Department of Physics Courses 1
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Equilibrium Thermodynamics
Equilibrium Thermodynamics Instructor: - Clare Yu (e-mail [email protected], phone: 824-6216) - office hours: Wed from 2:30 pm to 3:30 pm in Rowland Hall 210E Textbooks: - primary: Herbert Callen “Thermodynamics and an Introduction to Thermostatistics” - secondary: Frederick Reif “Statistical and Thermal Physics” - secondary: Kittel and Kroemer “Thermal Physics” - secondary: Enrico Fermi “Thermodynamics” Grading: - weekly homework: 25% - discussion problems: 10% - midterm exam: 30% - final exam: 35% Equilibrium Thermodynamics Material Covered: Equilibrium thermodynamics, phase transitions, critical phenomena (~ 10 first chapters of Callen’s textbook) Homework: - Homework assignments posted on course website Exams: - One midterm, 80 minutes, Tuesday, May 8 - Final, 2 hours, Tuesday, June 12, 10:30 am - 12:20 pm - All exams are in this room 210M RH Course website is at http://eiffel.ps.uci.edu/cyu/p115B/class.html The Subject of Thermodynamics Thermodynamics describes average properties of macroscopic matter in equilibrium. - Macroscopic matter: large objects that consist of many atoms and molecules. - Average properties: properties (such as volume, pressure, temperature etc) that do not depend on the detailed positions and velocities of atoms and molecules of macroscopic matter. Such quantities are called thermodynamic coordinates, variables or parameters. - Equilibrium: state of a macroscopic system in which all average properties do not change with time. (System is not driven by external driving force.) Why Study Thermodynamics ? - Thermodynamics predicts that the average macroscopic properties of a system in equilibrium are not independent from each other. Therefore, if we measure a subset of these properties, we can calculate the rest of them using thermodynamic relations. - Thermodynamics not only gives the exact description of the state of equilibrium but also provides an approximate description (to a very high degree of precision!) of relatively slow processes. -
Einstein Solid 1 / 36 the Results 2
Specific Heats of Ideal Gases 1 Assume that a pure, ideal gas is made of tiny particles that bounce into each other and the walls of their cubic container of side `. Show the average pressure P exerted by this gas is 1 N 35 P = mv 2 3 V total SO 30 2 7 7 (J/K-mole) R = NAkB Use the ideal gas law (PV = NkB T = V 2 2 CO2 C H O CH nRT )and the conservation of energy 25 2 4 Cl2 (∆Eint = CV ∆T ) to calculate the specific 5 5 20 2 R = 2 NAkB heat of an ideal gas and show the following. H2 N2 O2 CO 3 3 15 CV = NAkB = R 3 3 R = NAkB 2 2 He Ar Ne Kr 2 2 10 Is this right? 5 3 N - number of particles V = ` 0 Molecule kB - Boltzmann constant m - atomic mass NA - Avogadro's number vtotal - atom's speed Jerry Gilfoyle Einstein Solid 1 / 36 The Results 2 1 N 2 2 N 7 P = mv = hEkini 2 NAkB 3 V total 3 V 35 30 SO2 3 (J/K-mole) V 5 CO2 C N k hEkini = NkB T H O CH 2 A B 2 25 2 4 Cl2 20 H N O CO 3 3 2 2 2 3 CV = NAkB = R 2 NAkB 2 2 15 He Ar Ne Kr 10 5 0 Molecule Jerry Gilfoyle Einstein Solid 2 / 36 Quantum mechanically 2 E qm = `(` + 1) ~ rot 2I where l is the angular momen- tum quantum number. -
Otto Sackur's Pioneering Exploits in the Quantum Theory Of
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Catalogo dei prodotti della ricerca Chapter 3 Putting the Quantum to Work: Otto Sackur’s Pioneering Exploits in the Quantum Theory of Gases Massimiliano Badino and Bretislav Friedrich After its appearance in the context of radiation theory, the quantum hypothesis rapidly diffused into other fields. By 1910, the crisis of classical traditions of physics and chemistry—while taking the quantum into account—became increas- ingly evident. The First Solvay Conference in 1911 pushed quantum theory to the fore, and many leading physicists responded by embracing the quantum hypoth- esis as a way to solve outstanding problems in the theory of matter. Until about 1910, quantum physics had drawn much of its inspiration from two sources. The first was the complex formal machinery connected with Max Planck’s theory of radiation and, above all, its close relationship with probabilis- tic arguments and statistical mechanics. The fledgling 1900–1901 version of this theory hinged on the application of Ludwig Boltzmann’s 1877 combinatorial pro- cedure to determine the state of maximum probability for a set of oscillators. In his 1906 book on heat radiation, Planck made the connection with gas theory even tighter. To illustrate the use of the procedure Boltzmann originally developed for an ideal gas, Planck showed how to extend the analysis of the phase space, com- monplace among practitioners of statistical mechanics, to electromagnetic oscil- lators (Planck 1906, 140–148). In doing so, Planck identified a crucial difference between the phase space of the gas molecules and that of oscillators used in quan- tum theory. -
