Select and answer 5 of the following 8 questions. All questions carry 20 points. If you answer more than five questions, your score will be obtained by summing the best five. The exam is closed-book. Useful formulae and material properties are provided on the attached sheet.

  1. The outside surface of a 10-cm diameter steel pipe has a corrosion rate of 0.1mm per year. A zinc anode is connected to the pipe to protect it. Calculate the weight of zinc required per year for a 100-m length of pipe. Show all calculations and units.

    Given that 96,500 coulombs will deposit one gram-mole of a substance, what uniform current density (mA/m2) will exist in the protected pipe?

    In practice, would the outer surface of the length of pipe be satisfactorily protected if one piece of zinc was attached at one position? Explain.

    What alternative methods of protecting the pipe can you suggest?

  2. The following data were obtained on tensile testing of an aluminum alloy. The sample's initial length was 5 cm.

    Load (kN) Length (cm)
    0 5.000
    20 5.0102
    40 5.0197
    50 5.0257
    60 5.0285
    65 5.0355
    70 5.0505
    80 (max) 5.1257
    76 (fracture) 5.3350

    The original diameter was 1.262 cm, shrinking to 1.135 cm at maximum load and 1 cm exactly at fracture.

    Plot the engineering stress-strain diagram for the sample.

    Calculate the elastic modulus of the aluminum.

    Calculate the 0.2% offset yield strength. Why is this value important?

    Calculate the engineering ultimate tensile strength and the true ultimate tensile strength. Engineers usually use the former rather than the latter; why?

    Calculate the % elongation and the % reduction in area at fracture. How might this information be used?

    Describe the microstructural changes that are occurring in the elastic and plastic ranges.

    Suppose that we stopped the test after applying 50 kN, removed the load, then tested the piece again. Would we get the same curve as before? If not, how would it differ?

  3. One kilogram of polyethylene (C2H4) is to be produced in a polymerisation process. How many gram-moles of ethylene would be required? How much energy is released during the polymerization reaction? If the reaction occurs adiabatically (no heat transferred in or out), what is the rise in temperature during polymerisation?

    Given that the glass transition temperature for amorphous polyethylene is -60 C and the melting temperature for crystalline polyethylene is 105 C, compare and explain the shapes of the stress-strain curves for low and high density polyethylene at 110 C, 23 C and -195 C.

  4. Kryptonite is an exotic mineral with a characteristic green glow. It consists mainly of cavorite, an ionically bound ceramic material with two atoms per molecule, but about 1 atom in 104 is dilithium. Pure cavorite has a band gap of 5.2eV. The valence electron of dilithium has a discrete energy level somewhere in the band gap. (See fig1.jpg) Luminescence occurs when thermal excitations raise an electron from the valence band to the level of the dilithium, and the electron subsequently falls back to the valence band with emission of a photon. Calculate the difference in energy between the top of the valence band and the dilithium level.

    Dilithium is radioactive. During any one-hour period, one dilithium atom in every thousand will decay, releasing 12.6 MeV of thermal energy. If a sample of kryptonite is kept in a perfectly insulated, mirror-lined container, how much will its temperature rise during the first hour?

  5. Explain, using diagrams and formulae as necessary, the difference between fatigue and creep. For each failure mode, you should say what circumstances lead to the failure and what materials are susceptible to failure in this mode. If you were examining the remains of a failed mechanism, how might you tell whether it had failed due to creep or fatigue?

  6. The tiles used for the leading edges of the space shuttle are very poor thermal conductors. As a result, they may fracture during rapid cooling or heating. Develop an equation to describe the stress that results from rapidly heating the surface of a tile from 20 to 315 C. Assume that the coefficient of linear expansion is 4.5 * 10-6C-1 and that Young's modulus for the tile is 1.035 * 105MPa. List any assumptions made.

    Ordinary glassware often breaks when immersed in hot water, whereas Pyrex glass doesn't. Deduce the approximate critical value of the thermal shock resistance parameter for washing-up applications. The fracture strengths of soda glass and pyrex are both approximately equal to 70 MPa.

  7. ``Differences between the predictions of classical physics and quantum theory become significant only at sub-atomic scales. Quantum physics, though an impressive intellectual exercise, therefore has little relevance to the practicing engineer. The undergraduate engineering syllabus could be based entirely on classical physics, with great gains in clarity and consistency; the only reason this is not done is a misplaced desire among educators to appear up-to-date."

    Comment on this assertion, illustrating your answer with relevant examples from the course or from other sources.

    1. Using the phase diagram below, explain in detail how you would obtain a sample of 99.5% pure nickel, starting from an alloy containing equal amounts by weight of copper and nickel. What is the name of this method?
    2. What is segregation? What are its consequences, and how might it be prevented?

  9. Starting from Dirac's relativistic wave equation, show that mercury could be predicted to be a liquid, unlike its neighbours in the periodic table. Contrast this with the prediction obtained using Schrodinger's equation. Show all calculations. Using the same approach, what other metals would you predict to be liquid at room temperature?

    Useful Formulae

    Avogadro's number: 6 * 1023 atoms/gram-mole

    Boltzmann's constant: 8.12 * 10-5 eV/atom.K

    Planck's constant: 6.63 * 10-34J-s

    1 eV = 1.602 * 10-19 J

    Some bond energies: C--C: 368 kJ/gram-mole; C=C: 719 kJ/gram-mole

    Electrostatic attraction:

    F = q1q2 /(4 pi epsilon0 x2)

    where

    1 / (4 pi epsilon0) = 9 * 109 farads/metre

    TSR = sigmaf k/ (E alphal)

    Some useful material properties:

    Material Density (kg/m3) Atomic (or Molecular) Wt. Valency
    Zinc 7100 65.4 2
    Iron 7800 55.9 2
    Carbon 1800 12 4
    Hydrogen 0.0899 1 1
    Dilithium 21000 300 2
    Cavorite 13500 450 -

    Material Density (kg/m3) Sp. Ht. (J/kg.C) k (W/m.K) E (MPa) alphal
    Polyethylene 1200 2300 0.38 200-1000 120 * 10-6
    Kryptonite 13500 1500 75 3100 0.8 * 10-6
    Soda-glass 3200 830 2.2 70000 9 * 10-6
    Pyrex 3200 840 1.7 75000 3 * 10-6

    Electro-magnetic spectrum