Planck's Quantum Theory of Ideal
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
5Th World Congress on Physics July 17-18, 2018 Prague, Czech Republic
Štefan Zajac, J Laser Opt Photonics 2018, Volume:5 DOI: 10.4172/2469-410X-C2-025 5th World Congress on Physics July 17-18, 2018 Prague, Czech Republic Štefan Zajac Czech Technical University, Czech Republic Physics and Prague hysics has been cultivated in Prague since at least 1348, when a University was founded here by Emperor Charles IV. At Pthe beginning the main emphasis was on Astronomy. First astronomers Křišťan from Prachatice (1360 – 1439) and Jan Ondřejov Šindel (1375 – 1456) in co-operation with clockmaker Mikuláš of Kadaň around 1410 had designed and installed the astronomical clock placed on the Old Town Hall tower in Prague. Astronomer and Chief Physician Tadeuš Hájek of Hájek (1525-1600) had inluenced Emperor Rudolph II to invite Tycho Brahe (1546 – 1601) and Johannes Kepler (1571 – 1630) to come to Prague where the first two of his laws of planetary motion have been formulated. Jan Marcus Marci of Kronland (1595 – 1667), a physicist, physician and rector of Prague University made original research in mechanics (impact of bodies) and optics (diffraction of light, explanation of rainbow). In the middle of the 18th century at the Clementinum, the Jesuit College, physicist Josef Stepling (1716 -1778) and his successors at the Prague Faculty of Philosophy promoted Newtonian Physics . Christian Doppler (1803 – 1853) as professor at Prague Polytechnic in 1842 published important phenomenon of the frequency shift due to the velocity of the source of waves relative to the observer. His younger colleague Bohumil Kučera (1874 – 1921) had started pioneering research in radioactivity and had inspired professor Jaroslav Heyrovský (1890 – 1967) to develop polarography for which he in 1959 earned Nobel Prize for chemistry. -
Redalyc.On the Sackur-Tetrode Equation in an Expanding Universe
Revista Mexicana de Física ISSN: 0035-001X [email protected] Sociedad Mexicana de Física A.C. México Pereira, S.H. On the Sackur-Tetrode equation in an expanding universe Revista Mexicana de Física, vol. 57, núm. 1, junio, 2011, pp. 11-15 Sociedad Mexicana de Física A.C. Distrito Federal, México Available in: http://www.redalyc.org/articulo.oa?id=57024209002 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative ENSENANZA˜ REVISTA MEXICANA DE FISICA´ E 57 (1) 11–15 JUNIO 2011 On the Sackur-Tetrode equation in an expanding universe S.H. Pereira Universidade Federal de Itajuba,´ Campus Itabira, Rua Sao˜ Paulo, 377 – 35900-373, Itabira, MG, Brazil, e-mail: [email protected] Recibido el 5 de abril de 2010; aceptado el 2 de febrero de 2011 In this work we investigate the thermodynamic properties satisfied by an expanding universe filled with a monoatomic ideal gas. We show that the equations for the energy density, entropy density and chemical potential remain the same of an ideal gas confined to a constant volume V . In particular the Sackur-Tetrode equation for the entropy of the ideal gas is also valid in the case of an expanding universe, provided that the constant value that represents the current entropy of the universe is appropriately chosen. Keywords: Expanding universe; ideal gas; Sackur-Tetrode equation. En el presente trabajo investigamos las propriedades termodinamicas´ que son satisfechas por un universo en expansion,´ el cual es lleno por un gas ideal monoatomico.´ Se prueba que las ecuaciones para la densidad de la energ´ıa, la densidad de la entrop´ıa y el potencial qu´ımico son las mismas que las de un gas ideal, el cual se encuentra confinado en un volumen V. -
August/September 2009
