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

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Unformatted text preview: PHYS4125 Spring 2007 Exam 3 (Schroeder Ch. 5 (1-3) 6 (1-3)) Formulas and Constants First and Second Law 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 Ideal Gas Law: PV = nRT = NkBT N 3 2 Transport t RMS velocity: vrms = (3kBT/m)1/2 Viscosity: Fx A ! Diffusion, Fick's Law: & % Scattering time: t v rms du x dz $ # Mean Free Path: l 1 r 2 4 V N l Jx D dn dx " ! Heat Conduction: Q kt A S Nk B ln 3Nh dT dx kt 1 CV lv 2 V Sackur-Tetrode Equation: V N 4 mU 2 ' ( Ideal Gas: 3N 2 1 V 2mU N ! h 3 N 3N 2 ! N 3N 2 Entropy of mixing: Entropy: S k B ln S k B ln n1 n2 ! n1 ! n 2 ! N ,V P Heat Capacity: C = Q/T or f P V dV Vo C Q T U T N ,V P 5 2 Statistics N ,n N! n! N n ! U ,N U ,V Engines and Refrigerators Definition of Coefficient of Performance: Joule-Thompson Throttling Process: H f Hi Free Energy Enthalpy: H U PV COP benefit cost Qc W Qh Definition of Efficiency: e Qh Th Qc Qc Th Tc Tc benefit cost W Qh Qh Qc Th y Definition of Chemical Potential: T S N Thermodynamic Identity: dU T dS x w u x hvt sPr q g i hf e ep d Definition of Pressure: P T S V U V S ,N P dV dN U N Tc c c b i a processes. Third Law of Thermodynamics: T CV Y `X W V V Entropy and heat: dS dQ T C V dT U U T Definition of Temperature: S degrees of freedom and R PQ or more generally 2 U for fN n pN systems with only quadratic Interactions T U S N ,V ; S CV T dT for quasi-static 0 0 0 as T 0 ;S T I PH D (C G F E E A @ q N 1 ! q! N 1 ! Stirling's Approximation: ln N ! Nln N 1 e n Gaussian Distribution: P N n 2 9 B 6 5 Einstein Solid: N ,q 0 8 ) Binomial Distribution: PN n N N n 2 2 2 1 N! pn r n! N n ! n and 7 4 3 2 where Npr S ,V Boltzmann Statistics Es kB T Boltzmann Factor: Partition Function: Average Values: e e Es Probability function: Z X ave P s s 1 e Z Es E s e s s Equipartition (Again): if E q cq 2 then E ave 1 2kB T u X s P s 1 Z X s e E s E ave 1 Z van der Waals Equation of State: P aN 2 V 2 V Nb Nk B T Clausius Clapeyron Relation for a Phase ~ } h| h { z y w xv t us 1 dF T 1 For fixed P, N: dS total T dG Chemical Potential: G N ; For fixed V, N: dS total T ,P o k B T ln P P dP Boundary: dT T r hq p SdT h Pg o n Helmholtz Free Energy: F U TS Gibbs Free Energy: G U TS PV Thermodynamic Identities: dH TdS dF SdT PdV dN , dG f e d m Pl P VdP dN , dN VdP k j i o L T V Z Reference Data: kB = 1.3807 x 10-23 J/K = 8.617 x 10-5 eV / K NA = 6.022 x 1023 R = 8.315 J/mol K h = 6.626 x 10-34 J s = 4.136 x 10-15 eV s c = 2.998 x 108 m/s G = 6.673 x 10-11 Nm2/kg2 e = 1.602 x 10-19 C me = 9.109 x 10-31 kg mp = 1.673 x 10-27 kg B = 9.2741x10-24 J/T Unit Conversions: 1atm = 1.013 bar = 1.013 x 105 Pa = 14.7 lb / in2 = 760 mm Hg (T in oC) = (T in K) 273.15 (T in oF) = 9/5 (T in oC) + 32 1 oR = 5/9 K 1 cal = 4.186 J 1 Btu = 1054 J 1 eV = 1.602x 10-19 J 1 u = 1.661 x 10-27 kg ...
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This note was uploaded on 05/20/2011 for the course PHYS 4125 taught by Professor Staff during the Spring '07 term at LSU.

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