Intermediate Statistics in Thermoelectric Properties of Solids
Intermediate statistics in thermoelectric properties of solids André A. Marinho1, Francisco A. Brito1,2 1 Departamento de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, Paraíba, Brazil and 2 Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970 João Pessoa, Paraíba, Brazil (Dated: July 23, 2019) Abstract We study the thermodynamics of a crystalline solid by applying intermediate statistics manifested by q-deformation. We based part of our study on both Einstein and Debye models, exploring primarily de- formed thermal and electrical conductivities as a function of the deformed Debye specific heat. The results revealed that the q-deformation acts in two different ways but not necessarily as independent mechanisms. It acts as a factor of disorder or impurity, modifying the characteristics of a crystalline structure, which are phenomena described by q-bosons, and also as a manifestation of intermediate statistics, the B-anyons (or B-type systems). For the latter case, we have identified the Schottky effect, normally associated with high-Tc superconductors in the presence of rare-earth-ion impurities, and also the increasing of the specific heat of the solids beyond the Dulong-Petit limit at high temperature, usually related to anharmonicity of interatomic interactions. Alternatively, since in the q-bosons the statistics are in principle maintained the effect of the deformation acts more slowly due to a small change in the crystal lattice. On the other hand, B-anyons that belong to modified statistics are more sensitive to the deformation. PACS numbers: 02.20-Uw, 05.30-d, 75.20-g arXiv:1907.09055v1 [cond-mat.stat-mech] 21 Jul 2019 1 I. -
Applied Physics
Physics 1. What is Physics 2. Nature Science 3. Science 4. Scientific Method 5. Branches of Science 6. Branches of Physics Einstein Newton 7. Branches of Applied Physics Bardeen Feynmann 2016-03-05 What is Physics • Meaning of Physics (from Ancient Greek: φυσική (phusikḗ )) is knowledge of nature (from φύσις phúsis "nature"). • Physics is the natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves. • Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the scientific revolution in the 17th century, the natural sciences emerged as unique research programs in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. • New ideas in physics often explain the fundamental mechanisms of other sciences, while opening new avenues of research in areas such as mathematics and philosophy. 2016-03-05 What is Physics • Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. • For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization, and advances in mechanics inspired the development of calculus. -
Relativity in Classical Physics
PHYSICS IV COURSE TOPICS 1 - The Birth of Modern Physics 2 - Special Theory of Relativity 3 - The Experimental Basis of Quantum Physics 4 - Structure of the Atom 5 - Wave Properties of Matter 6 - Quantum Mechanics The Birth of Modern Physics Lecture 1 • The word physics is derived from the Latin word physica, which means «natural thing». • Physics is a branch of science that deals with the properties of matter and energy and the relationship between them. • The scope of physics is very wide and vast. It deals with not only the tinniest particles of atoms, but also natural phenomenon like the galaxy, the milky way, solar and lunar eclipses, and more. Branches of Physics • Classical physics • Modern physics • Nuclear physics This branch is mainly • Atomic physics • Geophysics concerned with the • Biophysics theory of relativity • Mechanics and • Acoustics quantum mechanics. • Optics • Thermodynamics • Astrophysics • The term modern physics generally refers to the study of those facts and theories developed in this century starting around 1900, that concern the ultimate structure and interactions of matter, space and time. • The three main branches of classical physics such as mechanics, heat and electromagnetism – were developed over a period of approximately two centuries prior to 1900. • Newton’s mechanics dealt succesfully with the motions of bodies of macroscopic size moving with low speeds. • This provided a foundation for many of the engineering accomplishments of the 18th and 19th centuries. • Between 1837 – 1901, there were many remarkable achievements occured in physics. • For example, the description and predictions of electromagnetism by Maxwell. Partly responsible for the rapid telecommunications of today. -
Outline of Physical Science
