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Unformatted text preview: PHYS4125 Fall 2006 Exam 1 (Schroeder Ch. 1 2) Formulas and Constants Equipartition Theorem: Uthermal = N f kBT 1st Law of Thermodynamics: U = Q + W
V Compressive Work: W Adiabatic Processes: PV = constant; VTf/2 = constant; = (f+2) / f Heat Capacity: C = Q/T or Enthalpy: H = U + PV Mean Free Path: Scattering time:
A l C Q T kt A
2 kt 1 4 V r N RMS velocity: vrms = (3kBT/m)1/2
t l v rms Jx only quadratic q N 1 ! q! N 1 ! Stirling's Approximation: ln N ! Nln N N 1 e n n 2 Gaussian Distribution: P N n 2 2 U for systems with or more generally fN N ,q Einstein Solid: N ,n N! n! N n ! Binomial Distribution: PN n N 2 2 Diffusion, Fick's Law: Viscosity: Fx du x dz D dn dx
n N! pn r n! N n ! Heat Conduction: Q t dT dx f P V dV Vo at constant V or P.
1 CV lv 2 V and where Npr Ideal Gas Law: PV = nRT = NkBT
N 3 2 3Nh " Sackur-Tetrode Equation: S Nk B V ln N 4 mU
2 # $ " ! Ideal Gas: N 1 V 2mU N ! h 3N 3N 2 ! 3N 2 # Entropy of mixing: Entropy: S k B ln S k B ln degrees of freedom and n pN n1 n 2 ! n1 ! n2 !
3N 5 2 ...
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