Ph.D. Qualifying Exam: Statistical Mechanics, Thermodynamics and Modern Physics, Exams of Physics

Download Ph.D. Qualifying Exam: Statistical Mechanics, Thermodynamics and Modern Physics and more Exams Physics in PDF only on Docsity! Ph.D. Qualifying Exam. Statistical Mechanics, Thermodynamics and Modern Physics. January 2044 Part L statistical Mechanics Thermodynamics. (Pick 2 out of 3) If you answer all three note that only the first two will be graded. 1) Calculate the total electomagnetic energy inside an oven of volume 1 m3 heated to a temperature of 600 degrees Fahrenheit. 2) Anideal monatomic gas undergoes a reversible expansion from specific volume vr to specific volume vz. (a) Calculate the change in specific entropy As if the expansion is isobaric. (b) Calculate As if the process is isothermal. (c) Whioh is larger? By how much? 3) For N distinguishable coins the thermodynamic probability i, , =ffi, where Nr is the number of heads andN-Nr ttre number of tails. (a) Assume thatN is large enough that Stirling's approximation (lnn!-nlnn -n) is valid. Show that lno is ma:rimum forNr : N/2. (b) Show that @^o-eNro2. Possible useful information Boltzmann constant, k: 1.38 x 10 -23 J/K: 8.617 x 10-5 eV/K Stefan-Boltzmann constan! o:5.670 x 104 JK4m-2s-1 Planck's constanL h:6.62x 10-34 Js Speed of l^ight, c:2.99792458 x 108 ms-l R: 8-.34 x 103J knole-r K-l dU: TdS - PdV H:U+PV F : U.TS G: F+PV