Teaching Thermal Physics - - to integrate or not. Brian Cowan

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1 Teaching Thermal Physics - - to integrate or not Brian Cowan 1

2 Thermal Physics Ludwig Boltzmann, who spent much of his life studying sta8s8cal mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in Now it is our turn to study sta8s8cal mechanics. Perhaps it will be wise to approach the subject cau8ously. David Goodstein in States of Matter, 1975, Dover N.Y. 2

3 Back in the dark ages Thermodynamics was taught as a core course probably in the second year. Sta=s=cal Mechanics was taught as an advanced op=on in the third (final) year. Ques=ons: 1 Is this correct pedagogically? 2 is there space in today s crowded curriculum for the dis=nct treatment? 3

4 Distinction Thermodynamics is the study of the relationship between macroscopic properties of systems, such as temperature, volume, pressure, magnetisation, compressibility etc. etc. Statistical Mechanics is concerned with understanding how the various macroscopic properties arise as a consequence of the microscopic nature of the system. In essence it makes macroscopic deductions from microscopic models. 4

5 Albert Einstein. A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me; it is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, will never be overthrown. Autobiographical Notes, Albert Einstein: Philosopher- Scien=st, Ed. P. A. Schilpp, Open Court Publishing Co

6 Lev Landau.. Sta8s8cal physics and thermodynamics together form a unit. All the concepts and quan88es of thermodynamics follow most naturally, simply and rigorously from the concepts of sta8s8cal physics. Although the general statements of thermodynamics can be formulated non- sta8s8cally, their applica8on to specific cases always requires the use of sta8s8cal physics. In the Preface to Sta%s%cal Physics, vol 5 of Landau and Lifshitz Course of Theore=cal Physics. 6

7 Arnold Sommerfeld (not actually relevant, but.) Sommerfeld was asked why he had never wrixen a book on thermodynamics having wrixen books on most other areas of physics. He replied: Thermodynamics is a funny subject. The first %me you go through it, you don't understand it at all. The second %me you go through it, you think you understand it, except for one or two small points. The third %me you go through it, you know you don't understand it, but by that %me you are so used to it, it doesn't bother you anymore. However later, in 1951, wri=ng a book on thermodynamics and sta=s=cal mechanics, he was killed following a traffic accident. The book was published posthumously the following year. 7

8 Relationship between Statistical Mechanics and Thermodynamics PARADOX Landau: disciplines are similar reductionism Thermodynamics explained by Statistical Mechanics Einstein: disciplines are opposites the domain of Thermodynamics is independent of the microscopics The paradox is that neither Landau nor Einstein lived these ideals Einstein was much-concerned with microscopics and Landau with Macroscopics. 8

9 Probabilistic interpretation of the First Law E = PE j j j de = P de + E dp j j j j j j j P de = dw E dp = dq j j j j j Shifting energy levels Changing populations of states Work Heat 9

10 1.3.1 Thermal interaction Temperature E 1 and E 2 can vary subject to E 1 + E 2 = const = E 0. Ω=Ω ( E ) Ω ( E ) ( E) ( E E) Ω=Ω Ω Maximise entropy subject to varying E. dω dω1 dω = Ω 2 2 Ω 1 = 0 de de de 1 dω1 1 dω2 = Ω1 de Ω2 de dlnω1 dlnω2 ds1 ds2 = or = de de de de 10

11 The Canonical Distribution Function EkT ( ) e P E The Boltzmann factor is a key result. Richard Feynman says: This fundamental law is the summit of statistical mechanics, and the entire subject is either a slidedown from the summit, as the principle is applied to various cases, or the climb-up to where the fundamental law is derived and the concepts of thermal equilibrium and temperature clarified. R. P. Feynman, Statistical Mechanics, Benjamin

12 Treatments of Classical Thermodynamics 1 Zemansky completely traditional approach 2 Pippard (and Adkins) beautiful traditional approach and includes Caratheodorey approach. (Zemansky s late conversion) 3 Callen revolutionary formulation: postulate Entropy. 4 Non-affine differential geometry: Brillouin, (Gibbs), Lieb & Yngvason, Luca (chapter in book) Postulates expedience vs reasonableness of postulates, Bertrand Russell: The method of postulating what we want has many advantages; they are the same as the advantages of theft over honest toil. 12

13 Treatments of Statistical Mechanics 1 Ensembles Exemplified in Hill s book(s) 2 Separate domains with bridge equations. 3 Quantum vs classical treatment probably explains historical late coverage of statistical mechanics in UG curriculum, as you need either Quantum Mechanics or Hamiltonian Mechanics. 4 Information theory approach (Jaynes) expedience. Expedience can obscure understanding. Philosophical difficulties with concept of ptobability. 13

14 Integrated Treatments 1 Landau & Lifshiz 2 Reif (both Fundamentals of Statistical and Thermal Physics and the Berkley Physics Series) 3 Mandl is often the text book of choice Expedience can obscure understanding. Philosophical difficulties with concept of probability. 14

15 My Conclusion 1 I was taught Thermodynamics and Statistical Mechanics as separate subjects. 2 Statistical Mechanics was taught from the Information Theory perspective ugh!! 3 I don t believe todays (2 nd year) undergraduates are prepared for the intellectual gymnastics of Classical Thermodynamics. 4 I was convinced by Landau (and Reif) of the value of the integrated approach (with Callen support). 5 I introduced fully-integrated 2 nd yr course some 25 years ago. But. 15

16 Now Classical Thermodynamics has become the poor relation of thermal physics. Perhaps the tables should be turned completely, and an early-years integrated treatment be followed by a 3 rd year or 4 th year module on Classical Thermodynamics! 16

4211 Statistical Mechanics Brian Cowan

4211 Statistical Mechanics Brian Cowan Email b.cowan@rhul.ac.uk Course web pages h7p://personal.rhul.ac.uk/uhap/027/ph4211/ You will be redirected here from the MOODLE page 4211 Statistical Mechanics Week