By Sidney B. Cahn, Gerald D. Mahan, Boris E. Nadgorny, Max Dresden
In order to equip hopeful graduate scholars with the data essential to move the qualifying exam, the authors have assembled and solved general and unique difficulties from significant American universities – Boston collage, collage of Chicago, college of Colorado at Boulder, Columbia, college of Maryland, college of Michigan, Michigan country, Michigan Tech, MIT, Princeton, Rutgers, Stanford, Stony Brook, college of Tennessee at Knoxville, and the collage of Wisconsin at Madison – and Moscow Institute of Physics and know-how. a variety of fabric is roofed and comparisons are made among related difficulties of other faculties to supply the scholar with adequate info to think cozy and assured on the examination. Guide to Physics Problems is released in volumes: this ebook, Part 2, covers Thermodynamics, Statistical Mechanics and Quantum Mechanics; Part 1, covers Mechanics, Relativity and Electrodynamics.
Praise for A consultant to Physics difficulties: half 2: Thermodynamics, Statistical Physics, and Quantum Mechanics:
"… A consultant to Physics difficulties, half 2 not just serves a massive functionality, yet is a excitement to learn. via settling on difficulties from diverse universities or even varied medical cultures, the authors have successfully refrained from a one-sided method of physics. all of the difficulties are solid, a few are very fascinating, a few definitely fascinating, a couple of are loopy; yet them all stimulate the reader to contemplate physics, no longer in simple terms to coach you to go an examination. i myself got massive excitement in operating the issues, and that i may wager that anybody who desires to be a certified physicist may adventure related entertainment. … This e-book could be an outstanding aid to scholars and professors, in addition to a resource of enjoyment and enjoyment." (From Foreword via Max Dresden)
"An very good source for graduate scholars in physics and, one expects, additionally for his or her teachers." (Daniel Kleppner, Lester Wolfe Professor of Physics Emeritus, MIT)
"A great collection of difficulties … Thought-provoking, exciting, and simply simple enjoyable to solve." (Giovanni Vignale, division of Physics and Astronomy, college of Missouri at Columbia)
"Interesting certainly and stress-free. the issues are creative and their ideas very informative. i might definitely suggest it to all graduate scholars and physicists commonly … rather worthwhile for lecturers who wish to take into consideration difficulties to provide of their course." (Joel Lebowitz, Rutgers University)
"A very completely assembled, fascinating set of difficulties that covers the most important components of physics addressed via Ph.D. qualifying checks. … Will turn out most valuable to either college and scholars. certainly, I plan to take advantage of this fabric as a resource of examples and illustrations that might be labored into my lectures." (Douglas generators, collage of California at Irvine)
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Extra resources for A Guide To Physics Problems. Thermodynamics, Statistical Physics, And Quantum Mechanics
B) Using the result of (a), calculate for one mole of a van der Waals gas. 50 Return of Heat Capacities (Michigan) In a certain range of temperature and pressure of a substance is described by the equation the specific volume where are positive constants. 51 27 Nonideal Gas Expansion (Michigan State) A gas obeys the equation of state where is a function of the temperature only. The gas is initially at temperature and volume and is expanded isothermally and reversibly to volume a) Find the work done in the expansion.
They depend only on the fact that is monotonically decreasing. At some step of the derivation, you might find it useful to do an integration by parts. 22 Puncture (Moscow Phys-Tech) A compressed ideal gas flows out of a small hole in a tire which has a pressure inside. 23 Cylinder with Massive Piston (Rutgers, Moscow Phys-Tech) Consider moles of an ideal monatomic gas placed in a vertical cylinder. 23). Initially the piston is fixed, and the gas has volume and temperature Next, the piston is released, and after several oscillations comes to a stop.
Express I in terms of b) Derive the canonical conjugate momenta Hamiltonian of this system in terms of c) The classical partition function is defined as and and Express the and I. TLFeBOOK PROBLEMS 24 Calculate Calculate the heat capacity for a system of N molecules. d) Assume now that the rotational motion of the molecule is described by quantum mechanics. Write the partition function in this case, taking into account the degeneracy of each state. Calculate the heat capacity of a system of N molecules in the limit of low and high temperatures and compare them to the classical result.