Phys 328 Midterm 2: Statistical Physics Exam - Prof. Marjorie Olmstead, Exams of Physics

Download Phys 328 Midterm 2: Statistical Physics Exam - Prof. Marjorie Olmstead and more Exams Physics in PDF only on Docsity! Phys 328 Midterm 2 20 May 05 Page 1 of 6 Professor M. Olmstead Name 1 /40 Signature 2 /30 Student Number 3 /30 Total /100 Physics 328: Statistical Physics Midterm 1 Friday, 20 May 2005 Professor Marjorie Olmstead Instructions and Advice Solve all three problems in the space provided. Use the back if you need to, but make sure it is clear to the grader where to find your answers. EXPLAIN YOUR REASONING. A CORRECT ANSWER WITH NO SUPPORTING INFORMATION WILL RECEIVE NO CREDIT. You may use any unit system, but you must make it clear what your units are. One significant figure is sufficient for all numerical answers. You may find some of the following to be useful: If you think you need a constant or integral that isn’t here, PLEASE ASK. k b = 1.38 10–16 erg/K = 1.38 10–23 J/K = 8.62 10–5 eV/K; kbT(300 K) = 26 meV h = 2 h = 6.63 10–27 erg-s = 6.63 10–34 J-s = 4.13 10–15 eV-s. hc = 1.24 10-6 eV-m h = 1.055 10–27 erg-s = 1.055 10–34 J-s = 6.58 10–16 eV-s. hc = 2.0 10-7 eV-m c = 2.998 1010 cm/s = 2.998 108 m/s; e = 4.80 10–10 esu = 1.602 10–19 C me = 9.11 10-31 kg; 1 amu = mH = 1.67 10-27 kg SB = 2 2 kB 4 15h3 c2 = 5.67 10-8 W/m2K4; 1 Å = 10–8 cm = 10–10 m; 1 eV = 1.602 10-12 erg = 1.602 10-19 J e a 2x 2 dx 0 = 2a ; x2e a 2 x2dx 0 = 4a3 ; xn n=0 N = 1 xN+1 1 x (x<1); x3 ex 1 dx 0 = 4 15 ; x2 ex 1 dx 0 = (3) (3) = 2.40 2 coshx = e x + e x ; 2sinhx = ex e x ; tanh x = sinh x cosh x ; d dx cosh ax( ) = a sinh ax; d dx tanh ax( ) = a 1 tanh2 ax[ ] = a cosh2 ax d dx ln f (x) = 1 f (x) df dx d dx f (x)( ) n = nf n 1 df dx lim N N!= 2 N( ) 1/2 N Ne N ; lim N ln N!= N ln N N ; c(N ,r) = N! (N r)!r! lim x 0 ln(1 + x) = x ; lim x 0 ex = 1 + x dU1D = TdS fdl; dU2D = TdS dA; dU3D = TdS pdV . H =U + pV ; F =U TS; G =U TS + PV Name Points / . Phys 328 Midterm 2 20 May 05 Page 2 of 6 Professor M. Olmstead 1. Adsorbed gases [40 pts] Consider a crystal surface with o = 1015 sites/cm2. The surface is in equilibrium with Argon, a monoatomic gas with the following properties: Atomic mass mo = 40 amu volume density n = 2.5 106/cm3 pressure p = 1.0 10-8 N/m2 quantum concentration nq = 2.5 1026 cm-3. Temperature kT = 26 meV, T = 300 K. surface binding energy o (to be determined in part D) Under these conditions, one Ar atom lands on each surface site about once/second. They do not all stick. The atoms that do stick have a binding energy o (lower energy on surface than off). A. [8 pts] Find the chemical potential s (in eV) of the Ar molecules on the surface . How does it compare to g, the chemical potential of the Ar gas? Explain your reasoning. B. [9 pts] When an Ar atom leaves the gas phase to stick to the surface, do the following increase, decrease, or stay the same? Explain your reasoning. i. free enthalpy (Gibbs free energy) G. ii. entropy S iii. enthalpy H Name Points / . Phys 328 Midterm 2 20 May 05 Page 5 of 6 Professor M. Olmstead D. [6 pts] Find the heat capacity of the radiation in the (constant volume) box at 300 K. E. [6 pts] How do you expect the total number of photons (integrated over all energies) to scale with temperature? (e.g., if N ~ T , what is , or if it is a non-power law, what is the functional dependence?) Explain your reasoning. Name Points / . Phys 328 Midterm 2 20 May 05 Page 6 of 6 Professor M. Olmstead 3. Short Answer [30 pts] Choose any 3 of the following terms. For each term you choose: (4 pts) Give a definition in words and/or equations. Define all variables in any equations. (6 pts) Describe an example of how this concept is used and how/why it is significant. [10 pts each, your best three will count if you answer more than three] A. Grand partition function B. Chemical potential C. Internal partition function Zint D. Ideal gas E. Quantum concentration nQ