k + 2) Maxwell equations result from cross differentiation of Equations (2-8) of THEORETICAL BACKGROUND the type a2u _ a2u For a homogeneous phase of k components in asav = avas ( 10) an open system a fundamental equation of ther­ to yield, for example, modynamics2,3 is given by the expression for the internal energy of the system : H: )v N = - ff ls N ( lll ' i ' i U • U(S,V,Ni); i = 1,2, . .. , k (1) gross differentiation of Equation (9) yields re­ The total differential of the internal energy is: lations of the type k dU • TdS - PdV + l JJidN.
    [Show full text]
  • 72273 2 En Bookfrontmatter 1..33
    Springer Textbooks in Earth Sciences, Geography and Environment The Springer Textbooks series publishes a broad portfolio of textbooks on Earth Sciences, Geography and Environmental Science. Springer textbooks provide comprehensive introductions as well as in-depth knowledge for advanced studies. A clear, reader-friendly layout and features such as end-of-chapter summaries, work examples, exercises, and glossaries help the reader to access the subject. Springer textbooks are essential for students, researchers and applied scientists. More information about this series at http://www.springer.com/series/15201 Jibamitra Ganguly Thermodynamics in Earth and Planetary Sciences Second Edition 123 Jibamitra Ganguly Department of Geosciences University of Arizona Tucson, AZ, USA ISSN 2510-1307 ISSN 2510-1315 (electronic) Springer Textbooks in Earth Sciences, Geography and Environment ISBN 978-3-030-20878-3 ISBN 978-3-030-20879-0 (eBook) https://doi.org/10.1007/978-3-030-20879-0 1st edition: © Springer-Verlag Berlin Heidelberg 2008 2nd edition: © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
    [Show full text]
  • Sir Jagdish Chandra Bose, James Clerk Maxwell and There On….. Dr
    Sir Jagdish Chandra Bose, James Clerk Maxwell and there on….. Dr. S. Pal Dr. DS Kothari DRDO Chair Former: Vice Chancellor, DIAT, Pune Distinguished Scientist and Senior Advisor SATNAV-ISRO Abstract IEEE India Council, Bangalore & Bombay sections arranged lectures on Sunday 17th Feb 2019, on the topic “Celebrating Sir Jagdish Chandra Bose”; I had an opportunity to deliver a talk on: Sir. Jagdish Chandra Bose, Maxwell and there on. There is quite a bit commonality between Acharya Jagdish Chandra Bose and Maxwell. Both of were “Polymath”, who influenced the science of that era, in their own way, while their work & theories are quite relevant even today. Due to the efforts of some dedicated Indian Scientists in US, IEEE in 2012 recognized Sir Jagdish Chandra Bose as one of the founding fathers of RF/EM. The talk mostly concentrated on Acharya Jagdish Chandra Bose, his work and impression of his contemporary, workers and friends like Swami Vivekananda, Gurudeo Tagore and his students on his life and work. Similarly, a brief is given on James Clerk Maxwell and his work on various topics with more emphasis on EM equations. Acharya (Sir) Jagdish Chandra Bose CSI, CIE, FRS, IPA (Nov 1858 – Nov 1937) CSI-Companion of Star of India CIE-Companion of the Indian Empire KB-Knight Bachelor Acharya Jagdish Chandra Bose born on 30 Nov 1858, at Mymen Singh (now in Bangladesh), was an Indian Plant Physiologist & Physicist of great repute. He was a Polymath (Physicist, Biophysicist, Botanist and Archaeologist). He was also a science & science fiction writer in Bengali, in early British India.
    [Show full text]