What happens to the specific heat of a solid as the temperature drops towards absolute zero? What is the significance of the Debye temperature?
A sample of copper-zinc alloy is in the form of a cylinder, 10 cm long and 0.8 cm in radius. The curved faces of this cylinder are insulated, and the two plane faces maintained at 30 and 40 degrees Celsius. Once steady-state is achieved, 1.66 watts of heat flow along the cylinder.
The same cylinder is then put into a different apparatus, and a potential difference of 1 V is maintained between the two plane faces. What current flows in the cylinder?
A block of alpha-ferrite has a volume of 1 cubic metre at room temperature. It is first heated to 900 C; then its temperature is slowly increased to 915 C, at which point it undergoes a phase transformation to austentite. What is its volume after each of these two stages?
Does the Wiedemann-Franz Law apply to diamond? Why? (Or why not?)
Show that the minimum radius ratio for an ion to have a coordination number of 8 is 0.732.
Sketch the distribution of stress along a fibre in the matrix for:
Assuming that most of the fibres are much longer than the critical length, and that a fraction Vf of the total volume of the composite is made up of fibre, show that the ratio of the load carried by the fibres to that carried by the matrix is:
Ff/Fm = EfVf/EmVm
Describe the differences in structure between thermosetting and thermoplastic polymers, and the resultant differences in their properties. How would you determine experimentally which category a sample polymer belonged to?
What is tempered glass? How is it made, and in what applications can it be used?
To preserve a badly decayed or damaged tooth, a dentist may remove the top portion of the tooth and replace it with a cap made from some synthetic material. Write out a detailed list of the properties that would be desirable in such a material, and suggest one or two possible candidates.
Avogadro's number: 6 * 1023 atoms/gram-mole
Gas constant R = 8.31 J/mol-K
Boltzmann's constant: 8.12 * 10-5 eV/atom.K
Planck's constant: 6.63 * 10-34J-s
Bohr Magneton muB = 9.27 * 10-24 A-m2
Permeability of free space mu0 = 1.257 * 10-6 H/m
1 eV = 1.602 * 10-19 J
Wiedemann-Franz's law:
L = k/(sigma T), where L = 2.44 * 10-8 ohm-watts/K2.
Magnetic field strength in a solenoid:
H = NI/l
Magnetization of a solid:
M = chimH
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)
Temperature dependence of diffusion coefficients:
D = D0exp(-Q
Concentration of a diffusant at a depth x below the surface of a semi-infinite
slab is given by:
(Cx - C0)/(Cs - C0)) = 1 - erf(x/(2(Dt)0.5)
Fick's First Law of Diffusion: (you're meant to know this)
Fick's Second Law of Diffusion: (you're meant to know this too)
Magnetic moment of a cobalt atom = 1.72 Bohr magnetons
Relative permeability of cobalt (approximately equal to its magnetic susceptibility),
mur = chim = 250 (unitless)
Density of cobalt = 8900 kg/m3
Atomic weight of cobalt = 59 amu
Linear thermal expansion coefficient of iron = 14.2 * 10-6 K-1
Diffusion data for a carbon-nickel system:
D0 = 2.3 * 10-5 m2/s
Qd= 148 kJ/mole
If you need to look up values of the error function, you're
not on the right track.
Properties of Materials
Tabulation of the Error Function