Physics 7A (A/B) Winter 2007 Final Cover Sheet
Keep This Page Attached to the Exam Physics 7A (A/B) Winter 2007 Final Cover Sheet INSTRUCTIONS: Right now, as soon as you get this part of the exam: 1. Fill in this cover sheet completely. 2. Put your name, DL section number, and the first three letters of your last name on each page of the exam. This is important!!!! The pages are separated for grading! 3. Count the pages of the final exam. There should be 9 pages total, including problems and questions on pages 2 - 8. If you find this is not the case, inform the proctor IMMEDIATELY. It is your responsibility to have a complete exam -- any missing problems or questions will be given the lowest grade. Remember: * You will probably not know the answer or immediately know what to do when you first read a question. You are being tested on your ability to think. So think about how you can apply the general models and methods you have learned to the particular situations discussed in the questions. Then do it. * Do Your Own Work! We automatically report anyone suspected of cheating to Student Judicial Affairs! I certify by my signature below that I have read the above and below instructions and that I will abide by the UC Davis Code of Academic Conduct. This includes • not copying from anyone else’s final • not letting any other student copy from my final • not discussing this final exam with any student who has not yet taken it, nor providing any information, written or oral, that might get to a student who has not yet taken it. Circle the room you are taking this final exam in: 1100 Social Sciences 198 Young Hall 158 Roessler Count from the front row which number (or letter) row you are sitting in: Enter the row number/letter here: Name (Print Clearly): Last DL Section Number: first (This is a number between 1 and 11) Lecture Section: (A, B) Signature:______________________________________ You may begin the final as soon as you have completed this and the following 7 pages: put your name, DL section number, and first three letters of your last name on this and each of the following six pages. Tear off the formula page stapled to the back of the exam (page 9); remove it from the exam in order to use it (you do not have to return the formula sheet). 7A-1 W07 Final Last name First name DL Sec | | | | p2 First three letters of last name grade (for office use only) Problem 1. (14% of exam) Assume that we have two separate physical systems: one mole of Gas 1 and one mole of Gas 2. Each gas undergoes a reversible, constant-pressure process that takes it from an initial state to a final state, as represented in the two state diagrams below. The two gases have the same initial values of H and T (Ha and T1), and the same final values of T (T2), but the final value of H is greater for the Gas 2 (Hc > Hb). Assume that both gases behave as ideal gases. Enthalpy (H) Enthalpy (H) Gas 1 Gas 2 Hc Hb Ha final final Ha initial T1 T2 Temperature (T) initial T1 T2 Temperature (T) 1a. Compare the magnitudes and direction (in/out) of the heat transferred for the two processes. You must explain your response! 1b. A student says that Gas 1 is N2 (nitrogen) and Gas 2 is He (helium). Explain if this is possible using the concept of modes. 7A-1 W07 Final Last name First name DL Sec | | | | p3 First three letters of last name grade (for office use only) Problem 2 (16%) 2a. A solid substance has a structure that allows each atom to have 6 nearest neighbors (called simple cubic packing: 4 nearest neighbors in the same plane, one above, and one below). Calculate the bond energy for 2 moles of this solid. Refer to PE (r) plot for more information. The vertical scale of the graph is in units of 10-21 Joules. Briefly comment whether your estimation of bond energy is an underestimation, overestimation, or neither. Explain. Horizontal scale: units of 10-10 m m Lennard-Jones PE(r) for an atom-atom pair 2b. A heat pack (HP), like the ones in DL, is initially in liquid phase at room temperature. The HP is then triggered and as it becomes a solid it gives off heat to the environment. The final state of the HP is a solid at room temperature. Describe the change in entropy (S) for the HP from a statistical (microstates) view. Is S for the HP positive, negative, or zero? 7A-1 W07 Final Last name First name DL Sec | | | | p4 First three letters of last name grade (for office use only) Problem 3. (16% of exam) 3a. Inside a sealed, insulated container (where no work or heat can be exchanged with the environment) are three moles of neon gas [Ne(g); 20.2 g/mole] containing 14, 965 J of thermal energy, and in a separate sealed, insulated container are two moles of ammonia gas [NH3(g); 17 g/mole] containing 23,279 J of thermal energy. Both gases can be considered ideal, and both are at 400 K. Which gas molecule, if either, has the greater average translational kinetic energy? Briefly, but completely, explain your answer. 