formulasheetfinal

formulasheetfinal - PHYS4125 Spring 2011 Final...

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PHYS4125 Spring 2011 Final Exam (Schroeder Ch. 1 – 7) Formulas and Constants First and Second Law Equipartition Theorem:  U thermal = N f 2 k B T 1 st  Law of Thermodynamics:  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 / 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 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 !
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formulasheetfinal - PHYS4125 Spring 2011 Final...

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