3 Problems on Thermodynamics and Statistical Mechanics with Solution | PHYS 4420, Exams of Physics

Download 3 Problems on Thermodynamics and Statistical Mechanics with Solution | PHYS 4420 and more Exams Physics in PDF only on Docsity! Co x Exam 1 NAME: _ ob hows Thermo. & Stat. Mech. PHYS 4420, Spring 2010 In this exam, you can use a double-sided equation/formula sheet, a calculator, and an integral table. You cannot discuss the problems with anyone, and cannot give or receive help from anyone. You must hand in your paper by the end of class time (9:50am) unless prior arrangements have already been made with the instructor. Good luck! Problem 1: Problem 2: Problem 3: Total : Problem 1. (20pts total) Multiple Choice Questions, NO PARTIAL CREDIT) You must CIRCLE the correct attswer. 1.1 (2pts) Of the following, which might NOT vanish over one cycle of a cyclic process? (U/ is the internal energy, P is the pressure, W is the work done on the system, V is the volume, and 7 is the absolute temperature.) (A) AU. (B) AP. (yw. @) AV. (E) AT. 1.2 (2pts) When work w is done adiabatically on one kilomole of ideal gas with constant specific heat c, , the temperature of the gas increases by the amount: (Ay 2%. u(r) 2 CT al, Se, Aus Cy,4T 2w Ben Aus $our KN, w Le c,+R° Cp {E) It depends on the particular path the system is undertaking between the initial and final states, and cannot be determined with the information given. @) 1.6 (6pts) Two blocks, one block with mass 7m and the other one with mass 27m, are made of the same metal with specific heat (per unit mass) c. They are isolated from the rest of the outside world, but not from each other. Initially, the block of mass m is at a temperature T, and the other block is at a temperature T,. They are then brought into contact with each other, and eventually they come to thermal equilibrium with each other. What is the total change in entropy AS,,,,, for the system (the two blocks combined)? (A) 3mec of Bat) mre @) sme 2 aie | © onenl L+2h) » | () 45, 2 2. (20pts) The Helmholtz free enctgy of a gas is given by F(T,V) = “yr : (a) (10pts) The gas initially is at temperature 7 and has volume V . This gas then undergoes (Gay-Lussac — Joule) “free expansion” from V to 16V . Obtain the final temperature 7, of the gas. (You must express your answer in terms of the variables and constants given, i.e. initial temperature 7’, initial volume V , and the constant a, but your final answer may not necessarily include all of them.) Me - GAT - IY , F eu-rs -@ = #ary 756 elo # ; __k Ue Feros Srv +hartye aT pre Lxpasrou : U (TW) 2 ot UCT WY) © UCT: UD TeT Viv Tet ,UYelev| al “Y . al, “ley 7 wD L/L ee >" 2 (b) (10pts) Calculate the total entropy change of this gas during the above free expansion. (As in part (a), you must express your answer in terms of the initial temperature and volume, 7 and V , and possibly the constant a.) ¢ ¢. _ - > 2 45° 452 Bavy,- sen £01) 0) -T v3 = far] 2- i! Ber’y | br 3. (20pts) Consider the following equation of state for a gas: [r- where a and b are positive material-specific constants. (Note that despite the close resemblance, this is NOT the van der Waals gas, so do not copy those results, possibly being on your equation sheet, as doing so will yield zero credit.) a »—b)= RT, fe bbear p RT 4 bh Ty (a) (8pts) Obtain (#) » where u(/’,») is the specific internal energy of the system, y r (2) rf) -p rf & AAT os - = ka Oe 97 we Tad 9h Ty | _ «a Ta” ~~ dc, . . (b) (8pts) Obtain > , Where ¢,(7,v)is the constant-volume specific heat of the v Jp system. oa 228) 24, Pu (2 ¢ (24) ) ou (z= v)_- Or OT IT Me or J i) Be] a | LT” | (c) (Apts) Write down the most general form of the specific internal energy u(7',v) this system can have. a && Ares fee = i above; G. CHT T)e= JE s). du + gir) =e a) Ou Ou eS pT f) dv = & oe) dr 3 +47) dT a8 dtr a ee => UulTw) = Pgq) aT - 24 ! {0 -#2 / mH yp mw | 4 .