3b. In an experimental measurement of heat capacity, the internal energy of an unknown quantity of an ideal gas increases by 561 Joules when 925 Joules of heat are added to the gas (no heat is allowed to leave the gas). The initial temperature of the gas (just before the heat is added) is 250 K. The final temperature of the gas is 265 K. There are no phase changes during this process. This is either a measurement of C V or of CP. From the given information, which is it? Explain. 7A-1 W07 Final Last name First name | DL Sec | | | p5 First three letters of last name grade (for office use only) Problem 4. (16%) A mass (m = 0.20 kg) has an initial horizontal speed of 3.0 m/s. The mass slides through a distance of 30 cm across a horizontal surface where it collides with a stationary, horizontal spring (which has spring constant, k = 180 J/m2). The spring is initially at its equilibrium position (x = 0 cm). Its final position is the compressed position as seen in the figure below (x = xfinal). [Watch your units!]. The mass is not attached to the spring. The mass compresses the spring and momentarily comes to rest. Initial: v = 3.0 m/s x = 0 cm x = -30 cm Final: v = 0 m/s xfinal = + ? cm Assume that the horizontal surface is frictionless and that no energy is transferred to or from thermal systems. 4a. Write out an expression for ETOT in terms of the energy systems, and then find its value in units of Joules. 4b. Find the final position of the spring, xfinal. 4c. On the axis below sketch a graph of the kinetic energy (KE) of the block as a function of the block's distance from the equilibrium position of the spring (which is at x = 0 cm), and sketch the potential energy of the spring (PES) as a function of the block's distance from x = 0 cm. Make your plot go from x = - 30 cm to xfinal. Clearly identify the two kinds of energies (KE & PE S) on your graph, and label all axes with values. On your plot, clearly show where the KE max and the PES, max are. Energy (Joules) x=0 x (cm) Distance from equilibrium (cm) 7A-1 W07 Final Last name First name DL Sec | | | | p6 First three letters of last name grade (for office use only) Problem 5. (8% of exam) Calculate the binding energy (BE) of a Polonium-210 nucleus (84210Po). The mass of the 84210Po nucleus is 209.93 u (excluding electrons). Make it clear to the grader what the steps are in your calculation. 7A-1 W07 Final Last name First name DL Sec | | | | p7 First three letters of last name grade (for office use only) Problem 6. (16% of exam) 6a. An ideal gas is taken from state A to state B by an adiabatic (Q = 0) process as shown in the PV state diagram at right. How does the temperature at state B compare to the temperature at state A? Explain the steps of your answer. P A B V 6b. A student who has not taken Physics 7A says that bonds store energy and release that energy when they break. Using any relevant concepts, models, and/or examples, explain whether you agree or disagree. Use only the space provided here. 7A-1 W07 Final Last name First name DL Sec | | | | p8 First three letters of last name grade (for office use only) Problem 7. (14%) Heat is added to a sample of material at a constant rate. The sample starts off as a solid at a temperature of 60 K, and as heat is added the sample melts, and then vaporizes. The temperature as a function of energy added to the sample is shown on the plot. T [K] 300 K 200 K 100 K 60 K 0J 150 J 450 J 1050 J 1500 J 1800 J Energy added [J] 7a. From the information provided, determine which is greater, the heat of vaporization or the heat of melting? Explain how you know. 7b. From the information provided, determine in which phase, solid, liquid or gas, the sample has the greatest heat capacity? Explain and support your answer with calculations. 7A-1 W07 Final p9 Physics 7A-A/B Winter 2007 Final Exam Formulae and Constants Separate this sheet from the exam packet. You may keep this page after the final. 1 2 m v 2 ∆U = Q + W ∆U = ∆Eth + ∆Ebond + ∆Eatomic + ∆Enuclear H = U + PV ∆H = Q (at constant pressure) G = H + TS PEgrav mgy G = H - TS (at constant T & P) ∆G < 0 if spontaneous ∆G = 0 if in equilibrium ∆G > 0 if not spontaneous gEarth 10 N/kg = 10 m/s2 W = – Fdr Favg∆r kB = 1.38 x 10-23 J/K KE PEspring 1 2 kx 2 NA = 6.02 x 1023 molecules (or atoms)/mole R = NA kB = 8.31 J / K•mol W = – PdV Pavg∆V Q = TdS Tavg∆S Patm = 1 atm = 105 Pa (= 105 J/m3) Q = CdT C∆T 1,000 g = 1 kg 4.18 J = 1.0 cal PV = nRT 1 kcal = 1000 cal Suniverse 0 1 kJ = 1,000 J = 1000 Nm = 1000 kgm2/s2 S k B ln Ssystem 1 W = 1 J/s Q T 1 N = 1 kgm/s2 1 eV = 1.602 x 10-19 J ∆Ssystem = C ln(Tf / Ti) 1 u = 1 amu = 1.6605 x 10-27 kg = 1 g/mole C = Q/∆T A( nucleons) Z(protons) C = cmassm = cmn mproton = 1.007276 u CV = dEth/dT Cp = Cv + nR X(element) or cp = cv + R mneutron = 1.008665 u Ethermal/mode = 1/2kBT (on average) E = mc2 Ethermal = (# of modes/molecule) 1/2nRT c = 3 x 108 m/s (speed of light) c2 = 932 MeV/amu Ethermal/mole = NA (# of modes/molecule) 1/2kBT Ethermal CT Ebond = all pairs (PEpair-wise) Ebond -N(# nn/2) or -nNA(# nn/2) nn = nearest neighbors pairs |Ebond| = ∆mHvap |Ebond| = ∆mHmelt Area of rectangle = heightbase Area of triangle = (1/2)heightbase Area of parallelogram = heightbase Prob (state) = State / Total 7A-1 W07 Final
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