Final Exam PH 235: Thermodynamics and Statistical Mechanics, Exams of Physics

Download Final Exam PH 235: Thermodynamics and Statistical Mechanics and more Exams Physics in PDF only on Docsity! Final Exam PH 235 MJM November 16, 2004 Name __________________________ Box____ 8 AM - Noon O-257 215 points = constant :  = o + ot + 1/2  t2  = o +  t 2 = o2 + 2  ( - o) Moments of inertia about cm: I solid disc cm = 1/2 MR2 I thin rod cm = 1/12 ML2 IP = Icm + Md2 linear motion equations : p = mv F = dp/dt P = Fv angular equations : s= R  -> vt = R  -> at = R  vt =  x r L = r x p dL/dt = r x F =  L = I   = F l = F (arm)  = r F sin  When axis of rotation is moving : Ktotal = Kabout cm + Kof cm = 1/2 I2 + 1/2 Mvcm2 pV = nRT Av = constant p + ½ v2 + gh = constant vrms = ( 3RT/M) = (3kT/m) (p+an2/V2)(V-nb) = nRT dW = Fdx f(v) = 4(m/(2kT))3/2 v2 exp(-mv2/(2kT)) H = kA (TH-TC)/L Y = stress/strain L = L T V =  V T 1 atm=105 Pa R = 8.315 J/mol-K k=1.38x10-23 J/K =1.38x10-23 J/atom-K g = 9.8 N/kg 1 BTU/hr = 0.293 watts A# = 6.023 x 1023 R = 8.315 J/mol/K k = 1.38 x 10-23 J/molecule/K  = Cp / Cv R = Cp - Cv pV = constant T V-1 = constant S = Q/T dS = dQ/T (reversible process) S = k ln  (Harmonic oscillators)  = q+N-1)! /q! /(N-1)! probability of being in energy state E in contact with reservoir at temp T  exp(-E/(kT)) relative probability of being in state E1 vs in state E2 = exp(-E1/(kT) / exp(-E2/(kT)) Efficiency of ideal Carnot engine = 1 - Tc/Th For more working room, use the back of the page. Show all your work. 1. (25) (a) State the equipartition of energy theorem. This has to do with the average energy of a molecule. 1 b) From this theorem, show that vrms = (3kT/m). Be sure to identify the symbol m in this equation. c) Find the rms speed of a nitrogen molecule at -100 oC. [Diatomic nitrogen has 28 g/mol ] 2. (30) The sketch shows water flowing in a pipe whose area changes. water = 1000 kg/m3 a1 = 0.0045 m2 a2 = 0.0095m2 a1 a2 a3 = 0.0090 m2 a4 = 0.0083m2 a3 a4 The inlet pressure is 65000 Pa above atmospheric and the exit velocity is 4.05 m/s in the pipe whose area is a4 = 0.0083m2 . The difference in height between inlet and exit is 6.2 m. Determine the exit pressure of the water. 3. (35) a) (15) Show that if you have a single atom in equilibrium with a temperature reservoir at temperature T, the ratio of probabilities of finding the atom in state of energy E2 to that of finding it in state E1 is 2 there is a pivoted hinge. The support rod is held horizontal by a massless guy wire. 1.6 m a) Draw and label all forces acting on the rod. P Physics Spoken Here b) Find the tension in the guy wire. 2.4 m P 3.2 m c) Find the force components acting on the rod at point P 6. (20) The vapor pressure curve of water may be approximated as P = 5.45 x 108 exp(-E/(kT)) mm Hg, where E = 6.94 x 10-20 J/molecule . Find the dew point when the temperature is 32 oC and the relative humidity is 60% . 7. (50) An ideal monatomic gas is taken reversibly 150 kPa a b through the p-V cycle shown at the right. The initial temperature at point a is 400 K. 400K adiabat 5 isotherm c The sketch is not to scale! a) Determine the number of moles of gas present 0.0030 m3 0.0090 m3 b) Determine the temperature in K at point b. c) Fill out all parts of the following chart a -> b b -> c c -> a cycle Q W U S What is the efficiency of the cycle? efficiency = 6