August-September 2009 Volume 18, No. 8 TM www.aps.org/publications/apsnews PhysicsQuest APS NEWS Goes to Kenya A PublicAtion of the AmericAn PhysicAl society • www.aps.org/PublicAtions/apsnews See page 5 APS Awards Three Hildred Blewett Scholarships Presidents Two This year APS has announced electrical properties. three women as recipients of the “It was amazing how many ses- M. Hildred Blewett scholarship. sions there were on graphene at the Chosen by the Committee on March Meeting,” Guikema said. the Status of Women in Physics, She plans to use funds from the three are Janice Guikema at the Blewett Scholarship to further Johns Hopkins University, Marija research the feasibility of using Nikolic-Jaric at the University of graphene as a sensitive magnetic Manitoba, and Klejda Bega at Co- detector. She said that graphene has lumbia University. a lot of potential for use as a Hall Each year the committee se- effect detector to detect nanoscale lects women who are returning to particles and map out magnetic their research careers that had been Janice guikema structures. Currently she is continu- interrupted for family or other rea- ing to look for ways to make the sons. The scholarship is a one-year as a second-time recipient of the material as sensitive as possible. grant of up to $45,000 that can be Blewett Scholarship. She currently In addition she will use scanning used towards a wide range of ne- has a part-time research position at probe microscopy to further ex- cessities, including equipment pro- Johns Hopkins University, where plore the nature of graphene. -
Cesta Ke Hvězdám I Do Nitra Molekul
Matematický ústav Akademie věd Èeské republiky Cesta ke hvězdám i do nitra molekul Osudy Vladim´ıra Vanda, konstruktéra počítačů Alena Solcovˇ ´a, Michal Kˇr´ıˇzek Praha 2011 Recenzenti RNDr. Pavla Pavlíková, Ph. D. RNDr. Václav Vopravil Vydal Matematický ústav AV ÈR, Praha Sazbu programem TEX pøipravil Michal Křížek c Alena ©olcová, Michal Křížek Obálka Pavel Křížek Vydání 1., Praha 2011 ISBN 978-80-85823-56-1 Věnováno prof. Vladimíru Vandovi ke 100. výročí jeho narození. 4 A. ©olcová, M. Křížek: Cesta ke hvězdám i do nitra molekul Obsah Pøedmluva : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1. Úvod : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :9 2. Období dospívání : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2.1. ®ivot na Ukrajině : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2.2. Rodina a dětství : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2.3. Studium na Univerzitě Karlově : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 2.4. Vzpomínka Zdeňka Kopala : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 21 3. Vladimír Vand v Říši hvězd : : : : : : : : : : : : : : : : : : : : : : : : : : -
MOTION MOUNTAIN the Adventure of Physics – Vol.Iv Quantum Theory: the Smallest Change
Christoph Schiller MOTION MOUNTAIN the adventure of physics – vol.iv quantum theory: the smallest change www.motionmountain.net Christoph Schiller Motion Mountain The Adventure of Physics Volume IV Quantum Theory: The Smallest Change Edition 24.1, available as free pdf at www.motionmountain.net Editio vicesima tertia. Proprietas scriptoris © Christophori Schiller secundo anno Olympiadis vicesimae nonae. Omnia proprietatis iura reservantur et vindicantur. Imitatio prohibita sine auctoris permissione. Non licet pecuniam expetere pro aliquo, quod partem horum verborum continet; liber pro omnibus semper gratuitus erat et manet. Twenty-third edition, ISBN 978-300-021946-7. Copyright © 2009 by Christoph Schiller, the second year of the 29th Olympiad. This pdf file is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Germany Licence,whosefulltextcanbefoundonthewebsite creativecommons.org/licenses/by-nc-nd/3.0/de, with the additional restriction that reproduction, distribution and use, in whole or in part, in any product or service, be it commercial or not, is not allowed without the written consent of the copyright owner. The pdf file was and remains free for everybody to read, store and print for personal use, and to distribute electronically, but only in unmodified form and at no charge. To Britta, Esther and Justus Aaron τῷ ἐμοὶ δαὶμονι Die Menschen stärken, die Sachen klären. PREFACE Primum movere, deinde docere.* Antiquity “ ” Motion Mountain – The Adventure of Physics pdf file available free of charg This book is written for anybody who is curious about nature and motion. Have you ever asked: Why do people, animals, things, images and space move? The answer leads to many adventures; this volume presents those due the discovery that there is a smallest change in nature. -
