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formulasheet3 - PHYS4125 Spring 2007 Exam 3(Schroeder Ch...

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PHYS4125 Spring 2007 Exam 3 (Schroeder Ch. 5 (1-3) – 6 (1-3)) Formulas and Constants First and Second Law Equipartition Theorem: U thermal = N f ½ k B T 1 st Law of Thermodynamics: Δ U = Q + W Compressive Work: W V o V f P V dV Adiabatic Processes: PV γ = constant; VT f /2 = constant; γ = ( f +2) / f Heat Capacity: C = Q / Δ T or C Q T N , V P U T N , V P Entropy: S k B ln Entropy of mixing: S k B ln n 1 n 2 ! n 1 ! n 2 ! Ideal Gas Law: PV = nRT = Nk B T Ideal Gas: N 1 N ! V N h 3N 3N 2 3N 2 ! 2mU 3N 2 Sackur-Tetrode Equation: S Nk B ln V N 4 mU 3Nh 2 3 2 5 2 Transport Heat Conduction: Q t k t A dT dx k t 1 2 C V V l v Mean Free Path: l 1 4 r 2 V N RMS velocity: v rms = (3 k B T / m ) 1/2 Scattering time: t l v rms Viscosity: F x A du x dz Diffusion, Fick's Law: J x D dn dx
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Statistics Binomial Distribution: P N n N ! n ! N n ! p n r N n and N , n N ! n ! N n ! Einstein Solid: N , q q N 1 ! q ! N 1 ! Stirling's Approximation: ln N ! Nln N N Gaussian Distribution: P N n 1 2 e n n 2 2 2 where Npr or more generally 2 fN U for systems with only quadratic degrees of freedom and n pN
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