Müller I. A history of thermodynamics. The doctrine of energy and entropy (Müller I. A history of thermodynamics. The doctrine of energy and entropy.pdf)

A History of ThermodynamicsIngo MüllerA Historyof ThermodynamicsThe Doctrine of Energy and EntropyABCProfessor Dr. Dr.h.c. Ingo MüllerThermodynamikTechnische Universität Berlin10623 BerlinGermanyE-mail: ingo.mueller@alumni.tu-berlin.deLibrary of Congress Control Number: 2006933419ISBN-10 3-540-46226-0 Springer Berlin Heidelberg New YorkISBN-13 978-3-540-46226-2 Springer Berlin Heidelberg New YorkThis work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, 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 publicationor 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 areliable for prosecution under the German Copyright Law.Springer is a part of Springer Science+Business Mediaspringer.comc Springer-Verlag Berlin Heidelberg 2007The 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 lawsand regulations and therefore free for general use.Typesetting: by the author and techbooks using a Springer LATEX macro packageCover design: design & production GmbH, HeidelbergPrinted on acid-free paperSPIN: 1155378689/techbooks543210PrefaceThe most exciting and significant episode of scientific progress is thedevelopment of thermodynamics and electrodynamics in the 19th centuryand early 20th century. The nature of heat and temperature was recognized,the conservation of energy was discovered, and the realization that massand energy are equivalent provided a new fuel, – and unlimited power.Much of this occurred in unison with the rapid technological advanceprovided by the steam engine, the electric motor, internal combustionengines, refrigeration and the rectification processes of the chemicalindustry.

The availability of cheap power and cheap fuel has had its impacton society: Populations grew, the standard of living increased, the environment became clean, traffic became easy, and life expectancy was raised.Knowledge fairly exploded. The western countries, where all this happened,gained in power and influence, and western culture – scientific culture –spread across the globe, and is still spreading.At the same time, thermodynamics recognized the stochastic andprobabilistic aspect of natural processes. It turned out that the doctrine ofenergy and entropy rules the world; the first ingredient – energy – isdeterministic, as it were, and the second – entropy – favours randomness.Both tendencies compete, and they find the precarious balance needed forstability and change alike.Philosophy, – traditional philosophy – could not keep up with the grandexpansion of knowledge.

It gave up and let itself be pushed into insignificance. The word came up about two cultures: One, which is mostly loosewords and subjective thinking – in the conventional style –, and scientificculture, which uses mathematics and achieves tangible results.Indeed, the concepts of the scientific culture are most precisely expressedmathematically, and that circumstance makes them accessible to only aminority: Those who do not shy away from mathematics. The fact hasforced me into a two-tiered presentation. One tier is narrative and largelydevoid of formulae, the other one is mathematical and mostly relegated toInserts. And while I do not recommend to skip over the inserts, I do believethat that is possible – at least for a first reading.

In that way a person mayacquire a quick appreciation of the exciting concepts and the colourfulpersonages to whom we owe our prosperity and – in all probability – ourlives.Berlin,July 2006Ingo MüllerContents1Temperature ....................................................................................... 12Energy .................................................................................................9Caloric Theory......................................................................................9Benjamin Thompson, Graf von Rumford...........................................10Robert Julius Mayer ...........................................................................13James Prescott Joule ...........................................................................21Hermann Ludwig Ferdinand (von) Helmholtz ...................................24Electro-magnetic Energy ....................................................................29Albert Einstein....................................................................................35Lorentz Transformation......................................................................37E = m c2 .............................................................................................40Annus Mirabilis..................................................................................433Entropy.............................................................................................

47Heat Engines ..................................................................................... 47Nicolas Léonard Sadi Carnot............................................................. 52Benoît Pierre Émile Clapeyron.......................................................... 55William Thomson, Lord Kelvin ........................................................ 57Rudolf Julius Emmanuel Clausius..................................................... 59Second law of Thermodynamics ....................................................... 65Exploitation of the Second Law ........................................................

68Terroristic Nimbus of Entropy and Second Law............................... 72Modern Version of Zeroth, First and Second Laws ........................... 73What is Entropy? ............................................................................... 774Entropy as S = k ln W.......................................................................79Renaissance of the Atom in Chemistry ..............................................80Elementary Kinetic Theory of Gases .................................................82James Clerk Maxwell .........................................................................87The Boltzmann Factor. Equipartition .................................................92Ludwig Eduard Boltzmann.................................................................94VIIIContentsReversibility and Recurrence .........................................................103Maxwell Demon ..............................................................................

107Boltzmann and Philosophy............................................................. 108Kinetic Theory of Rubber............................................................... 111Gibbs´s Statistical Mechanics......................................................... 117Other Extrapolations. Information.................................................. 1235Chemical Potentials ....................................................................... 127Josiah Willard Gibbs .......................................................................

128Entropy of Mixing. Gibbs Paradox ................................................. 129Homogeneity of Gibbs Free Energy for a Single Body................... 131Gibbs Phase Rule............................................................................. 133Law of Mass Action .......................................................................

134Semi-permeable Membranes ........................................................... 136On Definition and Measurement of Chemical Potentials................ 137Osmosis ........................................................................................... 139Raoult´s Law ................................................................................... 142Alternatives of the Growth of Entropy............................................

146Entropy and Energy in Competition................................................ 148Phase Diagrams ............................................................................... 149Law of Mass Action for Ideal Mixtures .......................................... 152Fritz Haber....................................................................................... 156Socio-thermodynamics .................................................................... 1596Third law of Thermodynamics ..................................................... 165Capitulation of Entropy ...................................................................

165Inaccessibility of Absolute Zero...................................................... 167Diamond and Graphite .................................................................... 168Hermann Walter Nernst................................................................... 170Liquifying Gases .............................................................................

172Johannes Diderik Van Der Waals.................................................... 176Helium ............................................................................................. 182Adiabatic Demagnetisation ............................................................. 185He3-He4 Cryostats ............................................................................ 186Entropy of Ideal Gases ....................................................................

187Classical Limit................................................................................. 191Full Degeneration and Bose-Einstein Condensation ....................... 192Satyendra Nath Bose ....................................................................... 194Bosons and Fermions. Transition probabilities ............................... 1957Radiation Thermodynamics...........................................................197Black Bodies and Cavity Radiation................................................. 198Violet Catastrophy...........................................................................