TERMODYNAMIK En Kort Historik Christoffer Norberg
ISRN LUTMDN/TMHP-08/3032-SE ISSN 0282-1990 Institutionen f¨or Energivetenskaper TERMODYNAMIK en kort historik Christoffer Norberg Joules skovelanordning fr˚an 1845/7 f¨or att best¨amma den mekaniska v¨armeekvivalenten. Phil. Trans. Roy. Soc. 140 (1850). januari 2008 F¨orord Denna skrift g¨or inga anspr˚ak p˚aatt vara komplett eller utt¨ommande. D¨aremot har jag i m¨ojligaste m˚an f¨ors¨okt vara korrekt n¨ar det g¨aller ˚artal, biografiska data och prioritet av originalarbeten. F¨or en mer utt¨ommande beskrivning (fram till 1800-talets slut) re- kommenderas From Watt to Clausius av Donald Cardwell ([5]). Kommentarer och f¨orslag till korrigeringar emottages tacksamt. Portr¨att ¨ar huvudsakligen h¨amtade fr˚an Internet samt [2, 6, 25, 28, 20, 27], biografiska data v¨asentligen ur [1, 28, 7, 12, 21, 26, 30] och originalreferenser mestadels ur bibliotekss¨okningar, tillg¨angliga tidskrifter inom LU-n¨atet samt [23, 30]. 8 januari 20081 Christoffer Norberg Tel. 046-2228606 Christoff[email protected] Levnads˚ar f¨or 35 pionj¨arer inom termodynamikens historiska utveckling. Tjocka linjer motsvarar ˚aldern 20–65 ˚ar. “But although, as a matter of history, statistical mechanics owes its origin to investigations in thermodynamics, it seems eminently worthy of an independent development, both on account of the elegance and simplicity of its principles, and because it yields new results and places old truths in a new light in departments quite outside of thermodynamics.” Willard Gibbs 1Sedan tryckningen fr˚an januari 2008 har det gjorts ett par uppdateringar av biografiska data, liksom sm¨arre justeringar och till¨agg i texten samt i den bibliografiska delen; 15 december 2013. -
Paul Ehrenfest: De Leidse Onderzoekschool Van Een Fysicus in Diaspora
Paul Ehrenfest: de Leidse onderzoekschool van een fysicus in diaspora He was […] the best teacher in our profession Albert Einstein Eind augustus 1932 ontving Philip Idenburg, secretaris van het curatorium van de Leidse universiteit, een verontrustende brief. De schrijver van het epistel was Albert Einstein, het onderwerp de geestesgesteldheid van de Leidse hoogleraar Paul Ehrenfest. Einstein sprak openlijk zijn zorg uit over Ehrenfest, die naar zijn zeggen gebukt ging onder zware depressies en zou spelen met de gedachte aan zelfmoord. Einstein drong krachtig aan op snelle maatregelen. De oorzaak van Ehrenfests gemoedstoestand moest volgens Einstein gezocht worden in de stormachtige ontwikkelingen binnen de theoretische natuurkunde, Ehrenfests vakgebied. De nieuwe opvattingen karakteriseerde Einstein als ‘heterogeen, verwarrend en logisch onbevredigend, maar door de feiten afgedwongen.’ In deze chaotische situatie was het een theoretisch natuurkundige niet langer mogelijk het vakgebied in zijn geheel te beheersen en aldus als ‘leider en wegwijzer’ te dienen voor de jonge generatie onderzoekers. Voor een veeleisend en gewetensvol leraar als Ehrenfest was deze toestand eenvoudigweg ondraaglijk. Volgens Einstein bestond er maar één uitweg uit dit dilemma: de eventueel tijdelijke aanstelling van een tweede theoretisch natuurkundige. Wellicht zou na een jaar of tien de situatie in de natuurkunde weer genormaliseerd zijn. Hij wees er daarnaast op dat een verdeling van taken in de experimentele natuurkunde reeds gebruikelijk was. Idenburg reageerde voortvarend. Maar ondanks de steun van het College van Curatoren slaagde hij er niet in het gewenste te bewerkstelligen. Het ministerie weigerde extra geld uit te trekken voor de Leidse natuurkunde. Ruim een jaar later werden Einsteins angstige vermoedens bewaarheid. -
On the 100Th Anniversary of the Sackur–Tetrode Equation
