By Sidney B. Cahn, Gerald D. Mahan, Boris E. Nadgorny, Max Dresden
In order to equip hopeful graduate scholars with the data essential to cross the qualifying exam, the authors have assembled and solved average and unique difficulties from significant American universities – Boston college, collage of Chicago, collage of Colorado at Boulder, Columbia, college of Maryland, collage of Michigan, Michigan kingdom, Michigan Tech, MIT, Princeton, Rutgers, Stanford, Stony Brook, college of Tennessee at Knoxville, and the college of Wisconsin at Madison – and Moscow Institute of Physics and know-how. quite a lot of fabric is roofed and comparisons are made among comparable difficulties of other colleges to supply the scholar with adequate info to believe cozy and assured on the examination. Guide to Physics Problems is released in volumes: this e-book, Part 2, covers Thermodynamics, Statistical Mechanics and Quantum Mechanics; Part 1, covers Mechanics, Relativity and Electrodynamics.
Praise for A advisor to Physics difficulties: half 2: Thermodynamics, Statistical Physics, and Quantum Mechanics:
"… A advisor to Physics difficulties, half 2 not just serves a huge functionality, yet is a excitement to learn. through picking difficulties from assorted universities or even assorted medical cultures, the authors have successfully shunned a one-sided method of physics. all of the difficulties are strong, a few are very attention-grabbing, a few certainly exciting, a number of are loopy; yet them all stimulate the reader to consider physics, now not purely to coach you to move an examination. i actually obtained substantial excitement in operating the issues, and that i might wager that anybody who desires to be a qualified physicist may adventure comparable entertainment. … This publication can be a very good support to scholars and professors, in addition to a resource of delight and enjoyment." (From Foreword by means of Max Dresden)
"An first-class 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 choice of difficulties … Thought-provoking, enjoyable, and simply undeniable enjoyable to solve." (Giovanni Vignale, division of Physics and Astronomy, college of Missouri at Columbia)
"Interesting certainly and relaxing. the issues are creative and their options very informative. i might definitely suggest it to all graduate scholars and physicists in most cases … fairly worthwhile for academics who want 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 assessments. … Will turn out most beneficial to either school and scholars. certainly, I plan to exploit this fabric as a resource of examples and illustrations that may be labored into my lectures." (Douglas generators, collage of California at Irvine)
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Extra info for A Guide to Physics Problems Part 2: Thermodynamics, Statistical Physics, and Quantum Mechanics
68 Quantum Corrections to Equation of State (MIT, Princeton, Stony Brook) Consider a noninteracting, one-component quantum gas at temperature with a chemical potential in a cubic volume V. Treat the separate cases of bosons and fermions. a) For a dilute system derive the equation of state in terms of temperature pressure P, particle density and particle mass Do this derivation approximately by keeping the leading and next-leading powers of Interpret your results as an effective classical system.
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. 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.
What is the minimum work needed to collect the helium back into the bag? 56 Osmotic Pressure (MIT) Consider an ideal mixture of monatomic molecules of type A and monatomic molecules of type B in a volume V. THERMODYNAMICS AND STATISTICAL PHYSICS 29 a) Calculate the free energy Calculate the Gibbs potential G is the Legendre transform of F with respect to V. b) If the molecules of type A are called the solvent, and those of type B the solute. 56). There are particles in volume V (or in volume 2V), and and particles in volume V on the left and right of the membrane, respectively.