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A guide to physics problems part 2 thermodynamics, statistical physics, and quantum mechanics
[...]... in a Box (MIT) 5.11 Square Well (MIT) 5. 12 Given the Eigenfunction (Boston, MIT) 5.13 Combined Potential (Tennessee) 22 8 23 0 23 2 23 4 23 6 23 8 24 1 24 3 24 3 24 3 24 4 24 5 24 7 24 8 25 0 25 0 25 1 25 3 25 3 25 5 25 5 25 6 Harmonic Oscillator 25 7 25 7 5.14 Given a Gaussian (MIT) Harmonic Oscillator ABCs (Stony Brook) 25 8 5.15 26 0 5.16 Number States (Stony Brook) 26 2 5.17 Coupled Oscillators (MIT) 5.18 Time-Dependent Harmonic... Phys-Tech) A small amount of water of mass in a container at temperature K is placed inside a vacuum chamber which is evacuated rapidly As a result, part of the water freezes and becomes ice and the rest becomes vapor a) What amount of water initially transforms into ice? The latent heat of fusion (ice/water) and the latent heat of vaporization (water/vapor) g and original volume b) A piece of heated metal alloy... Electric and Magnetic Fields (Princeton) 5.76 Josephson Junction (Boston) 322 322 323 324 324 328 329 330 PART III: APPENDIXES Approximate Values of Physical Constants Some Astronomical Data Other Commonly Used Units Conversion Table from Rationalized MKSA to Gaussian Units Vector Identities Vector Formulas in Spherical and Cylindrical Coordinates Legendre Polynomials Rodrigues’ Formula Spherical Harmonics... 26 6 26 6 26 7 26 9 27 1 27 2 Contents 5 .27 5 .28 5 .29 5.30 xxiii Three Spins (Stony Brook) Constant Matrix Perturbation (Stony Brook) Rotating Spin (Maryland, MIT) Nuclear Magnetic Resonance (Princeton, Stony Brook) 27 2 27 4 27 5 27 6 Variational Calculations 5.31 Anharmonic Oscillator (Tennessee) 5. 32 Linear Potential I (Tennessee) 5.33 Linear Potential II (MIT, Tennessee) 5.34 Return of Combined Potential (Tennessee)... speed at temperature c) What is the average speed? d) What is the average square speed? 4.14 Slowly Leaking Box (Moscow Phys-Tech, Stony Brook (a, b)) An ideal gas of atoms of number density at an absolute temperature is confined to a thermally isolated container that has a small hole of area A in one of the walls (see Figure P.4.14) Assume a Maxwell velocity distribution PROBLEMS 10 for the atoms The... (Boston) 4.41 Ideal Gas in One-Dimensional Potential (Rutgers) 4. 42 Equipartition Theorem (Columbia, Boston) 4.43 Diatomic Molecules in Two Dimensions (Columbia) 4.44 Diatomic Molecules in Three Dimensions (Stony Brook, Michigan State) 4.45 Two-Level System (Princeton) 4.46 Zipper (Boston) 4.47 Hanging Chain (Boston) 4.48 Molecular Chain (MIT, Princeton, Colorado) 19 19 20 20 20 21 21 21 21 22 23 24 24 ... temperature He reasoned that, during collision with the hot surface, air molecules acquire additional momentum and therefore will transfer an equal momentum to the panel The back of the handkerchief estimates he was able to make quickly for of such a panel showed that if and = 373 K (air temperature 29 3 K) this panel would be able to levitate itself and a payload (the Baron) of about kg How did he arrive... Canonical Ensemble (Colorado, 21 2 Stony Brook) 4.94 Number Fluctuations (Colorado (a, b), Moscow 21 6 Phys-Tech (c)) 21 9 4.95 Wiggling Wire (Princeton) 22 1 4.96 LC Voltage Noise (MIT, Chicago) Applications to Solid State 4.97 Thermal Expansion and Heat Capacity (Princeton) 4.98 Schottky Defects (Michigan State, MIT) 4.99 Frenkel Defects (Colorado, MIT) 22 3 22 3 22 6 22 6 xxii Contents 4.100 4.101 4.1 02 4.103... 20 21 21 21 21 22 23 24 24 24 25 Nonideal Gas 4.49 Heat Capacities (Princeton) 4.50 Return of Heat Capacities (Michigan) 4.51 Nonideal Gas Expansion (Michigan State) 4. 52 van der Waals (MIT) 26 26 26 27 27 14 15 15 16 16 16 16 17 17 18 18 19 Contents 4.53 Critical Parameters (Stony Brook) xv 28 Mixtures and Phase Separation 4.54 Entropy of Mixing (Michigan, MIT) 4.55 Leaky Balloon (Moscow Phys-Tech)... Assume that the sublimation occurs at a constant temperature THERMODYNAMICS AND STATISTICAL PHYSICS The vapor pressure at this temperature is of the astronaut 4.7 7 and the total mass Grand Lunar Canals (Moscow Phys-Tech) In one of his novels, H G Wells describes an encounter of amateur earthling astronauts with a lunar civilization living in very deep caverns beneath the surface of the Moon The caverns