On the 100th Anniversary of the Sackur–Tetrode Equation Walter Grimus (University of Vienna) Seminar Particle Physics March 8, 2012, University of Vienna Walter Grimus (University of Vienna) On the 100th Anniversary of the Sackur–Tetrode Equation Sackur–Tetrode equation Entropy of a monoatomic ideal gas: 3 E V S(E, V , N)= kN ln + ln + s 2 N N 0 1912: Otto Sackur and Hugo Tetrode independently determined 3 4πm 5 s = ln + 0 2 3h2 2 Sackur–Tetrode equation = absolute entropy of a monoatomic ideal gas Walter Grimus (University of Vienna) On the 100th Anniversary of the Sackur–Tetrode Equation Contents 1 Motivation 2 Tetrode’s derivation 3 Sackur’s derivation 4 Test of the Sackur–Tetrode equation 5 Concluding remarks Walter Grimus (University of Vienna) On the 100th Anniversary of the Sackur–Tetrode Equation Motivation Absolute entropy: Boltzmann (1875), Planck (1900): S = k ln W + const. Argument: Nernst’s heat theorem (1906) (third law of thermodynamics) S should be calculable without any additive constant ⇒ Massive particles: phase space volume of “elementary cells” unknown Sackur (1911): Entropy of a monoatomic ideal gas as a function of the volume of elementary cell Walter Grimus (University of Vienna) On the 100th Anniversary of the Sackur–Tetrode Equation Tetrode’s derivation Ansatz: n degrees of freedom ⇒ n Elementary domains of volume σ = δq δp δqn δpn = (zh) 1 1 · · · N identical particles ⇒ W ′ S = k ln N! W ′ = number of configurations in phase space Total admissible volume in phase space space given E, V , N: 3 3 3 3 (E, V , N)= -
In Memory of Josef Král
Mathematica Bohemica Jaroslav Lukeš; Ivan Netuka; Jiří Veselý In memory of Josef Král Mathematica Bohemica, Vol. 131 (2006), No. 4, 427–448 Persistent URL: http://dml.cz/dmlcz/133976 Terms of use: © Institute of Mathematics AS CR, 2006 Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 131 (2006) MATHEMATICA BOHEMICA No. 4, 427–448 NEWS AND NOTICES IN MEMORY OF JOSEF KRAL´ Jaroslav Luke², Ivan Netuka, Jiří Veselý, Praha On May 24, 2006 a farewell ceremony for our teacher, colleague and friend Josef Král was held in the Church of St. Wenceslas in Pečky. He died on May 13, 2006, before his seventy-fifth birthday. Josef Král was an outstanding mathematician, ex- ceptional teacher, model husband and father, and above all, a man of extraordinary human qualities. The results of his research place him among the most important Czech mathematicians of the second half of the twentieth century. His name is asso- ciated with original results in mathematical analysis and, in particular, in potential theory. In 1967 Josef Král founded a seminar in Prague on mathematical analysis, with a particular emphasis on potential theory. He supervised a number of students and created a research group, which has been called The Prague Harmonic Group by friends and colleagues. At first lectures were organised, somewhat irregularly, at the Mathematical Institute of the Czechoslovak Academy of Sciences, Krakovská 10. -
On the 100Th Anniversary of the Sackur-Tetrode Equation
UWThPh-2011-34 On the 100th anniversary of the Sackur–Tetrode equation W. Grimus∗ University of Vienna, Faculty of Physics Boltzmanngasse 5, A–1090 Vienna, Austria 23 January 2013 Abstract In 1912, Otto Sackur and Hugo Tetrode independently put forward an equation for the absolute entropy of a monoatomic ideal gas and published it in “Annalen der Physik.” The grand achievement in the derivation of this equation was the discretization of phase space for massive particles, expressed as δqδp = h, where q and p are conjugate variables and h is Planck’s constant. Due to the dependence of the absolute entropy on Planck’s constant, Sackur and Tetrode were able to devise a test of their equation by applying it to the monoatomic vapor of mercury; from the satisfactory numerical comparison of h obtained from thermodynamic data on mercury with Planck’s value from black-body radiation, they inferred the correctness of their equation. In this review we highlight this almost forgotten episode of physics, discuss the arguments leading to the derivation of the Sackur–Tetrode equation and outline the method how this equation was tested with thermodynamic data. arXiv:1112.3748v2 [physics.hist-ph] 23 Jan 2013 PACS: 05.70.-a, 51.30.+i ∗E-mail: [email protected] 1 1 Introduction The formula for the absolute entropy of a monoatomic ideal gas is named after Otto Sackur and Hugo Tetrode who independently derived it in 1912 [1, 2, 3]. In classical thermodynamics the entropy of a monoatomic ideal gas is 3 E V S(E,V,N)= kN ln + ln + s0 , (1) 2 N N where E, V and N are the kinetic energy, the volume and the number of atoms, respec- tively. -