Outline of physical science “Physical Science” redirects here. It is not to be confused • Astronomy – study of celestial objects (such as stars, with Physics. galaxies, planets, moons, asteroids, comets and neb- ulae), the physics, chemistry, and evolution of such Physical science is a branch of natural science that stud- objects, and phenomena that originate outside the atmosphere of Earth, including supernovae explo- ies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a “physical sions, gamma ray bursts, and cosmic microwave background radiation. science”, together called the “physical sciences”. How- ever, the term “physical” creates an unintended, some- • Branches of astronomy what arbitrary distinction, since many branches of physi- cal science also study biological phenomena and branches • Chemistry – studies the composition, structure, of chemistry such as organic chemistry. properties and change of matter.[8][9] In this realm, chemistry deals with such topics as the properties of individual atoms, the manner in which atoms form 1 What is physical science? chemical bonds in the formation of compounds, the interactions of substances through intermolecular forces to give matter its general properties, and the Physical science can be described as all of the following: interactions between substances through chemical reactions to form different substances. • A branch of science (a systematic enterprise that builds and organizes knowledge in the form of • Branches of chemistry testable explanations and predictions about the • universe).[1][2][3] Earth science – all-embracing term referring to the fields of science dealing with planet Earth. Earth • A branch of natural science – natural science science is the study of how the natural environ- is a major branch of science that tries to ex- ment (ecosphere or Earth system) works and how it plain and predict nature’s phenomena, based evolved to its current state. -
Statistical Thermodynamics - Fall 2009
1 Statistical Thermodynamics - Fall 2009 Professor Dmitry Garanin Thermodynamics September 9, 2012 I. PREFACE The course of Statistical Thermodynamics consist of two parts: Thermodynamics and Statistical Physics. These both branches of physics deal with systems of a large number of particles (atoms, molecules, etc.) at equilibrium. 3 19 One cm of an ideal gas under normal conditions contains NL =2.69 10 atoms, the so-called Loschmidt number. Although one may describe the motion of the atoms with the help of× Newton’s equations, direct solution of such a large number of differential equations is impossible. On the other hand, one does not need the too detailed information about the motion of the individual particles, the microscopic behavior of the system. One is rather interested in the macroscopic quantities, such as the pressure P . Pressure in gases is due to the bombardment of the walls of the container by the flying atoms of the contained gas. It does not exist if there are only a few gas molecules. Macroscopic quantities such as pressure arise only in systems of a large number of particles. Both thermodynamics and statistical physics study macroscopic quantities and relations between them. Some macroscopics quantities, such as temperature and entropy, are non-mechanical. Equilibruim, or thermodynamic equilibrium, is the state of the system that is achieved after some time after time-dependent forces acting on the system have been switched off. One can say that the system approaches the equilibrium, if undisturbed. Again, thermodynamic equilibrium arises solely in macroscopic systems. There is no thermodynamic equilibrium in a system of a few particles that are moving according to the Newton’s law. -
Einstein's Physics
Einstein’s Physics Albert Einstein at Barnes Foundation in Merion PA, c.1947. Photography by Laura Delano Condax; gift to the author from Vanna Condax. Einstein’s Physics Atoms, Quanta, and Relativity Derived, Explained, and Appraised TA-PEI CHENG University of Missouri–St. Louis Portland State University 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Ta-Pei Cheng 2013 The moral rights of the author have been asserted Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available ISBN 978–0–19–966991–2 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work. -
MOLAR HEAT of SOLIDS the Dulong–Petit Law, a Thermodynamic
