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prelim1996 - Table of Contents Complete Partially Complete...

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Table of Contents Complete Partially Complete Not Complete Preliminary Examination 1996 2 Problem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Problem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Problem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Problem 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Problem 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Problem 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Problem 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Problem 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Problem 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Problem 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Problem 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Problem 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Problem 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Problem 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Problem 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Problem 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Problem 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Problem 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Problem 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Problem 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1
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Preliminary Examination September , 1996 1. 2
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Preliminary Examination September , 1996 2. 3
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Preliminary Examination September , 1996 3. 4
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Preliminary Examination September , 1996 4. 5
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Preliminary Examination September , 1996 5. Consider a classical gas of non-interacting particles which obey the relation ϵ = α | p | 3 , where ϵ is a particle’s kinetic energy and | p | is the absolute magnitude of it’s momentum. (a) Calculate the classical partition function for this gas. (b) From (a), find the equation of state (i.e., an equation relating pressure, volume, and temperature) for the gas. (c) What is the heat capacity of the gas? 6
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Preliminary Examination September , 1996 6. A particle decays in flight into two photons of energies ~ ω 1 and ~ ω 2 , whose trajectories make an angle θ with one another: (a) Show that the rest mass of the particle is M = 2 sin ( θ 2 ) ( ~ ω 1 )( ~ o mega 2 ) c 2 (b) What is its velocity? 7
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Preliminary Examination September , 1996 7. 8
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Preliminary Examination September , 1996 8. 9
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Preliminary Examination September , 1996 Wk Counts Wk Counts Wk Counts 1 575 11 612 21 597 2 582 12 591 22 596 3 604 13 587 23 618 4 608 14 618 24 624 5 621 15 609 25 592 6 584 16 594 26 628 7 605 17 617 27 594 8 581 18 621 28 624 9 585 19 589 29 623 10 610 20 595 30 597 Table 1: Data for Problem 9.
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