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PHYS664_HW2 - (c A system of N = 2 indistinguishable...

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Robert Szoszkiewicz, PHYS 664, HW # 2, Sept 15, 2009 DUE: on (or before) 10:20 am, Sept 23, 2009. 1. Manipulations of thermodynamic variables. Find internal energy ( U ), free energy of Helmholtz ( F ), statistical entropy ( σ ), mean pressure ( p ), and heat capacity at a constant volume ( c V ) for the following systems: (a) One atom in a box. Here a partition function Z 1 is: Z 1 = n Q /n , where n Q = ( Mτ/ (2 π ¯ h 2 )) 3 / 2 , n = 1 /V , M is the mass of a particle, τ is the statistical temperature, ¯ h is the ”h-bar” (the Planck constant over 2 π ), V is the volume of a box (notation like in the lecture 10). (b) N indistinguishable atoms of ideal gas in classical limit in a box. Here a partition function Z N = 1 N ! ( n Q V ) N (notation like in the lecture 10).
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Unformatted text preview: (c) A system of N = 2 indistinguishable particles with two available states only, one at energy 0 and another one at energy ² . Each state can be populated by up to two particles. Derive an appropriate partition function. 2. Energy fluctuations. Chapter 3, problem no. 4, page 83 from the course book (Ch. Kittel, Thermal Physics, second ed.) 3. Zipper problem. Chapter 3, problem no. 7, page 85 from the course book (Ch. Kittel, Thermal Physics, second ed.) 4. Elasticity of polymers. Chapter 3, problem no. 10, page 86 from the course book (Ch. Kittel, Thermal Physics, second ed.) 1...
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