MOLAR HEAT OF SOLIDS The Dulong–Petit law, a thermodynamic law proposed in 1819 by French physicists Dulong and Petit, states the classical expression for the molar specific heat of certain crystals. The two scientists conducted experiments on three dimensional solid crystals to determine the heat capacities of a variety of these solids. They discovered that all investigated solids had a heat capacity of approximately 25 J mol-1 K-1 room temperature. The result from their experiment was explained as follows. According to the Equipartition Theorem, each degree of freedom has an average energy of 1 = 2 where is the Boltzmann constant and is the absolute temperature. We can model the atoms of a solid as attached to neighboring atoms by springs. These springs extend into three-dimensional space. Each direction has 2 degrees of freedom: one kinetic and one potential. Thus every atom inside the solid was considered as a 3 dimensional oscillator with six degrees of freedom ( = 6) The more energy that is added to the solid the more these springs vibrate. Figure 1: Model of interaction of atoms of a solid Now the energy of each atom is = = 3 . The energy of N atoms is 6 = 3 2 = 3 where n is the number of moles. To change the temperature by ΔT via heating, one must transfer Q=3nRΔT to the crystal, thus the molar heat is JJ CR=3 ≈⋅ 3 8.31 ≈ 24.93 molK molK Similarly, the molar heat capacity of an atomic or molecular ideal gas is proportional to its number of degrees of freedom, : = 2 This explanation for Petit and Dulong's experiment was not sufficient when it was discovered that heat capacity decreased and going to zero as a function of T3 (or, for metals, T) as temperature approached absolute zero. -
PHYSICS Is the Study of Energy and Consists of Five Main Branches Each Studies a Different Form of Energy
S R E W S N A PHYSICS is the study of energy and consists of five main branches each studies a different form of energy: . Mechanics (The study of forces or work; work is a form of energy) . Thermodynamics (The study of heat; heat is a form of energy) . Acoustics (The study of sound; sound is a form of energy) . Optics (The study of light; light is a form of energy) . Electricity and magnetism (Both are forms of energy) Just as there are different forms of money (the nickel, the dime, the quarter, the "five-dollar" bill, the check, etc.), there are different forms of energy (heat, sound, light, electricity, etc.). Each different form is a different branch of physics. And, just as one form of money can be converted into a different form of money, likewise one form of energy can be converted into a different form of energy. Even matter is just a form of energy (E = mc2). The device used to convert one form of energy into another form of energy is called a TRANSDUCER. Some popular transducers include: . The light bulb (which converts electrical energy into light energy) . The electric motor (which converts electrical energy into mechanical energy) . The electric heater (which converts electrical energy into heat energy) . The generator (which converts mechanical energy into electrical energy) . The speaker (which converts electrical energy into sound energy) . The microphone (which converts sound energy into electrical energy) . The photocell (which converts light energy into electrical energy) The efficiency of a transducer tells us how well it converts one type of energy into another type of energy. -
First Principles Study of the Vibrational and Thermal Properties of Sn-Based Type II Clathrates, Csxsn136 (0 ≤ X ≤ 24) and Rb24ga24sn112
Article First Principles Study of the Vibrational and Thermal Properties of Sn-Based Type II Clathrates, CsxSn136 (0 ≤ x ≤ 24) and Rb24Ga24Sn112 Dong Xue * and Charles W. Myles Department of Physics and Astronomy, Texas Tech University, Lubbock, TX 79409-1051, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-806-834-4563 Received: 12 May 2019; Accepted: 11 June 2019; Published: 14 June 2019 Abstract: After performing first-principles calculations of structural and vibrational properties of the semiconducting clathrates Rb24Ga24Sn112 along with binary CsxSn136 (0 ≤ x ≤ 24), we obtained equilibrium geometries and harmonic phonon modes. For the filled clathrate Rb24Ga24Sn112, the phonon dispersion relation predicts an upshift of the low-lying rattling modes (~25 cm−1) for the Rb (“rattler”) compared to Cs vibration in CsxSn136. It is also found that the large isotropic atomic displacement parameter (Uiso) exists when Rb occupies the “over-sized” cage (28 atom cage) rather than the 20 atom counterpart. These guest modes are expected to contribute significantly to minimizing the lattice’s thermal conductivity (κL). Our calculation of the vibrational contribution to the specific heat and our evaluation on κL are quantitatively presented and discussed. Specifically, the heat capacity diagram regarding CV/T3 vs. T exhibits the Einstein-peak-like hump that is mainly attributable to the guest oscillator in a 28 atom cage, with a characteristic temperature 36.82 K for Rb24Ga24Sn112. Our calculated rattling modes are around 25 cm−1 for the Rb trapped in a 28 atom cage, and 65.4 cm−1 for the Rb encapsulated in a 20 atom cage.