Physical Constants and Formulae for Exam 2 in Physics 4230 - Spring 2007, Exams of Physics

Download Physical Constants and Formulae for Exam 2 in Physics 4230 - Spring 2007 and more Exams Physics in PDF only on Docsity! Physics 4230 Physical Constants and Formulae for Exam 2 - Spring 2007 k = 1.381 × 10−23 J/K R = 8.315 J/mol · K NA = 6.022 × 1023 h = 6.626 × 10−34 J · s CV = ∂U ∂T ∣∣∣∣ V α = ∆L/L ∆T B = − ∆p ∆V/V 1 T = ∂S ∂U ∣∣∣∣ N,V p = T ∂S ∂V ∣∣∣∣ N,U Cp = ∂U ∂T ∣∣∣∣ p β = ∆V/V ∆T S = k ln Ω dS = CV dT T µ = −T ∂S ∂N ∣∣∣∣ U,V For adiabatic ideal gas processes: V T f/2 =constant and pV (f+2)/f =constant. Multiplicities Ωosc(N, q) = (q + N − 1)! q!(N − 1)! Ωpara(N, n↑) = N ! n↑!(N − n↑)! Ωideal gas = 1 N ! V N h3N 2π3N/2 (3N 2 − 1)!m( √ 2mU)3N−2δU Paramagnetism ( B points “up”) U = µB(n↓ − n↑) M = µ(n↑ − n↓) Sacker-Tetrode Equation S = Nk [ ln ( V N ( 4πmU 3Nh2 )3/2 ) + 5 2 ] Thermodynamic Potentials and Identity H = U + pV G = U + pV − TS F = U − TS G = H − TS dU = T dS − p dV + µ dN 1