A Equação De Sackur Tetrode Ou Como a Entropia Se Encontrou Com
A equação de Sackur-Tetrode ou como a entropia se encontrou com a mecânica quântica 3=2 5=2 2 3=2 5=2 S = Nk ln M T =P + ln 2=NAvh k + 5=2 n h i o No início do século XX, cientistas ilustres lutavam para entender mais profundamente o conceito de entropia. Esse era o conceito central da toda poderosa “segunda lei da termodinâmica”, que já tinha sido utilizada para estabelecer uma escala absoluta de temperaturas, mas que ainda demandava boa dose de esclarecimento. Uma questão inquietante permanecia sem resposta. Será que o valor ab- soluto da entropia poderia ser determinado? Ou será que a entropia somente poderia ser determinada a menos de uma constante aditiva? Os cientistas daquela época passaram a prestar maior atenção às ideias de Ludwig Boltzmann. O extenso trabalho de Boltzmann nesse problema pode ser resumido pela inscrição no seu túmulo, no cemitério central de Viena, S = k ln W: Essa equação expressa a entropia S em termos do logaritmo do número W de estados disponíveis para o movimento, multiplicado pelo constante k, batizada mais tarde em homenagem a Boltzmann. No entanto, de acordo com a física clássica, não há limite para a proximidade dos estados mecânicos no espaço de fase. Portanto, não há limite para o número de estados, e nem seria possível enumerá-los. Como é então que seria possível obter um valor de W bem de…nido? Como é que obteríamos a constante aditiva da entropia? A resposta a essas questões foi dada em dois artigos separados, que apare- ceram nos Annalen der Physik, principal revista alemã de física. -
The Gibbs Paradox: Early History and Solutions
entropy Article The Gibbs Paradox: Early History and Solutions Olivier Darrigol UMR SPHere, CNRS, Université Denis Diderot, 75013 Paris, France; [email protected] Received: 9 April 2018; Accepted: 28 May 2018; Published: 6 June 2018 Abstract: This article is a detailed history of the Gibbs paradox, with philosophical morals. It purports to explain the origins of the paradox, to describe and criticize solutions of the paradox from the early times to the present, to use the history of statistical mechanics as a reservoir of ideas for clarifying foundations and removing prejudices, and to relate the paradox to broad misunderstandings of the nature of physical theory. Keywords: Gibbs paradox; mixing; entropy; irreversibility; thermochemistry 1. Introduction The history of thermodynamics has three famous “paradoxes”: Josiah Willard Gibbs’s mixing paradox of 1876, Josef Loschmidt reversibility paradox of the same year, and Ernst Zermelo’s recurrence paradox of 1896. The second and third revealed contradictions between the law of entropy increase and the properties of the underlying molecular dynamics. They prompted Ludwig Boltzmann to deepen the statistical understanding of thermodynamic irreversibility. The Gibbs paradox—first called a paradox by Pierre Duhem in 1892—denounced a violation of the continuity principle: the mixing entropy of two gases (to be defined in a moment) has the same finite value no matter how small the difference between the two gases, even though common sense requires the mixing entropy to vanish for identical gases (you do not really mix two identical substances). Although this paradox originally belonged to purely macroscopic thermodynamics, Gibbs perceived kinetic-molecular implications and James Clerk Maxwell promptly followed him in this direction.