Physical Chemistry 457 Final

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Chemistry 457 - Statistical Thermodynamics, Final Exam Wednesday, June 11, 2008; 8:30 am - 10:20 am Name (please print clearly) [1 point].: This is a closed book exam. Only simple calculators are allowed. No graphing or programmable calculators will be permitted. Two cheat sheet are allowed. Please write neatly and be sure to show all work for each problem in the space provided. Useful constants: kB = 1.38 × 10−23 JK−1 , h = 6.626 × 10−34 Js, NA = 6.022 × 1023 mol−1 Problem 1 - Short answers [14 points]. No more than one word or equation is required per response. a) What is the Boltzmann factor? b) What are the units of the heat capacity? c) What are the units of the molecular partition function? d) How many vibrational modes does ethanol have? e) What is the high temperature molar vibrational heat capacity of HCN? f ) How does the molecular mean free path depend on pressure in the hard-sphere model? g) How does the diffusion constant D for a molecule or atom scale with temperature? h) What is the SI unit of viscosity? i) How does the viscosity of a gas depend on pressure in the hard-sphere model? j) How does the average molecular speed scale with temperature? k) What is the maximum occupation number ni for Fermions? l) How does the heat capacity scale with temperature in the Debye model for low temperatures? m) How many optical phonon branches does a crystal with 4 atoms per unit cell have? n) What are the names of the two (Austrian and the American) scientists who laid the foundations of statistical thermodynamics 1 Problem 2 - Basic thermodynamics [30 points]. Provide a short explanation possibly with equation or illustrating graph if necessary: a) State and explain the equipartition theorem and its relation to a system’s degrees of freedom. b) Sketch the experimental setup for the Brownian motion experiment shown in class and discuss the result and

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