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 common and unique difficulties from significant American universities – Boston college, college of Chicago, collage of Colorado at Boulder, Columbia, collage of Maryland, college of Michigan, Michigan nation, Michigan Tech, MIT, Princeton, Rutgers, Stanford, Stony Brook, collage of Tennessee at Knoxville, and the college of Wisconsin at Madison – and Moscow Institute of Physics and expertise. a variety of fabric is roofed and comparisons are made among comparable difficulties of other colleges to supply the scholar with sufficient details 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 consultant to Physics difficulties: half 2: Thermodynamics, Statistical Physics, and Quantum Mechanics:
"… A consultant to Physics difficulties, half 2 not just serves an incredible functionality, yet is a excitement to learn. through identifying difficulties from various universities or even diverse medical cultures, the authors have successfully refrained from a one-sided method of physics. the entire difficulties are solid, a few are very fascinating, a few absolutely exciting, a couple of are loopy; yet them all stimulate the reader to contemplate physics, now not only to coach you to cross an examination. i myself acquired enormous excitement in operating the issues, and that i may wager that any one who desires to be a qualified physicist could event comparable leisure. … This e-book could be a superb support to scholars and professors, in addition to a resource of delight and enjoyment." (From Foreword through 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, interesting, and simply undeniable enjoyable to solve." (Giovanni Vignale, division of Physics and Astronomy, college of Missouri at Columbia)
"Interesting certainly and stress-free. the issues are inventive and their options very informative. i might definitely suggest it to all graduate scholars and physicists commonly … quite precious for academics who want to take into consideration difficulties to provide of their course." (Joel Lebowitz, Rutgers University)
"A very completely assembled, attention-grabbing set of difficulties that covers the foremost components of physics addressed through Ph.D. qualifying assessments. … Will turn out Most worthy to either college and scholars. certainly, I plan to exploit this fabric as a resource of examples and illustrations that may be labored into my lectures." (Douglas turbines, collage of California at Irvine)
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Extra resources for A Guide to Physics Problems Part 2: Thermodynamics, Statistical Physics, and Quantum Mechanics
92 Isothermal Compressibility and Mean Square Fluctuation (Stony Brook) a) Derive the relation where is the isothermal compressibility: 44 PROBLEMS b) From (a), find the relation between and the mean square fluctuation of N in the grand canonical ensemble. How does this fluctuation depend on the number of particles? 93 Energy Fluctuation in Canonical Ensemble (Colorado, Stony Brook) Show that for a canonical ensemble the fluctuation of energy in a system of constant volume is related to the specific heat and, hence, deduce that the specific heat at constant volume is nonnegative.
Find the ratio (the gas may be considered ideal). 31). and are adiabatic compression and expansion, respectively; and are constant-volume processes. 32 and atm. 32). Assume that the heat capacities of the gas and are constant. 33). Assume and are constant. 34 shows container A of variable volume V controlled by a frictionless piston, immersed in a bath at temperature This container is connected by a pipe with a porous plug to another container, B, of fixed volume Container A is initially occupied by an ideal gas at pressure P while container B is initially evacuated.
To illustrate this consider the following problem. A one-dimensional harmonic oscillator has an infinite series of equally spaced energy states, with where is a positive integer or zero and is the classical frequency of the oscillator. a) Show that for a harmonic oscillator the free energy is b) Find the entropy S. 78 Photon Gas (Stony Brook) Consider a photon gas at temperature T inside a container of volume V. Derive the equation of state and compare it to that of the classical ideal gas (which has the equation Also compute the energy of the photon gas in terms of PV.
A Guide to Physics Problems Part 2: Thermodynamics, Statistical Physics, and Quantum Mechanics by Sidney B. Cahn, Gerald D. Mahan, Boris E. Nadgorny, Max Dresden